Material Requirements Planning MRP ENM308 Planning and Control I Spring 2013 Haluk Yapıcıoğlu, PhD Hierarchy of Decisions Forecast of Demand Aggregate Planning Master Schedule Inventory Control Operations Scheduling Vehicle Routing 1
Hierarchy of Decisions Forecasting: First, a firm must forecast demand for aggregate sales over the planning horizon. Aggregate planning: The forecasts provide inputs for determining aggregate production and workforce levels over the planning horizon. Master production schedule (MPS): Recall, that the aggregate production plan does not consider any real product but a fictitious aggregate product. The MPS translates the aggregate plan output in terms of specific production goals by product and time period. Hierarchy of Decisions Suppose that a firm produces three types of chairs: ladderback chair, kitchen chair and desk chair. The aggregate production considers a fictitious aggregate unit of chair and find that the firm should produce 550 units of chairs in April. The MPS then translates this output in terms of three product types and four work weeks in April. The MPS suggests that the firm produce 200 units of desk chairs in Week 1, 150 units of ladder back chair in Week 2, and 200 units of kitchen chairs in Week 3. Material Requirements Planning (MRP): A product is manufactured from some components or subassemblies. For example a chair may require two back legs, two front legs, 4 leg supports, etc. 2
Hierarchy of Decisions Master Schedule April May Ladder back chair 1 2 150 3 4 5 6 7 8 150 Kitchen chair 200 120 120 Desk chair 200 200 200 Aggregate production plan for chair family 550 790 Hierarchy of Decisions While forecasting, aggregate plan and MPS consider the volume of finished products, MRP plans for the components, and subassemblies. A firm may obtain the components by in house production or purchasing. MRP prepares a plan of in house production or purchasing requirements of components and subassemblies. Scheduling: Scheduling allocates resource over times in order to produce the products. The resources include workers, machines and tools. Vehicle Routing: After the products are produced, the firm may deliver the products to some other manufacturers, or warehouses. The vehicle routing allocates vehicles and prepares a route for each vehicle. 3
Hierarchy of Decisions: Materials Requirement Planning Back slats Seat cushion Leg supports Seat frame boards Back legs Front legs Material Requirements Planning The demands for the finished goods are obtained from forecasting. These demands are called independent demand. The demands for the components or subassemblies depend on those for the finished goods. These demands are called dependent demand. Material Requirements Planning (MRP) is used for dependent demand and for both assembly and manufacturing If the finished product is composed of many components, MRP can be used to optimize the inventory costs. 4
Importance of an MRP System Inventory without an MRP System Inventory with an MRP System Importance of an MRP System Without an MRP system: Component is ordered at time A, when the inventory level of the component hits reorder point, R So, the component is received at time B. However, the component is actually needed at time C, not B. So, the inventory holding cost incurred between time B and C is a wastage. With an MRP system: We shall see that given the production schedule of the finished goods and some other information, it is possible to predict the exact time, C when the component will be required. Order is placed carefully so that it is received at time C. 5
MRP Inputs: MRP Input and Output Master Schedule (MPS): The MPS of the finished product provides information on the net requirement of the finished product over time. Inventory file: For each item, the number of units on hand is obtained from the inventory file. MRP Input and Output MRP Inputs: Bill of Materials: For each component, the bill of materials provides information on the number of units required, source of the component (purchase/ manufacture), etc. There are two forms of the bill of materials: Product Structure Tree: The finished product is shown at the top, at level 0. The components assembled to produce the finished product is shown at level 1 or below. The sub components used to produce the components at level 1 is shown at level 2 or below, and so on. The number in the parentheses shows the requirement of the item. For example, G(4) implies that 4 units of G is required to produce 1 unit of B. For each item, the name, number, source, and lead time of every component required is shown on the bill of materials in a tabular form. 6
