Consumption-Driven Finite Capacity Inventory Planning and Production Control. A thesis presented to. the faculty of

Transcription

1 Consumption-Driven Finite Capacity Inventory Planning and Production Control A thesis presented to the faculty of the Russ College of Engineering and Technology of Ohio University In partial fulfillment of the requirements for the degree Master of Science Gökhan Eğilmez November Gökhan Eğilmez. All Rights Reserved.

2 2 This thesis titled Consumption-Driven Finite Capacity Inventory Planning and Production Control by EĞİLMEZ GÖKHAN has been approved for the Department of Industrial and Systems Engineering and the Russ College of Engineering and Technology by Gursel A. Suer Professor of Industrial and Systems Engineering Dennis Irwin Dean, Russ College of Engineering and Technology

3 3 ABSTRACT EĞİLMEZ, GÖKHAN, M.S., November 2009, Industrial and Systems Engineering Consumption-Driven Finite Capacity Inventory Planning and Production Control (132 pp.) Director of Thesis: Gursel A. Suer Consumption driven finite capacity multi independent item inventory planning problem is studied. Four models are generated to solve the problem to minimize the total cost of inventory carrying, ordering and backordering. The first model reflects the classic (s, Q) policy. Model 2 has a feature of dynamic order quantity which enables system to increase or decrease the amount of items released as production orders. Models 3 and 4 both have the features of dynamic order quantities and dynamic reorder points. Dynamic reorder point is used to allow a production order to be released before reorder point violation occurs with respect to the vulnerability of backlog. In addition system is protected from overproduction and excessive inventory built by limitation parameters for r and Q. As a result, significant amounts of backlogs are prevented and total cost reductions are obtained by model-4 in highly variable demand environments. Approved: Gursel A. Suer Professor of Industrial and Systems Engineering

4 4 ACKNOWLEDGEMENTS I would like to express my gratitude to my advisor, Gursel A. Suer, my family and my best friend Ali Yasar Yigit for their contributions, support and encouragement on this study.

5 5 TABLE OF CONTENTS Page ABSTRACT... 3 ACKNOWLEDGEMENTS... 4 LIST OF TABLES... 8 LIST OF FIGURES CHAPTER 1: INTRODUCTION Economic Order Quantity Statistical Inventory Control Periodic Review Policy Continuous Review Policy Materials Requirements Planning (MRP) Era Optimized Production Technology (OPT) Just-In-Time Paired Cell Overlapping Loops of Cards with Authorization (POLCA) Demand Management Justification Objective of the Study CHAPTER 2: PROBLEM STATEMENT Definition of the Problem Performance Measures... 44

6 6 CHAPTER 3: LITERATURE REVIEW Some of the Studies without Consideration of Capacity Single Item Multi-Item Some of the Studies with Consideration of Capacity as a Constraint Single Item Multi-item CHAPTER 4: METHODOLOGY Model 1: Multi-item Inventory Planning with (s, Q) Model Introduction Model Framework Conclusion Model-2: Multi-item Inventory Planning with Flexible Order Quantities Introduction Model Framework Conclusion Model 3: Multi-item Inventory Planning with Flexible Order Quantities Subject to Reorder Point- Inventory Status Relation Introduction Model Framework Conclusion... 76

7 Model 4: Multi-item Inventory Planning With Flexible Order Quantities Subject to Reorder Point- Inventory Status Relation with Restricted Ordering Introduction Program Framework Conclusion CHAPTER 5: EXPERIMENTATION & RESULTS Customer Demand Data Generation Determination of Initial Input Experimentation External Parameters of Experimentation Results Comparison of Results Summary of Results Cost Sensitivity Analysis Sensitivity of Backlog Cost Sensitivity of Order Cost Day off Affect CHAPTER 6: CONCLUSION REFERENCES

8 8 LIST OF TABLES Page Table 1 - Characteristics of Different Inventory Control and Production Planning Approaches Table 2 - General Features of Proposed Models Table 3 - Product Inventory Information Table 4 - Reorder Point Violation of Products 2, 5 and Table 5 - Information of Product Table 6 - Products to be produced Table 7 - Modified Order Quantities - Model Table 8 - Numerical example of k Qr Table 9 - Numerical Example for Model 3- Idle Capacity Case Table 10 - Products with Reorder Point Violation Table 11 - Remaining Products and Re-calculated Production Orders Table 12 - Uniform Distributions Used in Demand Generation Table 13 - The variances of demand distributions of products Table 14. Number of observations Table 15 - Number of replications run for models Table 16 - Results of 30 % customer demand load Table 17 - Summary of Results - 30 % Customer Demand Load Table 18 - Results of 40 % customer demand load Table 19 - Summary of Results - 40 % Customer Demand Load... 96

9 9 Table 20 - Results of 50 % customer demand load Table 21 - Summary of Results - 50 % Customer Demand Load Table 22 - Results of 60 % customer demand load Table 23 - Summary of Results 60 % Customer Demand Load Table 24 - Results of 80 % customer demand load Table 25 - Summary of Results - 80 % Customer Demand Load Table 26 - Results of 90 % customer demand load Table 27 - Summary of Results - 90 % Customer Demand Load Table 28 - Summary of Results Table 29 - Cost Parameters of Sensitivity Analysis Table 30 - Cost Sensitivity of Backlog Analysis Results 60 % Load Table 31 - Cost Sensitivity of Backlog Analysis Results 80 % Load Table 32 - Cost Sensitivity of Backlog Analysis Results 90 % Load Table 33 - Cost Sensitivity of Order Analysis Results 30 % Load Table 34 - Cost Sensitivity of Order Analysis Results 40 % Load Table 35 - Cost Sensitivity of Order Analysis Results 50 % Load Table 36 - Cost Sensitivity of Order Analysis Results 60 % Load Table 37 - Cost Sensitivity of Order Analysis Results 80 % Load Table 38 - Cost Sensitivity Analysis Results 80 % Load Table 39 - Cost Sensitivity of Order Analysis Results 90 % Load Table 40 - Day off Analysis Results 30 % Load Table 41 - Day off Analysis Results 40 % Load

10 10 Table 42 - Day off Analysis Results 50 % Load Table 43 - Day off Analysis Results 60 % Load Table 44 - Day off Analysis Results 80 % Load Table 45 - Day off Analysis Results 90 % Load Table 46 - Day off Effect on Total Cost

11 11 LIST OF FIGURES Page Figure 1. Periodic Order-Up to Policy (T, s, R) Figure 2. Periodic Order-Up to Policy (T, R) Figure 3. Continuous Review (s, Q) Policy Figure 4. Continuous Review (s, R) Policy Figure 5. Manufacturing Planning and Control System Figure 6. OPT Framework Figure 7. Process and Transfer Batch Sizes Figure 8: Signal Kanban Figure 9. Sequential Progress of Kanban System Figure 10. Kanban System Framework Figure 11: POLCA System Illustration Figure 12. Idle Capacity Situation Figure 13. Exceeded Capacity Situation Figure 14: Inventory Control Module Figure 15. Model 1- Flowchart Figure 16. Model-2 - Flowchart Figure 17. Model 3 Flowchart Figure 18. Idle Capacity Case - Model Figure 19. Insufficient Capacity Case - Model Figure 20: Model 4 Flowchart... 78

12 12 Figure 21. Idle Capacity Case - Model Figure 22. Insufficient Capacity Case - Model Figure 23. Customer Demand Intervals Figure 24. Variances of Customer Demand Distributions Figure 25. Behavior of Dataset - 30 % Load Figure 26. Behavior of Dataset - 40 % Load Figure 27. Behavior of Dataset - 50 % Load Figure 28. Behavior of Dataset - 60 % Load Figure 29. Behavior of Dataset - 80 % Load Figure 30. Behavior of Dataset - 90 % Load Figure 31. Sensitivity Analysis of Backlog Cost - 60 % Load Figure 32. Sensitivity Analysis of Backlog Cost - 80 % Load Figure 33. Sensitivity Analysis of Backlog Cost - 90 % Load Figure 34. Sensitivity of Order Cost 30 % Load Figure 35. Sensitivity of Order Cost 40 % Load Figure 36. Sensitivity of Order Cost 50 % Load Figure 37. Sensitivity of Order Cost 60 % Load Figure 38. Detailed Sens. Analysis - 80 % Load with Fixed Backlog Cost of $ Figure 39. Sensitivity of Order Cost 80 % Load Figure 40. Sensitivity of Order Cost 90 % Load

13 13 CHAPTER 1: INTRODUCTION Production planning and inventory control has been a vital issue in manufacturing industries for decades. Since inventory control always plays a significant role on meeting customer needs and on the performance of the system, plenty of models and production strategies have been developed to deal with relevant issues. In this section, main production planning and inventory control strategies are briefly explained Economic Order Quantity Economic Order Quantity (EOQ) model is the oldest model which was first published by Ford Harris, in 1915 and reviewed by Wilson in EOQ formula calculates economic lot size considering parameters such as annual demand, inventory carrying cost, ordering cost, and interest rate. Since a known and constant demand rate is assumed and no shortage is allowed, EQO is a robust and insensitive model in terms of cost when input parameters are changed. On the other hand, production systems having varying demand and leadtime need statistical methods to manage their inventory. Over the years, various different EOQ formulations have been developed and published in the literature. EOQ models are mostly single-item planning models. Some of the frequently used performance measures are minimizing shortage and reducing inventory. Various different lot sizing methods such as least-period cost, least-unit cost, part period balancing, etc. have been also developed to deal with known but time-varying demand. These lot sizing methods are also solved for each item individually.

14 Statistical Inventory Control As demand variability increases, EOQ does not provide sufficient inventory management support to manufacturing systems. Since demand rate is not constant in most real life situations, safety stock inventory is needed in reorder point models. Safety stock levels are determined such that shortages are minimized while keeping inventory levels at minimum. Until early 1960s, companies had been using statistical inventory control techniques to manage inventory systems. In the next few paragraphs, inventory policies are classified with respect to review type and ordering rule Periodic Review Policy i. (T, s, R) Periodic Order-Up To Policy with Reorder Point: In (T, s, R) policy, inventory level of corresponding item is checked at equal and predetermined intervals of time (T). This time interval of T is called review period. A predetermined reorder level (s) is checked at each T. If inventory level is less than or equal to the reorder point at checkpoints, an order quantity of (R-I) units is released to the shop floor. Otherwise, no order is given. It is shown in Figure 1.

15 15 Inventory Level (I) 4 4 Leadtime Leadtime : : : Figure 1- Periodic Order-Up to Policy (T, s, R) Time ii. (T, R) Periodic Order-Up To Policy (T, R) policy is similar to (T, s, R) policy. The only difference is that an order is automatically placed at each checking point, since there is no reorder point consideration. Figure 2 shows an example of this policy.

16 16 Inventory Level (I) Leadtime Leadtime Leadtime Leadtime : : Time Figure 2 - Periodic Order-Up to Policy (T, R) Continuous Review Policy In this policy, inventory status is checked continuously. Whenever it drops below or equal to reorder point (s), an order is placed. Depending on the order quantity, there are two main policies, (s, Q) and (s, R). i. (s, Q) Policy In this policy, order quantity is fixed and predetermined by using formulas such as economic order quantity (EOQ). Figure 3 shows an example of this policy.

17 17 Inventory Level (I) Leadtime Leadtime : : Time Figure 3 - Continuous Review (s, Q) Policy ii. (s, R) Policy (s, R) Policy: In this policy, inventory is checked continuously and whenever it drops below or equal to reorder point (s), an order is placed which should be equal to R (Maximum Inventory Level) Inventory. Figure 4 represents an example of this policy. Statistical inventory control techniques were widely used until computer software support became available to handle large amount of data in Materials Requirements Planning (MRP) era.

18 18 Inventory Level (I) 3 Leadtime Leadtime Leadtime : : Time Figure 4 - Continuous Review (s, R) Policy 1.4. Materials Requirements Planning (MRP) Era The problems of manufacturing planning and control are still alive in many aspects and in different shapes since Ford Harris first published the economic order quantity formula in According to Plossl s book, early simple forecasting techniques such as moving average and exponential average were still popular until 1960s. Orlicky, whom is called as the father of modern MRP, first applied Materials Requirements Planning (MRP) in 1961 on J.I. Case Company farm machinery. Before MRP, firms usually forecasted requirements by using simple forecasting techniques such as moving average, exponential smoothing (Robert G. Brown, 1959) for both independent (finished goods) and dependent (parts, subassemblies, raw materials) items. Since there was no

19 19 computer software support to handle tons of data, calculation and forecasting errors were still problems which were not easily surmountable. Orlicky s MRP has made many vital contributions to inventory control and production planning systems. First of all, Bill of Materials (BOMs) shows the components needed for finished products along with their usage. Secondly, MRP made production systems able to provide time-phased requirement records for items to be purchased or manufactured. A general framework of MRP is explained in Figure 5 by Vollman et al. They divided manufacturing planning and control system into three phases as front end, engine and back end. In the front end phase, actual demand and forecasts for independent items (finished products) are considered in building master production schedules of items. Master Production Schedule (MPS) is a build schedule for finished products. In the engine phase, by using bill of materials, routes and MPS, detailed materials planning is done. With routing files, capacity requirements to produce products and parts are calculated. In the back end phase, scheduling of production is planned and executed. Indeed, during execution and scheduling, depending on inventory status and dynamic demand, MPS can be modified to fit into available capacity and meet demand. According to Turbide, MRP has four main steps performed sequentially. The first step is to determine gross requirements of materials by using master production schedules. In the second step, gross requirements are compared with available balance of items on hand and then net requirements are calculated. The third step is to decide order quantities for the items which might have shortages (if no action is taken). One can choose from many lot sizing rules such as lot for lot, fixed quantity, etc. The last step is to decide start time

20 20 of orders by considering leadtimes and backward planning. The most critical factors for a successful MRP system are inventory data, BOMs, leadtime information. The accuracy of forecasting also affects the solution quality. MRP calculates capacity requirements with rough-cut capacity planning techniques such as capacity planning using overall factors (CPOF), capacity bills, and resource profiles while generating MPS. Once MRP records are generated, capacity planning is done by using Capacity Requirements Planning (CRP). However, MRP does not provide enough support to deal with finite capacity loading and leaves this task to the planners. Optimized Production Control is another philosophy to perform inventory planning and production control and is discussed in the next section Optimized Production Technology (OPT) Optimized Production Technology is advancement over MRP system because, it s a sophisticated shop floor control system which combines MRP logic and finite capacity loading for utilization of both bottleneck and non-bottleneck resources. Figure 6 illustrates the framework of OPT. First of all, it combines bill of materials, routing files and master production schedules to build product network which is a kind of tree diagram used to hold records of operational data of each item on network.