MRP Output: MRP Input and Output Every required item is either produced or purchased. So, the report is sent to production or purchasing. MRP Input and Output Orders Master Schedule Forecasts Bill of Materials file MRP computer program Inventory file To Reports To Purchasing 7
Bill of Materials: Product Structure Tree Level 0 Level 1 Level 2 Level 3 Bill of Materials BILL OF MATERIALS Product Description: Ladder back chair Item: A Component Quantity Source Item Description Required B Ladder back 1 Manufacturing C Front legs 2 Purchase D Leg supports 4 Purchase E Seat 1 Manufacturing 8
Bill of Materials BILL OF MATERIALS Product Description: Seat Item: E Component Quantity Source Item Description Required H Seat frame 1 Manufacturing I Seat cushion 1 Purchase On Hand Inventory and Lead time Component Units in Lead Time (weeks) Inventory Seat aubassembly 25 2 Seat Frame 50 3 Seat Frame Boards 75 1 9
MRP Calculation Suppose that 150 units of ladder back chair is required. The previous slide shows a product structure tree with seat subassembly, seat frames, and seat frame boards. For each of the above components, the previous slide also shows the number of units on hand. The net requirement is computed from top to bottom. Since 150 units of ladder back chair is required, and since 1 unit of seat subassembly is required for each unit of ladderback chair, the gross requirement of seat subassembly is 150x1 =150 units. Since there are 25 units of seatsubassembly in the inventory, the net requirement of the seat subassembly is 150 25 = 125 units. MRP Calculation Since 1 unit of seat frames is required for each unit of seat subassembly, the gross requirement of the seat frames is 125 1 = 125 units. (Note that although it follows from the product structure tree that 1 unit of seat frames is required for each unit of ladder back chair, the gross requirement of seat frames is not 150 units because each of the 25 units of seat subassembly also contains 1 unit of seat frames.) Since there are 50 units of seat frames in the inventory, the net requirement of the seat frames is 125 50 = 75 units. The detail computation is shown in the next two slides. A similar logic is used to compute the time of order placement. 10
MRP Calculation Units Quantity of ladder back chairs to be produced 150 Gross requirement, seat subassembly Less seat subassembly in inventory 25 Net requirement, seat subassembly Gross requirement, seat frames Less seat frames in inventory 50 Net requirement, seat frames Gross requirement, seat frame boards Less seat frame boards in inventory 75 Net requirement, seat frame boards Assume that 150 units of ladder back chairs are to be produced at the end of week 15 MRP Calculation Units Quantity of ladder back chairs to be produced 150 Gross requirement, seat subassembly 150 Less seat subassembly in inventory 25 Net requirement, seat subassembly 125 Gross requirement, seat frames 125 Less seat frames in inventory 50 Net requirement, seat frames 75 Gross requirement, seat frame boards 300 Less seat frame boards in inventory 75 Net requirement, seat frame boards 225 Assume that 150 units of ladder back chairs are to be produced at the end of week 15 11
MRP Calculation: Time of Order Placement Week Complete order for seat subassembly 14 Minus lead time for seat subassembly 2 Place an order for seat subassembly Complete order for seat frames Minus lead time for seat frames 3 Place an order for seat frames Complete order for seat frame boards Minus lead time for seat frame boards 1 Place an order for seat frame boards Assume that 150 units of ladder back chairs are to be produced at the end of week 15 and that there is a one week lead time for ladder back chair assembly MRP Calculation: Time of Order Placement Week Complete order for seat subassembly 14 Minus lead time for seat subassembly 2 Place an order for seat subassembly 12 Complete order for seat frames 12 Minus lead time for seat frames 3 Place an order for seat frames 9 Complete order for seat frame boards 9 Minus lead time for seat frame boards 1 Place an order for seat frame boards 8 Assume that 150 units of ladder back chairs are to be produced at the end of week 15 and that there is a one week lead time for ladder back chair assembly 12