21 21 Resource Planning Production Planning Demand Management Rough Cut Capacity Planning Master Production Scheduling Front End BOM Routing File Detailed Material Planning Inventory Status Data Detailed Capacity Planning (CRP) Time Phased Requirement (MRP) Records Engine Material and Capacity Plans Shop Floor Systems Vendor Systems Back End Source: Figure 5 - Manufacturing Planning and Control System

22 22 Data such as required capacities, inventory records, resource capacities, order quantities, minimum batch sizes, alternate machine routings, and labor constraints are going to be used in resource description. Buildnet feature combines product network and resource description. Serve analysis routine identifies the bottleneck and nonbottleneck resources. SERVE routine uses MRP and its infinite capacity assumption and backward scheduling. SPLIT routine separates the network into two networks. The OPT network reschedules the bottleneck resources and the following critical resources by using lot for lot. After SPLIT routine, with the combination of OPT and MRP logics both bottleneck and non-bottleneck resources are identified efficiently and finite scheduling is performed with respect to capacity restrictions. The first main feature of OPT is that, it makes MPS possible to be used directly to schedule shop floor system with its contribution on finite loading through bottleneck resources. The second feature is that, it uses MRP logic for scheduling non-bottleneck resources considering infinite capacity assumption as well. One of the main differences between OPT and MRP is that, OPT enables system to reduce lot sizes until some resources become bottleneck. This allows both inventory and flow time to be reduced. There are two batch size terms used in OPT: process and transfer batch sizes. The process batch size is the main starting batch size. It is broken down into smaller transfer sizes to move peaces faster and among machines and thus WIP and leadtime are reduced.

23 23 Product Network Resource Description BUILDNET Reports OPT/ SERVE Master Engineering Network SPLIT OPT Network Serve Network OPT SERVE Critical Resource Schedule Non-Critical Resource Schedule Reports Reports Source: F. Robert Jacobs, OPT Uncovered: Many Production Planning and Scheduling Concepts Be Applied with or without Software, Industrial Engineering, October, 1984 Figure 6 - OPT Framework

24 24 An example is given in Figure 7 where process batch size is 36 units and transfer batch size is 12 units. Once 12 units are completed at one machine, they all are transferred to the next machine. In the next section, another important approach, called Just-in-Time, will be discussed. Figure 7 - Process and Transfer Batch Sizes 1.6. Just-In-Time In early 80s, Japanese philosophy of production and planning system, Just-in- Time (JIT), had become another strong approach which enables the manufacturing system to be aware of wastes and weak sides of MRP. In 1988, O grady defined the main disadvantages of Orlicky s production planning and inventory control approach (MRP) as higher inventory holding costs, lack of responsiveness and risk of inventory s becoming

25 25 obsolete. He also categorized the problems with MRP as poor inventory level accuracy, inaccurate leadtimes and BOMs, poor MPS, out of date data and poor methodology. JIT has drawn interest among manufacturing and service companies over last two decades. Especially Kanban system at Toyota in Japan has been making an important contribution on naming this new approach as philosophy. From a planning point of view, Kanban system works as a replenishment method that manages and executes production planning and control via control cards (Kanbans) and containers. To apply JIT as a philosophy and Kanban as a replenishment method, manufacturing process should be under control, and quality requirements should be met. However, since MRP, OPT and JIT are discussed from a planning perspective, Kanban will be considered and compared to others in terms of replenishment method. Kanban is a Japanese word which stands for card or signal. Kanban system works based on pull concept whereas MRP supports push method. Whenever there is consumption on a downstream station, the upstream station is alerted by production cards to start manufacturing of parts for the downstream station to use. There are four main types of cards used in Kanban system to keep flow of production under control and execute. 1. Production Kanban: Whenever consumption occurs on a station, production Kanban is released and it triggers manufacturing. 2. Conveyance (Move) Kanban is, a Kanban type, basically used for moving items from the upstream machine or station to the downstream one. 3. Supplier Kanban is similar to conveyance Kanban except that supplier is considered as an upstream station.

26 26 4. Signal Kanban is shown in figure 8. There is a resemblance between signal Kanban and reorder point policy. Signal Kanban includes two components: triangle and rectangular signals. Triangle signal represents reorder point and rectangular one stands for order quantity. It is used between two consecutive stations to trigger production whenever on hand inventory level drops to a minimum level (reorder point). In the example shown in Figure 8, each container has 200 units. Therefore reorder point is 600 units (three containers) and order quantity is 1000 units (5 containers). When two containers are removed, triangular Kanban is exposed and order for 1000 units (five containers) is released. Order Quantity 1000 units Reorder Point 600 units Figure 8 - Signal Kanban Manufacturing in stations and moving buffer stock from previous stations to following ones are basically handled by Kanbans with no need of additional inventory control. Figure 9 shows a brief explanation of Kanban flow in a shop. Since there is no

27 27 need for inventory control, number of Kanbans is the main factor which affects buffer stock sizes. There are several formulas used to calculate of the number of Kanbans. One of the widely used formulas is given in equation 1. % Equation 1 The reorder point is calculated considering leadtime demand and safety stock (SS) as given in equation 2. Equation 2 = Daily Demand * Leadtime in Days + Safety Stock Both the number of Kanbans and reorder point calculations is taking leadtime into consideration. Leadtime is the amount of time between placing an order and receiving the items of the order. Most planning models and systems are suffering from uncertainty of demand during leadtime. Even though, Kanban system works as a reverse logic of MRP, which is shown in Figure 10, leadtime and leadtime demand remain as critical issues in both MRP and Kanban systems. However, Kanban system s consumption-driven production is better and more effective than MRP s combination of forecast and actual order based production. Suri stated that Just-in-Time education, total productive maintenance program, quick changeover program, zero defects, visual workplace etc. are necessary to implement and execute a successful Kanban system. Debates on benefits of pull and push systems still continue. However, Plossl s second

28 28 principle of planning and control of a manufacturing system, there is no single best way to control a manufacturing business, seems still valid. Suri lists disadvantages of JIT. First of all, having lack of ability to perform custom jobs and being designed for repetitive manufacturing systems make JIT hard to implement on such customized manufacturing systems. Secondly, as product variety increases, a classic Kanban system starts having large amount of WIP in spite of its philosophy of maintaining least possible WIP. Thirdly, since Kanban system and cards, container sizes are designated to meet current demand (not forecast), when there is a surging demand in a growing market, this will cause late deliveries, backlogs and shortages. Then he defines an extended method which encompasses both pull and push methodology named POLCA (Paired- cell Overlapping Loops of Cards with Authorization) Paired Cell Overlapping Loops of Cards with Authorization (POLCA) Kanban, a well-known type of pull systems, performs well in repetitive manufacturing environments. In make-to-order or make-to-engineer systems, using Kanban may become a wrong option. In Kanban system, there is a direct relation between cards, containers and product type. However, in make-to-order or engineer-to-order systems, implementing such a direct relation is not handy, since these systems have high product variety that usually creates higher WIP. One of the main contributions of POLCA is that POLCA cards work between two cells and represent jobs instead of products to be performed on corresponding pair of cells. The main context of POLCA is described as a combination of features: (1) a high level material requirements planning

29 29 system (HL/MRP), (2) cellular manufacturing organization, and (3) flat BOMs. Riezebos states that the synchronization of cells in terms of job sequence and routes is the main problem of planning cellular environments and this insufficient synchronization causes waiting times and incomplete product buffers.. According to him, refilling a stock position with respect to product specific control creates inefficiency in especially maketo-order companies. Product specific control is a kind of material control system which replenishes stock position with respect to specific product or component. CONWIP and Generic Kanban are alternative ways of product anonymous control instead of product specific control. The main idea of product anonymous control is that it focuses on releasing order to shop floor regardless of actual product type. POLCA uses route specific control which is a kind of product anonymous control. Suri listed five key features of POLCA. Firstly, releasing authorizations for jobs to cells are created by HL/ MRP. HL/ MRP is a feature which provides tickets to be used in shop floor planning and execution of systems. These tickets provide information about the routes of jobs, sequences of operations, components to be added during corresponding operations, and authorization times depending on lead times.

30 30 Source: Figure 9 - Sequential Progress of Kanban System

31 31 Source: Figure 10 - Kanban System Framework Secondly, POLCA cards are used to control material flow between cells. Kanban system can be used within cells as well. Thirdly, POLCA cards are assigned to jobs rather than products and used between two cells to control synchronization of production and flow by checking jobs over paired cell loops. Fourthly, POLCA card stays with corresponding job during its journey between two consecutive cells. In other words, a job

32 32 cannot be started in a cell until the right POLCA card is released from downstream station and become available for the upstream station for that job and the authorization time (ready time) which is determined by HL / MRP is satisfied. An example is shown in Figure 11 from Suri s book. There are 3 main operations performed. Two cells for operations A and B, one cell for operation C are allocated in system. There are two jobs defined, namely job 1 and job 2. The route for job 1 is A11 - B22 - C31. For job 2, it is B21 - A12 - C31. POLCA cards are designed with respect to shown paired cells. The originating and destination cell and the number of POLCA cards are included on the cards. For job 1, if raw material and A11 /B22 POLCA card are available at the beginning of cell 11, and the authorization time of job 1 is satisfied, then job 1 can be launched to cell 11 for operation A. After the completion of operation A of job 1 on cell 11, A11 / B22 POLCA card gets into the POLCA card queue of cell 22 for operation B with job 1. After job 1 arrives to cell 22, it is required that a free B22 / C31 POLCA card is available for job 1 to be processed on cell 22. When B22 / C31 POLCA card becomes available, job 1 is launched to cell 22 to start operation B. Here, there is a significant difference from Kanban system. Job 1 will carry two POLCA cards on cell 22 for operation B. These are A11 / B22 and B22 / C31. Therefore, both A11/B22 and B22 / C31 POLCA cards stay with job 1, on cell 22 for operation B. Thus, previous cell does not produce for the current cell, while operation B of job 1 is going on. Because of this issue, the term overlapping loop is used in acronym of POLCA. After the completion of operation B of job 1 on cell 22, A11 / B22 POLCA card can be brought back to cell 11 and can be used to launch new jobs.

33 33 For operation C of job 1, B22 / C 31 POLCA card should be available and the authorization time has to be satisfied to start operation C. In addition, if we consider operation C is the last operation for job 1, there is only one POLCA card, B22 / C31, is used for operation C. For job 2, the same procedure is applied as well. POLCA system works well since the POLCA cards make planners and executers sure that a cell only works on jobs for which the following cell also has enough capacity to make it through. POLCA differs from MRP with respect to this point, and offers a better and reasonable shop floor execution. POLCA system ensures that bottleneck resources are considered first during shop floor execution. Suri stated three main advantages of POLCA over MRP and pull systems : 1. Since POLCA cards are used among paired cells and stay with a job during its journey over two cells, they keep cells utilized with jobs which are more eligible to be done in near future by checking both authorization times and availability of corresponding cards before releasing the job to the cells. 2. HL/ MRP feature of POLCA mainly determines authorization times of jobs on their journey in the system with respect to their routes. These times are determined by using leadtimes and MRP logic.

34 34 (Source: Rajan Suri, Quick Response Manufacturing, 1998, Productivity Press, Oregon, Portland) Figure 11 - POLCA System Illustration

35 35 In shop floor execution of POLCA, both POLCA card and job s authorization time should be available to launch the job to the cell. This authorization time keeps system to do necessary jobs. In authorization time determination, POLCA uses leadtime information and BOMs. 3. In standard Kanban system, workstations are placed in close proximity to keep small amount of intermediate inventory and small number of bins and cards. In other words, POLCA cards can go over long loops in terms of physical distance or job route length. Especially in MTO systems, POLCA cards can perform better in terms of shorter throughput time and less WIP of items due to infrequent demand for items. For further information on POLCA, the reader can refer to Suri s Quick Response Manufacturing book and Reizebos s article Demand Management Vollman defines demand management as an activity which manages day-to-day interactions between customers and company. As a response to the question that why is demand management important?, Landvater states that stabilizing production plans and master production schedules through demand management results in vital production improvements, smoother and more effective operations of all planning and execution functions. Demand management in manufacturing planning and control systems is the main issue that is discussed in this study. Demand is the main trigger point in a company regardless of whether it is a service or manufacturing system. If a company does not

36 36 provide sufficient feedback from market place, company strategic plan is directly affected from this situation. For manufacturing companies, demand management includes such activities as forecasting, order entry, order delivery date promising, customer order service, and physical distribution. For planners, there are two main types of demand, namely, actual demand and forecasted demand. Some inventory management and production control systems such as Kanban do not use forecasted demand at all. They solely function based on actual demand. In push systems such as MRP and OPT, demand management includes both forecasted and actual demand. For a company which is seeking successful interactions among demand management, production planning, resource planning and master production scheduling and shop floor execution, as shown in front end part of figure 1 (MRP Framework), the linkage between market place and MPC must be strong. According to Vollman, the connection between demand management and production planning depends on the time interval of production plans, e.g. quarterly, monthly etc. and their statement type such as number of items or money. Three main activities are handled by demand management with respect to the relation with production planning as providing efficient synchronization and communication between market and production plan, and complete demand information. The relationship between demand management and Master Production Schedule varies depending on manufacturing environments. There are three main demand management strategies; Make-to-Stock (MTS), Assemble-to-Order (ATO), and Make-to- Order (MTO).

37 37 i. Make-to-stock: Future sales are forecasted based on historical data. The production orders are released to meet forecasted demand. Finally, customer demand is met from inventory. Therefore MPS works as a build to forecast plan. ii. Assembly-to-Order: In this environment, components and parts are built to the forecasted demand. However, the completion (assembly) of finished product is delayed until an actual order is received. One of the key responsibilities of schedulers is arranging viable customer order promise dates by using available-to-promise information. This approach is useful when different products have common parts and demand is uncertain. iii. Make-to-order: In this environment, the company builds the product only after an order is received. Most of the time, the product is designed to meet the specific requirements of customer. Therefore building to stock would be a risky strategy and is avoided. Some of key principles to have a successful coordination of demand management and production control are: i. All sources of demand should be considered and data should be sufficient in terms of time, quantity, location and source. ii. Available to promise concepts are required to be used during order promising. iii. iv. There should be stabilized and well developed customer service standards MPS should provide coordination for outbound product flows

38 v. MPS and demand management should be coordinated good enough to keep system stable and flexible. 38 In conclusion, demand management is a key requirement to provide stable and efficient coordination between market place (demand) and production planning and control. Demand management should also provide sufficient support to production and planning system in terms of accurate data of orders and forecasts depending on the replenishment type of system in use. Production system type is an important factor on decisions made about demand management strategies Justification In this chapter, seven main inventory planning and production control systems are briefly explained. Changes in time, needs, customer profiles, technology, economy and world have been having vital effects on planning systems. At the beginning of the 20 th century, EOQ was the most appropriate formula to find order quantity and use in inventory control and production planning systems. Its known and constant demand assumption provides robustness and insensitivity against changes made in cost parameters. On the other hand, lack of shortage consideration was a weak side. Lot sizing procedures such as least-unit cost, least-period cost were used to deal with varying demand situation since EOQ was not sufficient. Later on, statistical inventory control techniques (SICT) provided models which are able to deal with stochastic demand environments. However, all these three main methodologies are able to deal with single items. In our proposed approach, we will consider multiple items and stochastic demand

39 39 which are the most complicated situations and reflect the real life the best. On the other hand, MRP, JIT, OPT and POLCA are able to deal with multi-item cases too. MRPs contribution is that dependent and independent items planning became more efficient with the BOMs and MPSs. However, there is still lack of support in terms of finite capacity loading in MRP. JIT does not consider capacity as a constraint, during the execution of orders. It uses the principle of production demand. Production orders are released based on actual consumption. However, when demand and product variety increases and production system is more custom type than repetitive, JIT s advantages may not work. Optimized Production Technology (OPT) includes finite capacity loading by considering bottleneck resources as a decision parameter during the scheduling of production. POLCA s contribution on inventory control and production planning is that high level MRP execution on cellular environment with flat BOMs became possible with Suri s approach. Each approach on inventory control and production planning issues has strong and weak sides as well depending on the production system type, business, strategies, internal and external limits, etc. Some of the characteristics of these approaches are summarized in Table 1. The proposed approach reflects the features of pull system since its production planning is performed based on only consumption and there is no forecasted demand considered. Historical demand data is just used for the estimation of reorder points. From these aspects the proposed approach sits into the JIT and POLCAs category. However, at the same time, capacity utilization and capacity planning is done during production planning and inventory control processes which separates the proposed approach from

40 40 JIT and POLCA. Since the proposed approach works on a daily period and order decisions are made simultaneously with finite capacity allocation, it resembles to OPT. In addition, production system is utilized close to 100 % filling idle capacity with new production orders. Dynamic reorder point consideration makes the proposed approach different from SICT and JIT which are using fixed reorder point and order quantities. In conclusion, the proposed approach attempts to combine some features of pull and push systems, which makes it a combination of consumption-driven and capacitydriven production. Since the proposed approach is a consumption-driven production planning and inventory control system, these features put it into pull category. On the other hand, the proposed approach is a kind of push system, since capacity utilization is considered and system capacity is filled with new orders based on dynamic reorder point consideration when idle capacity is observed based on finite-capacity approach Objective of the Study The overall objective of this study is to propose new procedures for inventory control and production planning in a manufacturing company. These procedures aim to minimize the total cost of inventory carrying, backorder and ordering costs.

41 41 Table 1 - Characteristics of Different Inventory Control and Production Planning Approaches EOQ LOT SIZING PROCEDURES SICT MRP JIT OPT POLCA PROPOSED APPROACH DEMAND DETERMINISTIC CONSTANT x VARYING x STOCHASTIC - x x x x x x NUMBER OF ITEMS SINGLE x x x MULTIPLE x x x x x CAPACITY LOADING Infinite Finite Finite REORDER POINT CONSIDERATION - - Fixed - Fixed - - Dynamic ORDER QUANTITY Fixed Fixed / Varying Fixed / Varying Fixed / Varying Fixed Fixed / Varying Fixed Fixed / Varying SYSTEM TYPE (PULL / PUSH) Push Push Pull Push Pull Push Pull Pull

42 42 CHAPTER 2: PROBLEM STATEMENT In this chapter, the problem to be studied is described in detail along with performance measures considered Definition of the Problem The motivation for this problem comes from a boiler and thermo siphon manufacturing company in Turkey. There are ten products with deterministic processing and setup times. The volumes of products change from 20 liters to 120 liters. The main process of manufacturing is based on manual and machine-based welding. The steps of manufacturing are briefly bending sheet iron, spot welding of vertical body, spot welding of top and bottom lids, finite welding of top, bottom and vertical body and testing with high pressured water. As the volume of product increases, welding time also goes up. Backorder is allowed with a penalty cost. No customer order is considered as lost sale. Backorder cost, ordering cost (setup cost) and inventory carrying cost are included in the total cost function. In this environment, there might be days where no production orders released to the shop and manufacturing system is underutilized. On the contrary, there might be days where production orders are released all at once and capacity may not be sufficient. In this study, an attempt is made to strike a balance among avoiding backorders, maintaining high level of resource utilization, and holding lower inventory. The assumptions made in this study are as follows; Inventory positions checked once a day Equally important products

43 43 A system capacity of eight hours (1440 minutes) per day No overtime allowed Single cell shop floor configuration Partial delivery of customer order allowed Reorder points are estimated based on historical demand data for all products. However, no forecast is used for releasing production orders. Demand is generated on a daily basis and is supplied from on hand inventory, if available, and inventory position is adjusted. If on hand inventory is not sufficient, backorder occurs. As reorder points are violated, production orders are released for replenishment subject to available capacity. There are two main situations that the proposed approach deals with; 1. Idle capacity (underutilization of system) 2. Insufficient capacity (overutilization of system) Figures 12, 13 show illustrations of these two situations as examples. According to Figure 12, the reorder points of products 2, 4 and 10 are violated and production orders are released. The capacity utilization in this case is only 44 %. In this case, the proposed approach deals with the problem of underutilization of the system. An attempt is made to increase the system utilization. On the other hand, in Figure 13, several production orders are released and the capacity utilization is 108 %. Since overtime is not considered, the proposed approach deals with the overutilization of the system. In this situation, alternative methods are considered to lower utilization down to acceptable levels.

44 44 In conclusion, the problem to be studied is defined as the consumption-driven multi-independent item inventory planning and production control problem in a dynamic demand environment with finite capacity planning Performance Measures The tradeoff between the number of orders and lot size is an important factor on the total cost of inventory management. The total cost function consists of three cost elements which are order cost, inventory carrying cost and backorder cost. The total cost function to be used is shown in equation 3. Equation 3 Index t Number of days in the planning horizon Parameters Order cost for item i Inventory holding cost per day per item i Backorder cost per day per item i Variables TC Total cost Number of orders given for item i in day j (0,1) Number of items held per item i in day j

45 45 Number of items backordered per item i in day j The order cost measures the cost of total number of released production orders to shop floor. It is calculated by multiplying the order cost with the number of orders in the entire planning period. Inventory carrying cost is the cost of holding inventory on hand and is computed by multiplying inventory held with the unit carrying cost. Backorder cost is the cost of not meeting the demand of a customer as soon as he orders, in other words, not having enough amounts of items on hand to meet his orders exactly. Thus, the remaining units of order is delayed to the next available time (becomes backorder). The total backorder cost is computed by multiplying the number of backordered units with the unit backorder cost. In addition, it is assumed that no customer and customer order will be lost.

46 Figure 12 - Idle Capacity Situation 46

47 Figure 13 - Exceeded Capacity Situation 47

48 48 CHAPTER 3: LITERATURE REVIEW Many studies have been presented on inventory planning field in this century. Nowadays this field can be called as ocean in terms of many branches and hundreds of studies. Most of the studies related to inventory planning and control of manufacturing area do not include capacity as the part of problem. However, in this study, capacity is considered as constraint. A classification of the reviewed articles is built based on Summers s parameters as Consideration of capacity as a constraint or not Having single item or multi-item 3.1 Some of the Studies without Consideration of Capacity Single Item As the name suggests, these studies focus on a single item. Chikan s Inventory Models book is one of the best sources in terms of classification and explanation of inventory models since first EOQ model was published by Ford Harris in As an earlier study, Koenigsberg modeled single-item multi reorder point inventory policy which enables 1 to k*q orders depending on the amount of violation in reorder point with constant leadtime and deterministic demand. Another continuous review inventory model is applied by Jose, Sicilla and Garcia-Laguna to a single independent item planning problem. It includes parameters such as deterministic demand, shortage and backlogging. Customer impatience is included as a function in this analysis. The cost function consists of setup cost, holding

49 49 cost and shortage cost. The presented approach was used to determine economic lot size, reorder level and total cost.. Most of the companies still use leadtime as a constant variable in their planning system. However, since MRP and related approaches required backward planning from independent forecasted demand to dependent items by considering leadtime, many of firms have still been suffering from shortages or backorders as a result of leadtime errors. In 1958, Wagner and Whitin were the first who studied on dynamic lot sizing problem and found an answer to question of what to do when classic square root formula does not work efficiently due to non-steady state demand rate and varying inventory costs which is difficult to assume as average? on a single item planning problem. Karmarkar criticized the assumption of constant leadtime in planning and examined relationship between lot sizes and leadtime in terms of cost for batch type production oriented shop floors. Kim and Benton issued the same problem which has single independent item with deterministic demand over a finite time horizon based on Karmarkar s study in 1987 about questioning the connection between leadtime and lot size. They defined leadtime as a function of lot size which means that if order quantity is decreased, leadtime is going to be decreased otherwise leadtime is increased as order quantity is increased. Hariga modified Kim and Benton s model which is solving single item (Q, r) problem to find optimal or near optimal lot size as a function of leadtime and he proposed a new procedure which finds optimal or near optimal lot size and reorder point at the same time. As a result, his study produces better results in terms of lot sizes, leadtimes and total cost.

50 50 Gupta and Brennan studied uncertainty of demand and leadtime and their effects on single item with multi-level product structures. A simulation model is run to observe the influence of uncertainty Multi-Item Blyka and Rempa studied a joint replenishment problem which includes multiitem planning and scheduling with the objective of minimizing production and inventory carrying cost on a finite time period.. Downs, Matters and Semple worked on a multi-item planning problem with resource constraints, lags in delivery and lost sales concepts. A linear programming approach for inventory carrying and shortage costs is generated and used with respect to order up to R policy. Zipkin worked on a problem of multi-item planning with stochastic demand and no leadtime consideration. He proposed two alternative approaches; first in first out and longest queue. Both approaches attempt to provide sufficient solutions of when to order and which item to assign.

51 Some of the Studies with Consideration of Capacity as a Constraint Single Item As examples of earlier studies, Florian and Klein worked on a dynamic lot sizing single item problem with both backorder and non backorder cases with concave cost function and capacity as a constraint. Jagannathan and Rao extended Florian et al. s work by incorporating of inventory constraints with backlogging and a new production cost function. Baker et al. studied a single-item dynamic lot sizing problem with time varying demand and capacity constraints. An aggregate single item planning problem is studied by Ciarallo et al. with consideration of random capacity and demand. An order up to policy is used and tested in both single and multi period environments. The efficiency of order up to models is shown significantly in a multi period environment when capacity and demand are stochastic. Wang and Gerchaj extended the same study with the incorporation of random capacity and continuous review policy Multi-item Bretthauer et al. issued inventory planning and shop floor control problem of multiple items with constraints as capacity of machines, workforce, supplies, raw material availability, storage space, and number of orders and steady state (deterministic) demand. For large scale problems, their algorithms which include nonlinear knapsack and nonlinear OR model with lower and upper boundaries are working well with continuous and integer valued resource restrictions.

52 52 Federgruen and Katalan dealt with a multi-item stochastic economic lot scheduling problem with capacity constraints and demand uncertainty. They built a hybrid system which involves both Make-to-order and Make-to-stock strategies simultaneously considering Williams hybrid model which is one of the earliest models that combines both Make-to-order and Make-to-stock manufacturing strategies. Cakanyildirim, Bookbinder and Gerchak focused on a production control problem and tried to build a correlation between leadtime & lot size unlike the classical (s, Q) approach where leadtime and lot size are treated independently. In terms of capacity, for the aim of making shorter processing times of items, model gives permission to customers to reserve an amount of capacity at supplier s facility. In order to reduce processing time, model allows customers to reserve a certain percent of capacity at supplier s manufacturing facility. Nagendra and Das issued a finite capacity scheduling method for MRP lot size restrictions. The method, PCA (Progressive Capacity Analyzer), a model which can provide lot sizes and capacity plans simultaneously with respect to BOMs, has shown outperforming results compared to classic capacity planning approaches.