MRP Calculation: Some Definitions Scheduled Receipts: Items ordered prior to the current planning period and/or Items returned from the customer Lot for lot (L4L) Order quantity equals the net requirement Sometimes, lot for lot policy cannot be used. There may be restrictions on minimum order quantity or order quantity may be required to multiples of 50, 100 etc. MRP Calculation Example 1: Each unit of A is composed of one unit of B, two units of C, and one unit of D. C is composed of two units of D and three units of E. Items A, C, D, and E have on hand inventories of 20, 10, 20, and 10 units, respectively. Item B has a scheduled receipt of 10 units in period 1, and C has a scheduled receipt of 50 units in Period 1. Lot for lot (L4L) is used for Items A and B. Item C requires a minimum lot size of 50 units. D and E are required to be purchased in multiples of 100 and 50, respectively. Lead times are one period for Items A, B, and C, and two periods for Items D and E. The gross requirements for A are 30 in Period 2, 30 in Period 5, and 40 in Period 8. Find the planned order releases for all items. 13
MRP Calculation Level 0 Level 1 Level 2 MRP Calculation Item A LT= Q= Period 1 2 3 4 5 6 7 8 9 10 Gross Requirements Scheduled receipts On hand from prior period Net requirements Time phased Net Requirements Planned order releases Planned order delivery 14
Period 1 2 3 4 5 6 7 8 9 10 Item Gross Requirements 30 30 40 A Scheduled receipts LT= 1 wk On hand from prior period 20 Q= L4L Net requirements Time phased Net Requirements Planned order releases Planned order delivery MRP Calculation All the information above are given. MRP Calculation Period 1 2 3 4 5 6 7 8 9 10 Item Gross Requirements 30 30 40 A LT= 1 wk Scheduled receipts On hand from prior period 20 20 Net requirements Q= L4L Time phased Net Requirements Planned order releases Planned order delivery 20 units are just transferred from Period 1 to 2. 15
MRP Calculation Period 1 2 3 4 5 6 7 8 9 10 Item Gross Requirements 30 30 40 A LT= 1 wk Scheduled receipts On hand from prior period 20 20 Net requirements 10 Time phased Net Q= L4L Requirements 10 Planned order releases 10 Planned order delivery 10 The net requirement of 30 20=10 units must be ordered in week 1. MRP Calculation Period 1 2 3 4 5 6 7 8 9 10 Item Gross Requirements 30 30 40 A Scheduled receipts LT= 1 wk On hand from prior period 20 20 0 0 0 Net requirements 10 Time phased Net Q= L4L Requirements 10 Planned order releases 10 Planned order delivery 10 The net requirement of 30 20=10 units must be ordered in week 1. 16
MRP Calculation Period 1 2 3 4 5 6 7 8 9 10 Item Gross Requirements 30 30 40 A Scheduled receipts LT= 1 wk On hand from prior period 20 20 0 0 0 Net requirements 10 30 Time phased Net Q= L4L Requirements 10 30 Planned order releases 10 30 Planned order delivery 10 30 The net requirement of 30 00 = 30 units must be ordered in week 4. MRP Calculation Period 1 2 3 4 5 6 7 8 9 10 Item Gross Requirements 30 30 40 A LT= 1 wk Scheduled receipts On hand from prior period 20 20 0 0 0 0 0 0 0 0 Net requirements 10 30 40 Time phased Net Q= L4L Requirements 10 30 40 Planned order releases 10 30 40 Planned order delivery 10 30 40 The net requirement of 40 0 = 40 units must be ordered in week 7. 17
Item B MRP Calculation Period 1 2 3 4 5 6 7 8 9 10 Gross Requirements 10 30 40 Scheduled receipts 10 LT= 1 wk On hand from prior period Net requirements 0 0 0 30 0 0 0 40 Time phased Net Q= L4L Requirements 30 40 Planned order releases 30 40 Planned order delivery 30 40 MRP Calculation Item C LT= 1 wk Q= 50 Period 1 2 3 4 5 6 7 8 9 10 Gross Requirements 20 60 80 Scheduled receipts 50 On hand from prior period 10 40 40 40 30 30 30 0 0 0 Net requirements Time phased Net Requirements 20 50 20 50 Planned order releases 50 50 Planned order delivery 50 50 18
MRP Calculation Item D LT= 2 wk Q= 100 Period 1 2 3 4 5 6 7 8 9 10 Gross Requirements 10 100 30 100 40 Scheduled receipts On hand from prior period 20 10 10 10 80 80 80 40 40 40 Net requirements 0 90 20 20 0 Time phased Net Requirements 90 20 20 Planned order releases 100 100 100 Planned order delivery 100 100 100 MRP Calculation Item E LT= 2 Q= 50 Period 1 2 3 4 5 6 7 8 9 10 Gross Requirements 150 150 Scheduled receipts On hand from prior period 10 10 10 20 20 20 20 20 20 20 Net requirements Time phased Net Requirements 140 130 Planned order releases 150 150 140 130 Planned order delivery 150 150 19