53 53 CHAPTER 4: METHODOLOGY The problem studied has four main features which are briefly consumption-driven production, reorder point system, finite capacity loading and capacity utilization. Four models are developed to deal with this problem for the objective of minimizing the total cost. The first model is the base model which works same as the classical (s,q) statistical inventory control model. Other three models differ from the first model in terms of including dynamic order quantities and/or reorder points with finite capacity loading. General features of models are shown in Table 2. Table 2 - General Features of Proposed Models MODEL 1 MODEL 2 MODEL 3 MODEL 4 DEMAND STOCHASTIC STOCHASTIC STOCHASTIC STOCHASTIC ORDER QUANTITY FIXED DYNAMIC DYNAMIC DYNAMIC REORDER POINT FIXED FIXED DYNAMIC DYNAMIC BACKORDER ALLOWED ALLOWED ALLOWED ALLOWED SHORTAGE NOT ALLOWED NOT ALLOWED NOT ALLOWED NOT ALLOWED PRODUCT PRIORITY NO NO NO NO PRODUCTION WITHOUT RPV 1 NO NO YES YES PRIORITIZATION FOR BACKORDERED NO NO YES YES ITEMS LIMITATION on MAXIMUM NUMBER OF ORDERS NO NO NO YES Underutilization and overutilization of system capacity are dealt with in different models to achieve the minimum total cost. Fixed and dynamic order quantities and 1 RPV: Reorder point violation

54 54 reorder points are used to accomplish the management of inventory with the least cost, backorder and average on hand inventory, and meeting customer needs with the best timeliness. In the following sections, models are explained in detail Model 1: Multi-item Inventory Planning with (s, Q) Model Introduction Model 1 is the adaptation of classical (s, Q) model with finite capacity loading. Stochastic demand, fixed order quantities and reorder points and finite capacity are the main features of this model. Customer orders are received throughout the day and they are shipped at the end of the next day from the warehouse. On hand inventory levels are adjusted after demand is met from the inventory. If on hand inventory drops to reorder point or below, system generates production orders for the following day. The flowchart of model 1 is shown in Figure 15. In addition, inventory control module is the same in all models and this module is shown in Figure Model Framework Classical (s, Q) model is applied to multi-independent items inventory control and production planning. First of all, daily demand values for all 10 products are generated from predefined uniform distributions. After customer orders are received, each product s inventory status is checked to see if there are enough units on hand. If so, items are shipped from warehouse and inventory level is revised to reflect the shipment.

55 55 If there are not enough items in inventory, what is available is shipped and the remaining units are backordered. If on hand inventory after the subtraction of demand is below or equal to reorder point, this situation is called as reorder point violation (RPV) and a production order is released to the shop. Production orders continue to be released as long as system capacity is enough to produce order quantities. In other words, production orders are released one at a time as long as there is idle capacity for production. The sequence of products is determined randomly. Therefore, products are randomly picked and sent to the planning system to decide whether production is possible or not. The remaining capacity is calculated after each production order is released. As long as the remaining capacity is enough for production, current product s production order is released to the shop floor. Otherwise, the order quantity of the last possible product to be produced is modified (decreased to fit to the remaining capacity) not to exceed system capacity, since overtime is not allowed. Therefore, model works according to fixed order quantities, except; the order quantity of the last possible product to be produced is subject to change since there is not enough capacity to produce its original order quantity. A numerical example is given. There are ten products with information shown in Table 3..

56 Table 3 - Product Inventory Information INITIAL INV. CUSTOMER DEMAND INVENTORY AFTER SHIPMENT REORDER POINT 56 REORDER POINT VIOLATION PRODUCT NO PRODUCT (RPV) 97 YES PRODUCT NO PRODUCT NO PRODUCT (RPV) 52 YES PRODUCT NO PRODUCT (RPV) 58 YES PRODUCT NO PRODUCT NO PRODUCT NO Products 2, 5, and 7 are supposed to be produced since their inventory levels drop below reorder point which is called reorder point violation (RPV) as shown in Table 4. Table 4 - Reorder Point Violation of Products 2, 5 and 7 INVENTORY AFTER SHIPMENT REORDER POINT RPV ORDER QUANTITY PROCESS TIME SETUP TIME REQUIRED CAPACITY CUMULATIVE CAPACITY PRODUCT YES PRODUCT YES PRODUCT YES ; The required capacity for each of products 2, 5, and 7 are calculated with equation Equation 4

57 57 NO YES Figure 14 - Inventory Control Module

58 Figure 15 - Model 1- Flowchart 58

59 59 The total capacity required to produce products 2, 5 and 7 is 1140 minutes as shown in table 4. The procedure is applied as follows. First product 5 is randomly assigned and cumulative used capacity is 340 and system capacity (1440) is not violated. Therefore, production order for product 5 is released. Then, product 2 assigned and cumulative capacity usage becomes 660. Since system capacity is still not violated, production order of product 2 is released. Finally product 7 is assigned and production order is released after checking cumulative capacity which is 1140 and still less than system capacity. There might be situations where the remaining capacity cannot be enough to produce the last possible item. For example, regarding the first example, production orders of products 2, 5, and 7 are released and cumulative capacity is There is = 300 minutes of capacity remains as idle capacity. Now, suppose that product 10 s reorder point was also violated as well. It needs to be produced and its information is given in Table 5. Table 5 - Information of Product 10 INVENTORY AFTER DEMAND REORDER POINT REORDER POINT VIOLATION ORDER QUANTITY PROCESS TIME SETUP TIME REQUIRED CAPACITY PRODUCT YES According to table 5, 430 minutes of capacity is needed to produce 80 of product 10. However, there is only 300 minutes of system capacity available. Since 430 minutes of capacity is required but there is 300 minutes of capacity that can be used, the

60 remaining capacity is dedicated to produce product 10 and order quantity of product 10 is modified (decreased) to keep utilization at % 100 as shown in equation Equation 5 From the equation above, the last possible product s (product 10) new order quantity is 54. Even though 80 is the original fixed order quantity for product 10, order quantity of 54 is released to shop just for that day due to lack of capacity Conclusion In conclusion; this model is the base model which includes stochastic demand, fixed order quantities and reorder points. This model will be used mainly to compare with other proposed heuristic models with respect to performance measures Model-2: Multi-item Inventory Planning with Flexible Order Quantities Introduction In this model, order quantities of items which are required to be produced on are subject to change (dynamic order quantities). Order quantities are modified to keep the system utilized close to 100 %. The model is also called as multi-item inventory planning with flexible order quantities (MIP-FOQ). The flowchart of the model is shown in Figure 16.

61 Model Framework STEP 1. Demand Generation Daily demand values for all 10 products are generated from the predefined uniform distributions. STEP 2. Inventory Control Customer orders are met from inventory, as long as on hand inventory is sufficient. These items are shipped and inventory levels are adjusted. If on hand inventory is not sufficient, partial delivery is made and the balance (remaining units) is backordered. STEP 3. Production Orders Inventory levels are compared with reorder point and those items with inventory levels equal to or below reorder point are identified (RPV: Reorder Point Violation). After identifying what products to produce, the total capacity requirement is calculated (Total Capacity Needed). The total capacity needed stands for the total required capacity to produce items which are released on current day. STEP 4. Capacity Check and Finite Capacity Loading Once the total capacity needed is calculated, since system capacity is restricted to 1440 minutes and overtime is not allowed, there are three cases where the total capacity needed is adjusted to the real system capacity of 1440 minutes to keep system utilized. Case 1) Zero-Capacity Situation If there is no production order needed meaning that the total needed capacity is equal to 0, no production order is given and the day is considered as day off. Case 2) Idle Capacity Situation

62 62 This situation occurs when total needed capacity is between zero and system capacity (1440 minutes). Case 3) Excess Capacity Situation This situation occurs when the total capacity needed for production of items is higher than the system capacity. In both cases 2 and 3, the total capacity needed is adjusted to keep system utilization high and not to exceed the available capacity. This approach is named as flexible since order quantities are adjusted subject to system capacity. There is an adjustment coefficient used to stabilize production of items subject to capacity. This adjustment coefficient is calculated according to equation 6 as shown below. Equation 6 With respect to AC, order quantities of items are; decreased if total needed capacity exceeds 1440 increased if total needed capacity is below 1440 by multiplying initial order quantities with AC.

63 63 BEGIN INVENTORY CONTROL REORDER POINTS, ONHAND INVENTORY, DEMAND WHICH PRODUCTS ARE REQUIRED TO BE PRODUCED? ONHAND INVENTORY LEVEL COMPARISON WITH REORDER POINT TOTAL REQUIRED CAPACITY CALCULATION CAPACITY REQUIRED = SETUP + PROCESS TIME * ORDER QUANTITY YES IS TOTAL REQUIRED CAPACITY ZERO? NO IS SYSTEM CAPACITY EXCEEDED? YES ADJUST EXCEEDED CAPACITY TO THE SYSTEM CAPACITY NO ADJUST IDLE CAPACITY CLOSE TO THE SYSTEM CAPACITY NO ORDER IS RELEASED TO PRODUCTION SYSTEM CALCULATE IDLENESS RATE SYSTEM CAPACITY / TOTAL REQUIRED CAPACITY CALCULATE EXCESSION RATE CALCULATE NEW ORDER QUANTITIES WITH RESPECT TO IDLENESS RATE SYSTEM CAPACITY, EXCESSION RATE, ORDER QUANTITIES CALCULATE NEW ORDER QUANTITIES WITH RESPECT TO EXCESSION RATE RELEASE PRODUCTION ORDERS OF PRODUCTS WHICH ARE REQUIRED TO BE PRODUCED RELEASE PRODUCTION ORDERS OF PRODUCTS WHICH ARE REQUIRED TO BE PRODUCED END Figure 16 - Model-2 - Flowchart

64 64 Numerical Example: After subtracting demands from on hand inventories, according to reorder points of products, products 1, 4 and 8 are decided to be produced as shown below (Table 6). Table 6 - Products to be produced Products Order Quantity Process Time Setup Time Capacity Requirements Product Product Product Total 560 As a result, 560 minutes of capacity is needed to produce those items. This case is idle case since the total needed capacity is below The production is forced to produce more to keep utilization closer to % 100. Adjustment Coefficient (AC) = = 2.57 Then, AC is multiplied with order quantities. The modified order quantities are shown below (Table 7). Table 7 - Modified Order Quantities - Model 2 Products New Capacity (min.) New Order Quantity (units) Product x 2.57 = ( )/3 = 138 Product x 2.57 = ( )/4 = 162 Product x 2.57 = ( )/5 = 60

65 65 The same approach is applied when total needed capacity is higher than the system capacity (1440). Adjustment coefficient (AD) is going to be smaller than 1, since total needed capacity is bigger than STEP 5. STEP 6. Production orders are given with respect to new order quantities. Production order quantities are checked by a parameter, k Q. It is used to limit the increase in order quantity. For example, if k Q = 5, that makes model to produce an item up to 5 times of initial order quantity (when reorder point is violated). After new order quantities of items are checked and modified with respect to k Q, production orders are released to the system Conclusion In conclusion, the main difference of this model from model 1 is that, order quantities of needed items are dynamic. If the total needed capacity is lower than system capacity, order quantities are increased by using AC to make utilization close to % 100. Otherwise, they are decreased to keep utilization below % 100 since overtime is not considered. Twenty five replications are done with all datasets by varying k from 1 to Model 3: Multi-item Inventory Planning with Flexible Order Quantities Subject to Reorder Point- Inventory Status Relation Introduction The model works according to basic (s, Q) policy to fill capacity with products which are required to be produced on current day. In addition, if the required capacity to

66 66 perform daily production is more than the system capacity (insufficient capacity situation), order releases of items are made subject to prioritization with a different approach than models 1 and 2. If there is idle capacity after production orders of products which are required to be produced, new products are taken into consideration to keep utilization close to % 100. New products are released as new orders to shop floor by prioritization. Their priority is decided by the gap between reorder points and inventory status. Products which have smaller gaps are going to be considered as more important and the ones which have larger gaps are considered as less important. The flowchart of model is shown in Figure 17, 18 and Model Framework STEP 1. Demand Generation This step is the same as the one in model 2. STEP 2. Inventory Control This step is the same as the one in model 2. STEP 3. Production Orders This step is the same as the one in model 2. STEP 4. Capacity Check, Modification of Orders and Finite Capacity Loading Once total needed capacity is calculated, since system capacity is restricted to 1440 minutes and overtime is not allowed, three cases are likely to happen.

67 67 Case 1) Zero Capacity Situation If there is no production order needed in a day, it implies that the total needed capacity is equal to 0, no order is given. System is not utilized on that day and it is called as day off. Case 2) Idle Capacity Situation This situation occurs when the total needed capacity for production of items is below First of all, the production orders of products which are required to be produced (have reorder point violation) are released. After required production orders are released, remaining idle capacity is filled with remaining (non-released) items. The question is here that how many of which remaining item is going to be produced? The remaining items are prioritized by considering their vulnerability to reorder point violation. The gap between reorder point and on hand inventory level of an item determines, its importance or priority of production. With respect to gaps, the importance factor of each and every product is calculated. How many to produce for which product is decided by adjusting factors to the order quantities by considering capacity. An upper limit of order quantity and reorder point is used to keep system away from over production and excess inventory in experimentation. The parameter is k Qr and k Qr is used as a limitation tool in two things 1: Maximum order quantity: During the extra production decisions, it works as a limiting tool to keep an order quantity at a maximum level. 2: Maximum reorder point: It limits release of a production order, if on hand inventory of an item is higher than the maximum reorder point.

68 68 Since k Qr works simultaneously for both cases explained above, a numerical example is given to explain both situations. For example, assume that k Qr = 3. In a particular day, suppose that two products new order quantities are calculated according to their gaps as shown in Table 8. Table 8 - Numerical example of k Qr Reorder Point On hand Initial O.Q. New O.Q. Updated O.Q. k Qr PRODUCT PRODUCT As it can be seen from table above, product 3 has no reorder point violation, but on hand inventory is close to reorder point and new order quantity is calculated as 130. However, k Qr = 3 which means, 30 x 3 = 90 items can be produced at most. Therefore, model modifies the order quantity as 90 items and gives 90 items of production order for product 3. For product 4, there is no RPV as well and the gap between on hand and reorder point is 91 which is bigger than k Qr x reorder point 23 x 3 = 66. Therefore, production order is cancelled because of risk of excessive inventory. From 1 to 25, 25 different k Qr parameters are experimented with all datasets to see the impact of the limitation. In addition, no order is allowed when new quantity is smaller than the original order quantity. Case 3) Insufficient Capacity Situation This situation occurs when the total needed capacity for production of items is higher than The model works based on prioritizing the products according to their

69 69 inventory status. First of all, the model considers if there is any product which has negative inventory. Because negative inventory stands for the amount of item that system could not provide to past customer demand (backlog) and that is supposed to be considered first. Therefore, the model gives the highest-equal priorities (an importance factor of M is assigned, is used as M in the model) to products which have negative inventories and gives productions orders with amounts of their original order quantities. Then, the remaining capacity (if there is) is used to produce products which has reorder point violation but positive on hand inventory. The gap between reorder point and on hand inventory means the amount of violation on reorder point. According to gaps, importance values are calculated. Then beginning from products which have negative inventory, products are ordered in sequence of importance factors and original order quantities are released as production orders. In addition, no order is allowed if new quantity is smaller than the original order quantity. Numerical Example -1: This numerical example is about idle capacity case. Suppose that according to customer demands shown in Table 9, three products are required to be produced. According to Table 9, products 1, 6 and 8 have reorder point violations. Thus, production orders are released for these three products to the shop floor.

70 70 Table 9 - Numerical Example for Model 3- Idle Capacity Case INVENTORY AFTER SHIPMENT INITIAL INVENTORY CUSTOMER DEMAND REORDER POINT PRODUCT (RPV) 26 YES PRODUCT NO PRODUCT NO PRODUCT NO PRODUCT NO PRODUCT (RPV) 31 YES PRODUCT NO PRODUCT (RPV) 13 YES PRODUCT NO PRODUCT NO REORDER POINT VIOLATION Table 10 shows the information for products 1, 6 and 8. The capacity required is calculated by multiplying process time with order quantity and adding setup time. The total capacity required is 570 minutes. Therefore, there is = 870 minutes left as available capacity. The remaining products are used to release as new production orders. First of all, their priority is calculated which is shown in Table 10 as importance factors. Table 10 - Products with Reorder Point Violation PRODUCTS REORDER POINT VIOLATION PROCESS TIME SETUP TIME ORDER QUANTITY CAPACITY REQUIRED PRODUCT 1 YES PRODUCT 6 YES PRODUCT 8 YES TOTAL USED CAPACITY 570 REMAINING CAPACITY 870

71 Figure 17 - Model 3 Flowchart 71

72 Figure 18 - Idle Capacity Case - Model-3 72

73 Figure 19 - Insufficient Capacity Case - Model-3 73

74 74 Table 11 - Remaining Products and Re-calculated Production Orders INVENTORY AFTER SHIPMENT REORDER POINT REORDER POINT GAP IMPORTANCE FACTOR CAPACITY ALLOCATION OQ OQ ORDER? ORDER QUANTITY ALLOCATED CAPACITY PRODUCT YES PRODUCT NO 0 0 PRODUCT NO 0 0 PRODUCT YES PRODUCT YES PRODUCT NO 0 65 PRODUCT NO 0 0 TOTAL TOTAL 845 Importance factors are calculated via dividing the total reorder gap by reorder point gaps of each remaining products. According to importance factors, remaining capacity is allocated. After the allocation of capacity, new order quantities are calculated as shown in column with header OQ. Then, they are checked according to the k Qr parameter. The k Qr parameter is the last check point of an order to be released. After new order quantities are calculated as shown in Table 11, they are checked by k Qr to avoid overproduction. It s similar to k Q which is used in model-2, but it has r feature as well. Q feature of k Qr limits the maximum production with respect to k coefficient. For example, if k=5, for a product with order quantity of 30, at most 150 items can be given as an order. The parameter r part of k Qr decides whether to allow release of a production order or not. For example, if k=5, suppose that product 1 has reorder point of 20 and on hand inventory units of 105. Even though, there is no reorder point violation, model-3 takes this product into consideration. Whatever its order quantity comes out

75 75 from reorder point-on hand gap calculations, since it s on hand is more than 5 x 20 =100 items; it cancels the production order of corresponding product due to r limit violation. As a result, k Qr is a limit of production and order quantity. A value of k Qr simultaneously limits order quantity to a maximum value of k * Q and production decision to a maximum on hand value of k*r. Basically, no production order released if on hand is greater than k*r and a production order can be mostly k*q at the same time by k Qr parameter Conclusion In conclusion, this model tries to order required products initially as long as their total capacity requirements for production do not exceed the system capacity. If system capacity is exceeded, order quantities are modified (reduced) with respect to an approach which is explained in insufficient capacity case. Otherwise, in addition to given production, the remaining products are considered to fill the remaining capacity and according to their importance factors. Their importance is decided by the gaps between reorder points and on hand inventory levels. Model 3 works different than model 1 and 2 by considering other products vulnerability of reorder violation and backlog after the order release of products which have reorder point violation. Additionally, it takes overproduction into consideration and limits production by k Qr parameter. Like in model 2, a production order is not allowed to be smaller than its original order quantity to keep the number of orders lower and limit overproduction.

76 Model 4: Multi-item Inventory Planning With Flexible Order Quantities Subject to Reorder Point- Inventory Status Relation with Restricted Ordering Introduction In model 4, multi-item inventory planning is performed similar to model 3. The only difference is that the remaining capacity is used by the limited number of extra orders after capacity is allocated to must-produce products. When required capacity exceeds system capacity, this approach works in the same way with model-3. The flowchart for model 4 is shown in Figure 20, Figure 21, and Figure Program Framework Steps 1, 2, and 3 are the same as in model 3. STEP 4. There are 3 cases Total Needed Capacity is adjusted to real system capacity of 1440 minutes. Case 1) Zero Capacity Situation: Model works as model 3 in zero capacity situation. If there is no production order needed to be given which is also meaning that total needed capacity is equal to 0, no order is given. System is not utilized on that day and therefore is considered as day off. Case 2) Idle Capacity Situation: This situation occurs when the total needed capacity for production of items is below In this situation, this model works little different than previous model (model 3). As a reminder, in model 3 this case is solved as;

77 77 First of all, the production orders of products which are required to be produced are released to production floor. After required production orders are given, remaining idle capacity is filled with the remaining items. The question is here that how many of which remaining item is going to be produced? The gap between reorder point and on hand inventory level of an item determines its importance or priority of production. With respect to gaps, the importance factors of each and every product are calculated. How many to produce for which product is decided by adjusting factors to the order quantities with considering capacity. In model 4, the production orders of products which are required to be produced are released to the shop first as in model 3. However, during the assignment of remaining products to fill the idle capacity, there is a restriction rule applied. In other words, with a number between 1 and 10, the extra orders which can be given after required items production orders are released can be restricted to a maximum number. The TF (top n products) parameter is defined to be used as a limit of extra orders. For example, for TF = 3, top three products which have the most importance are considered as can-produce products, after the allocation of must-produce products. In the numerical example which is given in section in tables (Table 9, Table 10, Table 11) suppose that TF = 1. According to that example products 1, 6 and 8 are already released to shop floor as must-produce products. There is still 870 minutes of idle capacity that can be used by the production orders of remaining products 2, 3, 4, 5, 7, 9 and 10.

78 Figure 20 - Model 4 - Flowchart 78

79 Figure 21 - Idle Capacity Case - Model-4 79

80 80 Figure 22 - Insufficient Capacity Case - Model-4 Since the rule is to release extra production orders for top 1product, top 1 product from remaining products with respect to their importance factors is released to shop floor. According to Table 11, product-7 has the highest importance with 158. Therefore idle capacity is allocated with product-7. In this allocation, k Q and k r parameters are used. Remember k Qr parameter is used in model-3 and it considers the limits for r and Q simultaneously. In model-4, they are allowed to be simultaneously under the impact of

81 81 different k values. Basically, different k values can be used to limit production and order quantities. In experimentation, integer k values, from 1 to 25, are used for k Q and k r. Integer values, from 1 to 10, are used for top first function as well. As a result 25 x 25 x 10 = 6250 runs are done to find the best match of three parameters which provides the minimum total cost of inventory system. Idle capacity is filled by product 7 with respect to k Q =2 and k r =3 limitations. Product 7 s on hand inventory level is 60 and reorder point is 58 as shown in table Table 11. For k r =3, 60 < 58 *3 and production order can be given. For k Q = 2, since idle capacity is 870, after subtracting setup time from idle capacity =840, new order quantity is calculated dividing idle capacity by process time (5 min.). OQ = 870 / 5 = 174 items. Then, new order quantity is checked with k*original order quantity (90) as 174 < 2 *90 174<180. As a result 174 items of product 7 can be released to system as an extra order after parameter checking. If k r =1, model-4 only releases production orders of must-produce products whose basically reorder points are violated. The k r =1 value prevents extra production. This feature allows model-4 to be able to work with low customer demands as well and it becomes similar to exact production (kanban) by using k=1. Case 3) Excess Capacity Situation This situation occurs when total needed capacity for production of items is higher than When there is excess capacity situation, model 4 works same as model-3.

82 Conclusion In conclusion, this model is most similar to model 3. However, in terms of allocation of idle capacity with new orders, it is restricting the number of orders up to a maximum number. This helps to get rid of very small lots which are not efficient with respect to the tradeoff between set up cost and lot size. Secondly, by limiting the number of extra orders to fill idle capacity, the variation of lot sizes is decreased. Three external parameters TF, k Q and k r are used in experimentation to see their impact.

83 83 CHAPTER 5: EXPERIMENTATION & RESULTS In this chapter, experimentation performed and results obtained are explained in detail Customer Demand Data Generation Demand data is generated by using uniform distributions for each product. The intervals between lower and upper end points of uniform distributions affect the variation of demand. Demand data based capacity requirement load is considered as the main parameter for experimentation. This load stands for the percent usage of the total system capacity during the predetermined time horizon (640 days) to meet customer demand. There are six different load levels used in the experimentation varying from % 30 to % 90 of the system capacity as shown in Table 12. Table 12 - Uniform Distributions Used in Demand Generation 30 % 40 % 50 % 60 % 80 % 90 % Min. Max. Min. Max. Min. Max. Min. Max. Min. Max. Min. Max. Product Product Product Product Product Product Product Product Product Product

84 84 As the interval between lower and upper end points of uniform distributions increases, the required capacity to meet demand increases and the variation of demand is directly affected by the increase in the load. The variation of customer demand based on the uniform distribution intervals of all products is shown in Figure 23. The lower end point is set to zero (0) for all products customer demand. The upper end points have impact on the variance of distributions. As the upper level of uniform distributions for all products increase, capacity requirements and variation of demand increase as shown in Figure 23. Customer Demand Intervals 90% Rough cut capacity requirement 80% 60% 50% 40% 30% Product10 Product9 Product8 Product7 Product6 Product5 Product4 Product3 Product2 Product Customer Demand in Units Figure 23 - Customer Demand Intervals

85 85 According to Figure 24, there is a parallelization between capacity load level and variances of customer demand. All models are run with respect to all load levels to see the impact of load and variation of customer demand on inventory control and production planning system and models proposed. In Table 25, the variance of each dataset (customer demand load) is shown. By using variance equation of uniform distribution, the variances are calculated. The increase in variance is shown in the last row of Table 13. The % of increase is calculated by comparing to the first dataset s (30 %) variance. Especially on 80 % and 90 % demand loads, the variance went up five times compared to the first dataset. Variances of Customer Demand Distributions 90% Capacity Load Level 80% 60% 50% 40% 30% Product10 Product9 Product8 Product7 Product6 Product5 Product4 Product3 Product2 Product1 Variances Variance Values of Uniform Distributions Figure 24 - Variances of Customer Demand Distributions

86 86 In stabilized systems, planning is relatively a simple task whereas in highly variable customer demand environment, planning is a more challenging task and better capacity allocation procedures are needed. The proposed models have been developed to accomplish this task. Customer demand datasets for six different load levels (30 %, 40 %, 50 %, 60 %, 80 % and 90 % of system capacity) are generated for 640 days to test the proposed models. Table 13 - The variances of demand distributions of products 30 % 40 % 50 % 60 % 80 % 90 % Product Product Product Product Product Product Product Product Product Product TOTAL % - 124% 195% 342% 595% 728% 5.2. Determination of Initial Input A set of reorder point, order quantity and initial inventory is prepared for each product as initial input. Reorder point is calculated by adding expected lead time demand and safety stock (Equations 6, 7, 8). Safety stock is calculated multiplying standard deviation of demand by square root of (k x leadtime). The lead time is taken as one day

87 87 and k is the service level factor which is assumed as one. Order quantity is considered as upper end point of uniform distribution (B) which is the maximum expected demand. Initial inventory levels are determined arbitrarily. Equation 4 Equation 5 Equation 6 Index r: Reorder point LTD: Leadtime demand SS: Safety stock λ: Leadtime B: Upper end point of uniform distribution A: Lower end point of uniform distribution σ: Standard deviation of daily demand k: Service level coefficient 5.3. Experimentation Datasets are run with all four models. Since it is assumed that all products are equally important during the allocation of them to system capacity, the sequence of product allocation in terms of capacity is supposed to be random. This randomness makes