MATERIAL REQUIREMENTS PLANNING: LOT SIZING Lot sizing models Lot for lot "chase" demand EOQ fixed quantity, different intervals Silver Meal Least Unit Cost Part period balancing try to make setup/ordering cost equal to holding cost Wagner Whitin "optimal" method 20
Lot sizing example Week 1 2 3 4 5 6 7 8 9 10 Net Reqs 20 50 10 50 50 10 20 40 20 30 PlannedOrder1 20 50 10 50 50 10 20 40 20 30 Planned Order 2 80 130 90 Costs K = 100, h = 1, λ 30 Method 1 = $1000 Method 2 = $ 580 EOQ Lot sizing example (cont d) 77 Week 1 2 3 4 5 6 7 8 9 10 Total Net Req 20 50 10 50 50 10 20 40 20 30 300 Qt 77 77 77 77 308 Setup 100 100 100 100 $400 Holding 57 7 74 24 51 41 21 58 38 $371 Total $771 21
Silver Meal Heuristic C(T): average setup and holding costs per period if the current order covers the next T periods. C(1) = K C(2) = (K + hr 2 )/2 C(3) = (K + hr 2 + 2hr 3 )/3 C(4) = (K + hr 2 + 2hr 3 + 3hr 4 )/4 C(j) = (K + hr 2 + 2hr 3 + + (j 1)r j )=j Rule: Iterate until C(j) > C(j 1), set, and begin again at period j. Silver Meal Example C(1) = 100 C(2) = (100 + 1(50))/2 = 75 C(3) = (100 + 1(50) + 2(1)(10))/3 = 56.67 C(4) = (100 + 1(50) + 2(1)(10) + 3(1)(50))/4 = 80 So y 1 = 20 + 50 + 10 = 80, and we start over at t = 4. Week 1 2 3 4 5 6 7 8 9 10 Total Net Req 20 50 10 50 50 10 20 40 20 30 300 Qt 80 110 80 30 300 Setup 100 100 100 100 $400 Holding 60 10 60 10 60 20 $220 Total $620 22
Least Unit Cost Example C(1) = 100/20 = 5 C(2) = (100 + 1(50))/(20+50) = 2,143 C(3) = (100 + 1(50) + 2(1)(10))/(20+50+10) = 2,125 C(4) = (100 + 1(50) + 2(1)(10) + 3(1)(50)) /(20+50+10+50) = 2,462 So y 1 = 20 + 50 + 10 = 80, and we start over at t = 4. Week 1 2 3 4 5 6 7 8 9 10 Total Net Req 20 50 10 50 50 10 20 40 20 30 300 Qt 80 100 70 50 300 Setup 100 100 100 100 $400 Holding 60 10 50 60 40 30 $250 Total $650 Part period balancing At each step, compute total holding cost H k if we produce enough for the next k periods. Choose k such that H k is as near as possible to K. Order Horizon Total Holding Cost 1 0 2 50 3 70 4 220 For K = $100, y 1 = 20 + 50 + 10 = 80, and we start over at t = 4. 23
Part Period Balancing Example Week 1 2 3 4 5 6 7 8 9 10 Total Net Req 20 50 10 50 50 10 20 40 20 30 300 Qt 80 130 90 300 Setup 100 100 100 $300 Holding 60 10 80 30 20 50 30 $280 Total $580 Wagner Whitin: an optimal algorithm 1 2 3 4 5 6 Define f k as the minimum cost starting at node k, assuming we start a lot at node k. Then, f k = min j>k (c kj + f j ); where c kj is the setup and holding costs of setting up in period k and producing to meet demand through period j 1, and f n+1 = 0. 24
Wagner Whitin: an optimal algorithm 162 208 376 131 1 2 3 4 5 75 75 75 75 98 210 Wagner Whitin Example Week 1 2 3 4 5 6 7 8 9 10 Total Net Req 20 50 10 50 50 10 20 40 20 30 300 Qt 80 130 90 300 Setup 100 100 100 $300 Holding 60 10 80 30 20 50 30 $280 Total $580 25
Summary of Lot sizing Methods Week 1 2 3 4 5 6 7 8 9 10 Total Net Req 20 50 10 50 50 10 20 40 20 30 300 EOQ 77 77 77 77 $771 Silver Meal 80 110 80 30 $620 Least Unit Cost 80 100 70 50 $650 TotalPart Period Bal. 80 130 90 $580 Wagner Whitin 80 130 90 $580 LOT SIZING WITH CAPACITY CONSTRAINTS 26
Lot sizing with capacity constraints So far we have assumed that there is no capacity constraint on production. However, often, the production capacity is limited. Here we assume that it is required to develop a production plan (i.e., production quantities of various periods) that minimizes total inventory holding and ordering costs. Capacity constraints make the problem more realistic. At the same time, capacity constraints make the problem difficult. Lot sizing with capacity constraints Week 1 2 3 4 5 6 7 8 9 10 Total Net Req r t 20 50 10 50 50 10 20 40 20 30 300 Capacity c t 32 32 32 32 32 32 32 32 32 32 320 Cumulative r t 20 70 80 130 180 190 210 250 270 300 Cumulative c t 32 64 96 128 160 192 224 256 288 320 In general, we require that 27
Feasibility check For every period, compute the cumulative requirement and the cumulative capacity. If for every period, the cumulative capacity is larger than (or equal to) the cumulative requirement, then there exists a feasible solution. Else, if there is a period in which cumulative capacity is smaller than the cumulative requirement, then there will be a shortage in that period, and, therefore, there is no feasible solution. Checking feasibility Requirement Capacity June 10 15 July 14 11 August 15 12 September 16 17 Question: Is it possible to meet the production requirements of all the months? 28