88 88 results differ from each other in model 1, since there are 10! sequences and each sequence results in different number of backlog, inventory levels and number of orders. Therefore, 2000 replications are done with model 1, since there is a standard deviation of total cost resulting on each replication. On the other hand, other models (models 2, 3 and 4) have consideration of producing all products by fitting their production order quantities into system capacity. There is also another measure that is considered for comparing models; number of day off. In a day, if there is no production is required and customer demand can be met from on hand inventory, that day is considered as day off. Since models 2, 3 and 4 can increase the order quantity of items, these models can increase the number of day offs which can be considered as saving in worker cost. In this study, the worst, best, and average results of model 1 based on 2000 replications, are compared with the results of models 2, 3 and 4. The result of the total cost is subject to change if different cost parameters are used for backlog, inventory carrying and order cost. First the performances of models are compared considering backlog & number of orders. In the cost sensitivity analysis section, the results are compared using 12 different cost parameter sets. Models 2 and 3 are run by considering 25 different k Q values for all datasets (k Q value is the upper limit that order quantity can be increased mostly). The difference between the application in model 2 and model 3, the products order quantities whose reorder points are violated are subject to increase or decrease, whereas in model 3, first products whose reorder points are violated are produced based on their original order

89 89 quantities and if there is any idle capacity, remaining products order quantities which have no reorder point violation are subject to increase and limited to be mostly k times of original quantity. In model 4, there is a slight difference from model 3. Once the products whose reorder points are violated are allocated, then the remaining products are treated differently. These products are prioritized with respect to the gaps between their reorder points and on hand inventory levels. Then top n of them (n can be 1 to 10) are considered for production External Parameters of Experimentation In this section, external parameters entered on C# execution file are explained. There is no external parameter used in experimentation for model 1. Number of replications is 2000 for all datasets. The number of observations is calculated via equation 10.. Equation 7 Index N: Number of observations required : Mean : Standard deviation k: An acceptable percentage of

90 90 First 100 replications were made. The number of required replications was computed using equation 10 and it turned out to be 519 replications. Since the number of replications made was not sufficient, then 400 additional replications were made. This time 651 replications were needed base on the same equation. As a result 1500 more replications were made and the computations showed that this was sufficient for 99 % of confidence interval and 1 % of error (k). The results are shown in table below. As one can observe, execution time per run was very low and as a result keeping number of replications high was not a concern. Table 14. Number of observations Actual number of replications Required number of Total run time (min) replications In model 2, one external parameter is used, k Q. k Q is an integer to be used to limit the maximum value of order quantity that a production order can be released. For a k of 1 to 25, twenty five replications are done with all datasets. In model 3, the k Qr parameter is used and 25 replications are done for all datasets. This parameter works for two purposes. The first one is the same with the k Q parameter which is used in model-2. Second one is r parameter which stands for reorder point. This parameter is used to prevent unnecessary orders. For example, an order is placed for a product which has 100 items of inventory on hand and a reorder point value of 20. If the

91 91 k value is 4, the r limit is going to be kxr = 4 x 20 = 80 which is below of actual on hand inventory (100). Therefore, even though an order is calculated via the model-3 s approach, since on hand inventory is bigger than 4 times of reorder point, it prevents to release production order of corresponding products. Basically, k Qr is used for preventing overproduction by considering order quantity and on hand inventory. In model 4, there are three external parameters are considered; TF, k Q and k r.tf is the top first function of model which considers top first n number of products to be produced as extra which means after the products which have reorder point violation. The sequence of the products to be used in top first function is decided based on their priorities. Each and every product is equally important before planning, but on a day based on a gap between on hand inventory and reorder point levels, the less gap which product has the higher priority for production. k Q is the same k Q which is used in models 2 and 3. k r is a limit for production to prevent over production of an item. For k r, if on hand inventory level of an item is higher than k times of reorder point (r), this makes production order zero. 10 combinations from 1 to 10 are used for TF. 25 combinations from integer 1 to 25 are used for both k Q and k r parameters. So that 10 * 25 * 25 = 6250 replications are done for all datasets. Numbers of replications done for all models are shown in Table 15.

92 92 Table 15 - Number of replications run for models RUNS PARAMETERS MODEL # of reps MODEL 2 25 k Q (1-25) MODEL 3 25 k Qr (1-25) MODEL TF, k Q, k r (1-10) (1-25) (1-25) 5.4. Results Comparison of Results In this section, the results are presented in two forms i. backlog, inventory held and number of orders ii. total cost that consists of above elements The cost parameters used in total cost calculation are; inventory carrying cost = $1 / unit / day backlog cost = $3 /unit /day order cost. = $100 /order If the set of cost parameters are changed, it may affect minimum cost model and/ or other parameter settings. Therefore, in cost sensitivity analysis section, models performances in terms of total cost are compared. 30 % Customer Demand Load In this load, the variation of customer demand is very low and the backlogging probability is close to zero (0), since the total amount of customer demand can roughly require % 30 the of system capacity. The behavior of dataset based on capacity

93 93 requirement is shown in Figure 25. The average load is minutes and standard deviation of load is 98.7 minutes. The average capacity needed to meet customer demand is around 436 minutes during 640 days of analysis period. The capacity requirements fluctuate between 288 and 576 minutes. The results are shown in Table 16. The black line indicates the system capacity at 1440 minutes level. Capacity Requirements (min) % Demand Load Days Figure 25 - Behavior of Dataset - 30 % Load According to Table 16 in terms of backlog, all models are working perfect since there is no huge customer demand which can make system vulnerable to backlog. The other results are briefly compared in Table 17. In terms of external parameters, models 2 and 3 produced best result for k=2. Model 4 produced best result from 6250 runs, for top 1 st product and k q =3 and k r =2 (1-3-2).

94 94 Table 16 - Results of 30 % customer demand load BACKLOG IVN. HELD # of ORDERS # of DAYOFFS TOTAL COST EXTERNAL PARAMETERS MODEL 1 AVR ,873 3, ,173 - MODEL 1 - BEST - 176,873 3, ,173 - MODEL 1 - WORST - 176,873 3, ,173 - MODEL 2 - BEST - 241,458 1, ,258 k Q = 2 MODEL 3 - BEST - 239,728 2, ,228 k Qr = 2 MODEL 4 - BEST - 279,163 2, ,563 (1-3-2 ) In Table 17, models 2, 3 and 4 are compared to model 1 s best results from 2000 replications. To decrease the number of orders, proposed models increased inventory levels. Among three models, model 2 made a significant difference even though the inventory held increased 37 %, the number of orders is reduced 50 %, production to meet customer demand is done in = 605 days total cost is decreased 19 %. According to Table 17, models 2, 3 and 4 find better solutions than model-1 in terms of total cost. Table 17 - Summary of Results - 30 % Customer Demand Load BACKLOG IVN. HELD # OF ORDERS # OF DAYOFFS TOTAL COST MODEL 1 - BEST MODEL 2 - BEST - 37% -50% 35-19% MODEL 3 - BEST - 36% -21% 41-1% MODEL 4 - BEST - 58% -36% 52-2%

95 95 40 % Customer Demand Load In this dataset, the variation of demand is higher than previous dataset. The basic behavior of dataset is shown in Figure 26. The average load is minutes and standard deviation of load is minutes according to dataset. The amplitude of fluctuation increases in comparison to the previous load. The daily capacity requirement varies between minutes. However, the probability of backlogging is still low since roughly % 40 of system capacity is enough to meet customer demand. The results are shown in Table 18. Capacity Requirements (min) % Demand Load Days Figure 26 - Behavior of Dataset - 40 % Load

96 96 Table 18 - Results of 40 % customer demand load BACKLOG IVN. HELD # of ORDERS # of DAYOFFS TOTAL COST EXTERNAL PARAMETERS MODEL 1 AVR ,019 3, ,397 - MODEL 1 - BEST - 238,042 3, ,342 - MODEL 1 - WORST - 238,447 3, ,747 - MODEL 2 - BEST - 312,149 1, ,349 k Q = 2 MODEL 3 - BEST - 292,426 2, ,926 k Qr = 2 MODEL 4 - BEST - 291,284 2, ,384 (1-2-2 ) Models 2, 3, 4 led to higher inventory levels but managed to lower orders when compared with model-1. According to Table 19, models 2 and 3 increased the total amount of inventory held by 31 % and 23 % in comparison to model 1 s best result. On the other hand, the number of production orders decreased by 48 % when model 2 was used and 19 % when model 3 was used. The best result in terms of total cost is achieved by model 2 with a reduction of 14 %. Table 19 - Summary of Results - 40 % Customer Demand Load BACKLOG IVN. HELD # OF ORDERS # OF DAYOFFS TOTAL COST MODEL 1 - BEST MODEL 2 - BEST - 31% -48% 29-14% MODEL 3 - BEST - 23% -19% 29-1% MODEL 4 - BEST - 22% -19% 24-1% 50 % Customer Demand Load The main behavior of dataset is shown in Figure 27. The average load is minutes and standard deviation of load is minutes. There is no backlog observed in

97 97 50 % customer demand load either. The basic results are shown in Table 20. Except for model 2, the inventory levels held are around 280 thousand units. Similar to the previous datasets, model 2 increased inventory held while it led to reduction in the number of orders as shown in Table % Demand Load Capacity Requirements (min) Days Figure 27 - Behavior of Dataset - 50 % Load Table 20 - Results of 50 % customer demand load BACKLOG IVN. HELD # of ORDERS # of DAYOFFS TOTAL COST EXTERNAL PARAMETERS MODEL 1 AVR ,908 3, ,155 - MODEL 1 - BEST - 282,195 3, ,495 - MODEL 1 - WORST - 286,714 3, ,514 - MODEL 2 - BEST - 368,374 1, ,474 k Q = 2 MODEL 3 - BEST - 285,739 3, ,839 k Qr = 1 MODEL 4 - BEST - 285,739 3, ,839 (1-1-1 )

98 98 As shown in Table 21, model 2 still works better than others. It leads to a reduction in number of orders by 45 % and total cost by 10 %. On the other hand inventory level goes up by 31 %. Moreover, models 3 and 4 work similar to model 1 on the outcomes of inventory held, number of orders and total cost. Table 21 - Summary of Results - 50 % Customer Demand Load BACKLOG IVN. HELD # OF ORDERS # OF DAYOFFS TOTAL COST MODEL 1 - BEST - 282, ,495 MODEL 2 - BEST - 31% -45% 32-10% MODEL 3 - BEST - 1% 0% 2 1% MODEL 4 - BEST - 1% 0% 2 1% 60 % Customer Demand Load The capacity requirements to meet customer demand are roughly % 60 of the system capacity. The capacity requirement versus day chart is shown in Figure 28. The average load is minutes and standard deviation of load is minutes according to dataset. This is the first time, backlog is observed in the results of model 1. Table 22 gives information about results. Model 2 showed a similar performance as previous lower loads. The summary of the results is shown in Table 23.

99 99 60 % Demand Load Capacity Requirements (min) Days Figure 28 - Behavior of Dataset - 60 % Load Table 22 - Results of 60 % customer demand load BACKLOG IVN. HELD # of ORDERS # of DAYOFFS TOTAL COST EXTERNAL PARAMETERS MODEL 1 AVR. (50) 341,137 3, ,315 - MODEL 1 - BEST (13) 337,897 3, ,636 - MODEL 1 - WORST (9) 344,692 3, ,919 - MODEL 2 - BEST - 429,731 1, ,031 k Q = 2 MODEL 3 - BEST - 341,193 3, ,293 k Qr =1 MODEL 4 - BEST - 341,193 3, ,293 (1-1-1 ) According to Table 23, as observed on the 30 %, 40 % and 50 % loads, model 2 reduced the number of orders and the total cost by increasing the inventory held. There is a slight trade of between backlog and inventory held. Model 1 always results in a positive number of backlogs in contrast to other 3 models which give no backlog by increasing inventory held. The inventory held and the number of orders tradeoff is observed in the results of model 2 if compared to the best results of model 1 as given in Table 23.

100 100 Table 23 - Summary of Results 60 % Customer Demand Load BACKLOG IVN. HELD # OF ORDERS # OF DAYOFFS TOTAL COST MODEL 1 - BEST , ,636 MODEL 2 - BEST 0 27% -40% 13-6% MODEL 3 - BEST 0 1% 0% 1 1% MODEL 4 - BEST 0 1% 0% 1 1% 80 % Customer Demand Load To give a basic idea about the behavior of 80 % load, capacity requirements versus day chart is shown in Figure 29. The average load is 1148 minutes and standard deviation of load is minutes. The high variation of customer demand first resulted in thousands of backlogs in results of 80 % customer demand load. According to Table 24, model-1 gave more than 17 thousands of backlogged items on the average of 2000 replications. This shows its vulnerability to backlogging with highly variable customer demand as it was claimed. The summary of results is given in Table 25. Capacity Requirements (min) % Demand Load Figure 29 - Behavior of Dataset - 80 % Load Days

101 101 Table 24 - Results of 80 % Customer Demand Load BACKLOG IVN. HELD # of ORDERS # of DAYOFFS TOTAL COST EXTERNAL PARAMETERS MODEL 1 AVR. (17,316) 408,907 3, ,631 - MODEL 1 - BEST (5,057) 411,198 3, ,069 - MODEL 1 - WORST (44,735) 400,880 3, ,885 - MODEL 2 - BEST (52,827) 328,200 4, ,981 k Q = 2 MODEL 3 - BEST (16) 418,793 3, ,341 k Qr = 1 MODEL 4 - BEST (16) 418,793 3, ,341 (1-1-1 ) According to Table 25, the best result for model 1 gave 5057 backlogged items. Model 2 performs worse than model 1 by increasing backlogged items roughly 9 times. Model 2 decreases the order quantities when required capacity exceeds the system capacity and this increases the number of orders as well. In highly variable demand environment, it s difficult to meet demand on time with small order quantities. Therefore, model 2 performed worst among all models. However, models 3 and 4 allow extra production with respect to the importance of products which is calculated by considering vulnerability to reorder point violation (in other words closeness of on hand inventory to reorder point at a review time). Especially by decreasing the number of backlogged items from 5057 to 16, both of models 3 and 4 performed well enough. To achieve this, they actually did not increase the amount of inventory or the number of orders significantly. Therefore, by doing a reasonable allocation of system capacity, a system can manage better without need for overtime.

102 102 Table 25 - Summary of Results - 80 % Customer Demand Load BACKLOG IVN. HELD # OF ORDERS # OF DAYOFFS TOTAL COST MODEL 1 - BEST MODEL 2 - BEST 945% -20% 32% 1 22% MODEL 3 - BEST % 1.85% 0% % MODEL 4 - BEST % 1.85 % 0% % 90 % Customer Demand Load This dataset has the most fluctuating demand behavior among all. It is shown in Figure 30. The average load is 1295 minutes and standard deviation of load is minutes. The average load is the closest one to the system capacity of 1440 minutes among all datasets and the standard deviation of load is the highest. This high variation of demand and heavy load makes system more vulnerable to backlogging. Models 3 and 4 use idle capacity for allocation of items which are vulnerable to backlog. They also provide solution to insufficient capacity by allocating capacity based on prioritization of items in the order of 1. having negative inventory value (already backlogged) 2. the amount of reorder point violation

103 103 90% Demand Load Capacity Rquirements (min) Days Figure 30 - Behavior of Dataset - 90 % Load It is shown in Table 26 that, the results of all models run by using 90 % load dataset. Model 2 has the worst results in terms of the amount of backlogged items, inventory held and orders. Therefore, the total cost of model 2 is 5 times worse than the average of model 1. Model 2 has the feature of decreasing the order quantities when system capacity is not sufficient to meet demand. Since this approach increases the number of orders and tries to meet highly variable demand by decreasing order quantities, backlogged items cannot recover from negative inventory throughout the time period of 640 days. In backlog results, since the total amount of backlogged items are considered, the backlog result comes out over 5 million since the system is locked by continuous heavy demand. Table 27 gives summarized analysis on results.

104 104 Table 26 - Results of 90 % Customer Demand Load BACKLOG IVN. HELD # of ORDERS # of DAYOFFS TOTAL COST EXTERNAL PARAMETERS MODEL 1 AVR. (801,510) 314,412 3,407-3,059,659 - MODEL 1 - BEST (488,123) 325,799 3,427-2,132,868 - MODEL 1 - WORST (1,115,550) 303,015 3,414-3,991,065 - MODEL 2 - BEST (5,039,613) 25,922 6,284-15,773,161 k Q = 1 MODEL 3 - BEST (229,978) 183,994 3,465-1,220,428 k Qr = 6 MODEL 4 - BEST (169,759) 248,157 3, ,090,034 (1-6-2 ) According to Table 27, both models 3 and 4 perform better than models 1 and 2. The amount of backlogged items is decreased 53 % by model-3 and 65 % by model 4. The main difference of models 3 and 4 from first two models is briefly their prioritization approach to products which are more vulnerable to backlogging throughout the planning horizon. Model 4 performed the best among all models with parameters as TF =1, k Q =6 and k r =2. The explanations of these parameters are, TF =1 stands for allowing 1 additional production of an extra product which has the highest priority for the allocation of idle capacity, k Q = 6 stands for maximum order quantity of (6 * Q) that can be given for additional products. k r =2 is used to prevent release of a production order for a product if it s on hand inventory level is higher than a level of (2 * reorder point)

105 105 Table 27 - Summary of Results - 90 % Customer Demand Load BACKLOG IVN. HELD # OF ORDERS # OF DAYOFFS TOTAL COST MODEL 1 - BEST -488, , ,132,868 MODEL 2 - BEST 932% -92% 83% 0 640% MODEL 3 - BEST -53% -44% 1% 0-43% MODEL 4 - BEST -65% -24% -3% 2-49% As a result, model 4 made a significant reduction in Backlog by 65 % Inventory held by 24 % Total cost by 49 % Summary of Results As it can be seen from the graphs of customer demand loads and variation charts, for loads 30 %, 40 %, and 50 % of system capacity, all models work fine in terms of backlog, since probability of backlogging is lower. Therefore, models performances are compared according to the tradeoff between the amount of inventory held and the number of orders released to production system for these three datasets. Model-2 works better than other models in terms of reducing the number of orders. The amount of inventory held is increased to reduce the number of orders as well. However, according to the total cost results, since model-2 reduced the total cost as well (even though there increase in inventory held), model-2 is a better approach for lower loads which has no risk of backlogging.

106 106 In 60 % load, model-2 achieved to manage the system with the least total cost. It worked similar to previous loads by reducing the number of orders. Despite the 27% increase in inventory held, 40 % reduction is made on the number of orders and it resulted in 6% decrease in total cost. Models 3 and 4 worked similar to model-1 with 1% increase on total cost. After 60 % load, especially in 80 % and 90 % demand loads, backlogging started to happen and models 1 and 2 suffered from backlogging cost the most. This backlogging is the result of increase in variation of customer demand. Model 1 and 2 are not good enough to deal with insufficient capacity situations. The reason is that, model-1 randomly picks up products and allocates capacity with product(s) which have reorder point violation as long as the system capacity allows. Then, production order releases stop, when capacity limit is reached. Hence, for insufficient capacity situations, in model-1, some products cannot be produced because of lack of capacity. On the other hand, model-2, tries to produce every product which has reorder point violation in both cases (insufficient capacity or idle capacity). Especially for insufficient capacity situation, it decreases production order quantities not to exceed the system capacity. This is not a good enough solution while having highly variable customer demand on a continuous basis. As a result, model-2 works the worst with 80 % and 90 % loads because of this weakness. Models 3 and 4 s advantage comes out during the highly variable customer demand environment. Because, they both consider production of products which has vulnerability to backlogging if there is idle capacity. If an insufficient capacity situation occurs, they both give products priorities with respect to inventory status reorder point relation (see explanation of model-4, section 6.4). In Table 28, the summary of results are

107 shown. For each dataset, model-1 s best result and the model which has the best result in terms of cost for the corresponding load is shown in Table Table 28 - Summary of Results LOAD MODEL BACKLOG IVN. HELD # OF ORDERS # OF DAYOFFS TOTAL COST 90 % MODEL 1 - BEST -488, ,799 3, ,132,868 Best of 90 % MODEL 4 - BEST -65% -24% -3% 2-49% 80 % MODEL 1 - BEST Best of 80 % M.3 & 4 - BEST % 1.85 % 0% % 60 % MODEL 1 - BEST Best of 60 % MODEL 2 - BEST - 27% -40% 13-6% 50 % MODEL 1 - BEST Best of 50 % MODEL 2 - BEST - 31% -45% 32-10% 40 % MODEL 1 - BEST Best of 40 % MODEL 2 - BEST - 31% -48% 29-14% 30 % MODEL 1 - BEST Best of 30 % MODEL 2 - BEST - 37% -50% 35-19% 5.5. Cost Sensitivity Analysis As explained in problem definition, the total cost of inventory planning and production control system is used as the main comparison tool. All models were run with six different customer demand load datasets which are based on variability of demand. However, the total cost function includes three cost parameters which are inventory carrying, backlogging, and ordering cost and the result can change if these parameters are changed. To see how models results are sensitive to backlog and ordering cost and to

108 108 observe the effect of tradeoff between the amount of backlogged items and number of production orders, cost sensitivity analysis is done by using different cost parameters. The cost parameters used in the analysis are shown in Table 29. For observing sensitivity of a parameter, the other ones are assumed as constant. For the sensitivity analysis of backlog cost, an order cost of $100 and an inventory carrying cost of $1 are used. For the sensitivity analysis of order cost, a fixed $3 backlog cost and an inventory carrying cost of $1 are used. Table 29 - Cost Parameters of Sensitivity Analysis CASES FIXED COST OBSERVATION ORDER COST ($) BACKLOG COST ($) 1) ) ) ) ) ) BACKLOG COST ($) ORDER COST ($) 7) 3 0 8) ) ) ) ) Sensitivity of Backlog Cost For 30 %, 40 % and 50 % customer demand loads, models did not produce any backlog and therefore the results were unaffected from varying backlog cost.

109 % Customer Demand Load The results are shown in Table 30. In this load, only model 1 produced backlog which is 48 items from the best result of model 1. Since all other models gave zero (o) backlogged items, they are insensitive to different backlogging costs. Model 2 has the best results in terms of any backlogging cost as seen in Figure 31. Table 30 - Cost Sensitivity of Backlog Analysis Results 60 % Load Backlog Cost M1 - BEST 657, , , , , ,247 2 M2 - BEST 620, , , , , ,031 3 M3 - BEST 661, , , , , ,293 4 M4 - BEST 661, , , , , , % Load - Sensitivity of Backlog Cost with a Fixed Order Cost of $100 $670,000 $660,000 Total Cost $650,000 $640,000 $630,000 $620,000 $610,000 $600, M1-BEST M2 M3 M4 Backlog Cost Figure 31 - Sensitivity Analysis of Backlog Cost - 60 % Load

110 % Customer Demand Load In this demand load, models 1 and 4 produced backlog which are 5057 and 16. Models 2 and 3 gave zero (0) backlogged items. As seen on graph (Figure 32), model 1 is the only sensitive model to backlog cost. In view of the fact that other models either have low (16) backlogged items, they are insensitive to the backlog cost since they managed inventory planning and production control system more efficiently than model 1. In conclusion, models 3 and 4 is the best model in terms of having least total cost and being insensitive to increase in the backlogging cost. Table 31 gives run results for all models. Table 31 - Cost Sensitivity of Backlog Analysis Results 80 % Load Backlog Cost M1 - BEST 730, , , , , ,748 2 M2 - BEST 766, ,981 1,083,462 1,400,424 2,087,175 3,407,850 3 M3 - BEST 751, , , , , ,093 4 M4 - BEST 751, , , , , ,093

111 % Load - Sensitivity of Backlog Cost with a Fixed Order Cost of $100 $1,900,000 $1,700,000 Total Cost $1,500,000 $1,300,000 $1,100,000 $900,000 $700, M1-BEST M2 M3 M4 Backlog Cost Figure 32 - Sensitivity Analysis of Backlog Cost - 80 % Load 90 % Customer Demand Load The sensitivity of backlog cost is observed on 90 % customer demand load with 6 different backlog cost parameters as $0, $3, $6, $12, $25, and $50. The total cost results are shown in Table 32. The amount of backlogged items for models 1, 2, 3 and 4 are sequentially as Model-1 Best: 488,123; Model 2: 5,039,613; Model 3: 229,978; Model 4: Model 4 reflected the least sensitivity to increasing backlog cost since it has the lowest backlogged items with 90 %. The costs over $50 million are not shown in graph to show the sensitivity of models 1,3 and 4 better, since model 2 led to very high numbers of costs (Figure 33).

112 112 Table 32 - Cost Sensitivity of Backlog Analysis Results 90 % Load Backlog Cost M1 - BEST 621,441 2,132,868 3,597,237 6,525,975 12,871,574 25,074,649 2 M2 - BEST 654,322 15,773,161 30,892,000 61,129, ,644, ,634,972 3 M3 - BEST 524,851 1,220,428 1,910,362 3,290,230 6,279,944 12,029,394 4 M4 - BEST 519,177 1,090,034 1,599,311 2,617,865 4,824,732 9,068, % Load - Sensitivity of Backlog Cost with a Fixed Order Cost of $100 $60,000,000 $50,000,000 Total Cost $40,000,000 $30,000,000 $20,000,000 $10,000,000 M1-BEST M2 M3 M4 $ Backlog Cost Figure 33 - Sensitivity Analysis of Backlog Cost - 90 % Load

113 Sensitivity of Order Cost 30 % Customer Demand Load In this load, all models are sensitive to increase in order cost. However, according to Table 33, model-2 has the least sensitivity to change in order cost. Graphical illustration is shown in figure as well (Figure 34). Table 33 - Cost Sensitivity of Order Analysis Results 30 % Load Order Cost M1 - BEST 176, , , , ,623 1,748,373 2 M2 - BEST 176, , , , , ,739 3 M3 - BEST 182, , , , ,356 1,255,582 4 M4 - BEST 182, , , , ,806 1,000, % Load - Sensitivity of Order Cost with a Fixed Backlog Cost of $3 Total Cost $1,800,000 $1,600,000 $1,400,000 $1,200,000 $1,000,000 $800,000 $600,000 $400,000 $200,000 $ Order Cost M1-BEST M2 M3 M4 Figure 34 - Sensitivity of Order Cost 30 % Load

114 % Customer Demand Load According to Table 34, all models are sensitive to varying order cost. Since model-2 provided the least number of orders, it has the least sensitivity to change in the order cost. In Figure 35, numerical results are illustrated. The order of sensitivity from the least to most is model-2, model-4, model-3, and model-1. Table 34 - Cost Sensitivity of Order Analysis Results 40 % Load Order Cost M1- BEST 237, , , ,342 1,031,292 1,824,542 2 M2 - BEST 230, , , , , ,230 3 M3 - BEST 237, , , , ,981 1,407,981 4 M4 - BEST 237, , , , ,329 1,127, % Load - Sensitivity of Order Cost with a Fixed Backlog Cost of $3 Total Cost $2,000,000 $1,800,000 $1,600,000 $1,400,000 $1,200,000 $1,000,000 $800,000 $600,000 $400,000 $200,000 $ Order Cost M1-BEST M2 M3 M4 Figure 35 - Sensitivity of Order Cost 40 % Load