Checking feasibility Requirement Cumulative Capacity Cumulative June 10 10 15 15 July 14 24 11 26 August 15 39 12 38 September 16 55 17 55 Answer: The August requirement cannot be met even after full production in June, July and August. Hence, it is not possible to meet the production requirements of all the months. Lot sizing with capacity constraints Two methods: the lot shifting technique, a heuristic procedure that constructs a production plan, and another procedure that improves a given production plan. At times, capacity may be so low that it may not be possible to meet the demand of all periods. How to check feasibility? 29
Lot shifting technique Lot shifting technique constructs a feasible production plan, if there exists one or provides a proof that there is no feasible solution. Lot shifting method is a heuristic. The production plan obtained from the lot shifting technique is not necessarily optimal. It is possible to improve the production plan. An improvement procedure will be discussed after the lot shifting technique. Lot shifting technique The lot shifting method repeatedly does the following: Find the first period with less capacity. If possible, back shift the excess capacity to some prior periods. Continue. If it is not possible to back shift the excess capacity to some prior periods, stop. There is no feasible solution. 30
Lot shifting technique: example Requirement Capacity June 10 30 July 14 13 August 15 13 September 16 17 Question: Find a feasible production plan Lot shifting technique: example Requirement Capacity June 10 30 July 14 13 August 15 13 September 16 17 Rule: Find the first period with less capacity. The first period with shortage is July when the capacity = 13 < 14 = production requirement. 31
Lot shifting technique: example Requirement Capacity June 11 30 July 13 13 August 15 13 September 16 17 Rule: Find the first period with less capacity. The first period with shortage is July when the capacity = 13 < 14 = production requirement. Lot shifting technique: example Requirement Capacity June 13 30 July 13 13 August 13 13 September 16 17 Rule: Find the first period with less capacity. The second period with shortage is August when the capacity = 13 < 15 = production requirement. 32
Improvement rule Rule: Beginning at the last period, shift the entire production lot to the nearest time periods having excess capacity, if the savings in setup cost is greater than the additional holding costs. Improvement rule: example Requirement Capacity June 13 30 July 13 13 August 13 13 September 16 17 Question: Is it possible to improve the plan if K= $50, h=$2/unit/month? 33
Improvement rule: example Requirement Capacity Excess June 13 30 17 July 13 13 0 August 13 13 0 September 16 17 1 Back shift September production to June? Improvement rule: example Requirement Capacity Back shift August production to June? Excess June 13 30 17 July 13 13 0 August 13 13 0 September 16 17 1 34
Improvement rule: example Requirement Capacity Back shift July production to June? Excess June 13 30 17 July 13 13 0 August 13 13 0 September 16 17 1 Improvement rule: example Requirement Capacity Excess June 26 30 4 July 0 13 13 August 13 13 0 September 16 17 1 Final Plan The above is the result of the improvement procedure. 35
Shortcomings of MRP Uncertainty. MRP ignores demand uncertainty, supply uncertainty, and internal uncertainties that arise in the manufacturing process. Capacity Planning. Basic MRP does not take capacity constraints into account. Rolling Horizons. MRP is treated as a static system with a fixed horizon of n periods. The choice of n is arbitrary and can affect the results. Lead Times Dependent on Lot Sizes. In MRP lead times are assumed fixed, but they clearly depend on the size of the lot required. Shortcomings of MRP, cont. Quality Problems. Defective items can destroy the linking of the levels in an MRP system. Data Integrity. Real MRP systems are big (perhaps more than 20 levels deep) and the integrity of the data can be a serious problem. Order Pegging. A single component may be used in multiple end items, and each lot must then be pegged to the appropriate item. 36