115 % Customer Demand Load In 50 % demand load, the results (Table 35) are parallel to first two datasets. Model 2 is the least sensitive model among four models. The order of sensitivity from the least to the most is model-2, model-4, model-3, and model-1. The sensitivity analysis is illustrated in Figure 36. Table 35 - Cost Sensitivity of Order Analysis Results 50 % Load Order Cost M1-BEST 282, , , ,495 1,090,310 1,898,060 2 M2 - BEST 278, , , , ,813 1,029,799 3 M3 - BEST 285, , , ,839 1,001,807 1,620,307 4 M4 - BEST 285, , , , ,494 1,287, % Load - Sensitivity of Order Cost with a Fixed Backlog Cost of $3 Total Cost $2,000,000 $1,800,000 $1,600,000 $1,400,000 $1,200,000 $1,000,000 $800,000 $600,000 $400,000 $200,000 $ Order Cost M1-BEST M2 M3 M4 Figure 36 - Sensitivity of Order Cost 50 % Load

116 % Customer Demand Load Model 2 is the least sensitive model among four models (Table 36). Model-4, model-3, and model-1 follow model-2. Figure 37 shows the sensitivity of models base on increasing order costs. Table 36 - Cost Sensitivity of Order Analysis Results 60 % Load Order Cost M1-BEST 337, , , ,636 1,137,166 1,935,105 2 M2 - BEST 330, , , , ,691 1,161,624 3 M3 - BEST 341, , , ,293 1,072,416 1,724,416 4 M4 - BEST 341, , , ,293 1,009,172 1,417, % Load - Sensitivity of Order Cost with a Fixed Backlog Cost of $3 $2,500,000 $2,000,000 Total Cost $1,500,000 $1,000,000 $500,000 M1-BEST M2 M3 M4 $ Order Cost Figure 37 - Sensitivity of Order Cost 60 % Load

117 % Customer Demand Load The sensitivity results are shown in Table 37. According to table, the least sensitive model differs with respect to backlog cost. Therefore, a detailed backlog cost table is prepared and shown in Table 38. Table 37 - Cost Sensitivity of Order Analysis Results 80 % Load Order Cost M1- BEST 426, , , ,069 1,255,619 2,084,869 2 M2 - BEST 402, , , ,981 1,133,546 1,607,296 3 M3 - BEST 418, , , ,341 1,234,893 2,017,672 4 M4 - BEST 418, , , ,341 1,198,330 1,732,793 According to Table 38, between $0-$8 of backorder costs, model-2 is the least sensitive. Then, $9-$196 of backlog cost, model-3 and 4 are the least sensitive models. Between $197 and $500, model-2 is the least sensitive once again. The trend is shown in Figure 38. The results in Table 38 are illustrated in Figure 39. Table 38 - Cost Sensitivity Analysis Results 80 % Load Order Cost ($0 $8) ($9 $134) ($135 $196) ($197 $499) $500 1 M1 - BEST 426, , ,164 1,079,818 2,084,869 2 M2 - BEST 402, ,647 1,078,386 1,033,111 1,607,296 3 M3 - BEST 418, , ,716 1,067,943 2,017,672 4 M4 - BEST 418, , ,571 1,059,376 1,732,793 MIN 402, , ,571 1,033,111 1,607,296 THE BEST MODEL M2 M3 & M4 M3 & M4 M2 M2

118 118 1,800,000 1,600,000 1,400,000 1,200,000 1,000, , , , ,000 - Detailed Sensitivity Analysis - 80 % Load with Fixed Backlog Cost of $3 $0 - M2, 402,298 $9 - M3, 448,766 $135 - M4, 867,571 $197 - M2, 1,033,111 Figure 38 - Detailed Sens. Analysis - 80 % Load with Fixed Backlog Cost of $3 $500 - M2, 1,607,296 $0 - M2 $9 - M3 $135 - M4 $197 - M2 $500 - M2 $2,200,000 $2,000,000 $1,800,000 $1,600, % Load - Sensitivity of Order Cost with a Fixed Backlog Cost of $3 Total Cost $1,400,000 $1,200,000 $1,000,000 $800,000 $600,000 M1-BEST M2 M3 M4 $400, Order Cost Figure 39 - Sensitivity of Order Cost 80 % Load

119 % Customer Demand Load According to Table 39, model-4 is the least sensitive to order cost variability. The order from the least to the most sensitive is model-4, model-3, model-1 and model-2. As shown in table below, model-2 is significantly worse than other models. The illustration of results is shown in Figure 40. Table 39 - Cost Sensitivity of Order Analysis Results 90 % Load Order Cost M1-BEST 1,790,168 1,858,708 1,961,518 2,132,868 2,646,918 3,503,668 2 M2 - BEST 15,144,761 15,270,441 15,458,961 15,773,161 16,715,761 18,286,761 3 M3 - BEST 873, ,228 1,047,178 1,220,428 1,740,178 2,606,428 4 M4 - BEST 757, , ,734 1,090,034 1,588,934 2,420, % Load - Sensitivity of Order Cost with a Fixed Backlog Cost of $3 Total Cost $20,000,000 $18,000,000 $16,000,000 $14,000,000 $12,000,000 $10,000,000 $8,000,000 $6,000,000 $4,000,000 $2,000,000 $ Order Cost M1-BEST M2 M3 M4 Figure 40 - Sensitivity of Order Cost 90 % Load

120 Day off Affect During the experimentation, it was observed that models 2, 3 and 4 produced day offs in comparison to model-1 which works all the 640 days. Day off stands for a day in which no production is required and all of customer demand can be met from inventory in other words there is no reorder point violation observed. Model-1 always works all 640 days and never gave a day off. Therefore, a comparison of models in terms of total cost under the impact of day off is considered as necessary. Then the issue is that how to compare models in terms of number of day off related total cost in other words how to relate day off to the total cost. A simple equation is developed. Since there is a manufacturing line which produces the predefined products, the regular daily labor cost is considered and extended to 640 days. Daily labor cost is assumed as $875 and it amounts to $560,000 if 640 days are considered. Hence, basically a daily cost of $875 is cut from total cost for 1 day off. Following tables shows the results for six demand datasets with respect to number of day off impact. The total cost values are calculated by using cost parameters as $3 of backlog cost $1 of inventory carrying cost $100 of order cost. 30 % Customer Demand Load According to Table 40, models 2, 3 and 4 produced positive number of day offs. Each total cost result is the best result which is pulled from the replication set of the

121 121 corresponding model. Model 3 has the biggest day off value which is 254. Despite this result, since 356,582 items are held as inventory and 1798 orders are released, the total cost is decreased to 289,337. Model-2 is the best among all models, since 698 orders with 193 days off are achieved. Table 40 - Day off Analysis Results 30 % Load Order Cost BACKLOG ON HAND # OF ORDERS # OF DAYOFFS SAVING TOTAL COST 1 M1 - BEST - 176,873 3, ,173 2 M2 - BEST - 410, , ,383 3 M3 - BEST - 356,582 1, , ,103 4 M4 - BEST - 346,787 1, , , % Customer Demand Load In this load, the behaviors of models are similar to the previous load. The order of models according to cost is model 2, 4, 3 and 1. Model 1 is the worst in terms of number of orders, day off and total cost. The results are shown in Table 41 Table 41 - Day off Analysis Results 40 % Load Order Cost BACKLOG ON HAND # OF ORDERS # OF DAYOFFS SAVING TOTAL COST 1 M1 - BEST - 238,042 3, ,342 2 M2 - BEST - 448, , ,099 3 M3 - BEST - 351,981 2, , ,176 4 M4 - BEST - 464,293 1, , ,868

122 % Customer Demand Load According to Table, the maximum number of day off is 188 days which is reached by model-4. However, model-3 has a better result in terms of cost, because of having less amount of inventory held. Model-1 has the worst results among them. Table 42 - Day off Analysis Results 50 % Load Order Cost BACKLOG ON HAND # OF ORDERS # OF DAYOFFS SAVING TOTAL COST 1 M1 - BEST - 282,195 3, ,495 2 M2 - BEST - 368,374 1, , ,474 3 M3 - BEST - 417,867 2, , ,964 4 M4 - BEST - 505,761 1, , , % Customer Demand Load The results are shown in Table 43. Model-2 has the best total cost result because of having the least number of orders. The biggest number of day off is 116, reached by model-4. Model-2 is the worst among them in terms of number of orders and total cost. Table 43 - Day off Analysis Results 60 % Load Order Cost BACKLOG ON HAND # OF ORDERS # OF DAYOFFS SAVING TOTAL COST 1 M1 - BEST (13) 337,897 3, ,636 2 M2 - BEST - 429,731 1, , ,656 3 M3 - BEST - 381,811 2, , ,043 4 M4 - BEST - 536,116 1, , ,216

123 % Customer Demand Load In this load, only one model, model-2, resulted in with positive number of day off. However, the saving of day off is not sufficient to reduce total cost according to Table 44. Both of models 3 and 4 have the best results in terms of total cost. Table 44 - Day off Analysis Results 80 % Load Order Cost BACKLOG ON HAND # OF ORDERS # OF DAYOFFS SAVING TOTAL COST 1 M1 - BEST (5,057) 411,198 3, ,069 2 M2 - BEST (52,827) 328,200 4, ,106 3 M3 - BEST (16) 418,793 3, ,341 4 M4 - BEST (16) 418,793 3, , % Customer Demand Load According to Table 45, only model-4 resulted in with positive number of day off. However, 2 days off does have not important impact on total cost. Model-4 is the best model among all models in terms of having the least number of orders and total cost. Table 45 - Day off Analysis Results 90 % Load Order Cost BACKLOG ON HAND # OF ORDERS # OF DAYOFFS SAVING TOTAL COST 1 M1 - BEST (488,123) 325,799 3, ,132,868 2 M2 - BEST (5,039,613) 25,922 6, ,773,161 3 M3 - BEST (229,978) 183,994 3, ,220,428 4 M4 - BEST (169,759) 248,157 3, ,750 1,088,284 Summary of Day off Analysis According to results, models which produced positive number of day off worked better than model-1 which works 640 days and produces no day off. Table 46 gives brief

124 124 summary of results as one table. According to table, day off impact is observed significantly on lower loads such as 30 %, 40 %, 50 %. The amount of savings are important which are $ for 30 % load, $103, 250 for 40 % load, $154, 875 for 50 % load. If the system hires workers on a contract basis, these amounts become important savings. Other possibility is that those workers can be also used at other work stations which can increase the efficiency and productivity as well. Table 46 - Day off Effect on Total Cost % Order Cost BACKLOG ON HAND # OF ORDERS # OF DAYOFFS SAVING TOTAL COST 30 M1-BEST - 176,873 3, , M2 - BEST - 410, , , M1-BEST - 238,042 3, , M2 - BEST - 448, , , M1-BEST - 282,195 3, , M3 - BEST - 417,867 2, , , M1-BEST (13) 337,897 3, , M2 - BEST - 429,731 1, , , M1-BEST (5,057) 411,198 3, , M3 - BEST (16) 418,793 3, , M4 - BEST (16) 418,793 3, , M1-BEST (488,123) 325,799 3, ,132, M4 - BEST (169,759) 248,157 3, ,750 1,088,284

125 125 CHAPTER 6: CONCLUSION A consumption-driven finite capacity multi-item inventory planning and production control problem is studied and four models are proposed. Customer demand is considered as the only trigger for manufacturing and no forecasted demand data is used. From these perspectives, the proposed approach has similarity with kanban system. However, including dynamic reorder point and dynamic order quantity features differentiates the proposed approach from the kanban system. The base model (model-1) is built according to classic (s, Q) inventory policy. Model-1 is basically used as a benchmark in this study. Other three proposed approaches are compared with model-1. According to the results, depending on the load, the best model varied among models 2, 3 and 4. Indeed, model 1 has never performed the best among all demand loads. In 90 % of demand load, model-4, in 80 % of demand load, both model-3 and model-4, and in 60 %, 50 %, 40 % and 30 % of demand loads model-2 performed the best. It was claimed that if the variability of demand is high, classic (s, Q) policy (model 1) is not able to provide an efficient solution. In 90 % of demand load, certain number of backlogged items is observed in the results of model-1. Model-4 performed the best in terms of decreasing backordered units (65 % reduction). In 80 % of demand load, models 3 and 4 performed the best. Especially, total backordered items are decreased by % while inventory levels and number of orders increased less than 2 % compared to model-1.

126 126 In lower customer demand loads as 30 %, 40 %, 50 %, 60 %, model-2 performs the best. Model-2 s difference from models 3 and 4 is that, it only modifies (increase or decrease) the order quantities of items which have reorder point violation. No other products are considered for production in this model. As a result, it works well for loads up to 60 % of capacity by keeping fewer inventories. If current economic circumstances are considered, especially manufacturing firms are started suffering from varying demand since consuming behavior is affected from global economic crisis. Manufacturing decisions are becoming critical and forecasted data may not be helpful in terms of giving an idea about tomorrow. Therefore, consumption driven production is less risky than make-to-stock in terms of inventory levels. On the other hand, the probability of backlog is increased by switching to consumption driven production if there is high variation in demand. The proposed approach gives an opportunity to deal with high variation of demand by considering reorder point and current on hand inventory relationships. It allocates idle capacity by releasing production orders of the products which are more vulnerable to be backlogged. The number of extra orders can also be limited. In contrast to MRP, planner can see the products vulnerability by this approach and system can adjust changes faster, since production is driven by actual demand instead of forecasted-demand. There is a fixed cost of manufacturing system to run and firms cannot survive without manufacturing even in bad economic conditions. Therefore what to manufacture, how many to manufacture? and when to manufacture questions are still valid and may be even more important. Instead of producing just based on forecasted demand and/or actual demand,

127 127 the proposed approach produces first actual need and then checks the inventory of items which has vulnerability to have backlog or reorder point violation and responds quickly by manufacturing those items in advance with anticipation of future consumption if capacity is available. As a future work, genetic algorithms for optimization of parameters such as k Q, kr, TF, order quantity and reorder point and determination of product sequence can be used as alternative solution tool. More modifications to models in terms of ordering quantity, timing of orders and over time option can also be considered as future study.

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