Pre Pack Optimization

Transcription

1 Pre Pack Optimization Increasing Supply Chain Efficiency Inderlal Singh Chettri Divyanshu Sharma Retail Business Practice Cognizant Technology Solutions 500 Glenpointe Center West Teaneck, NJ Visit us at

2 Executive Summary Pre packing refers to packing of individual Stock Keeping Units (SKUs) of merchandise into bigger cases for easier handling in the supply chain. The pre packs consist of varying quantities of different SKUs clubbed together to form the lowest level of packaging hierarchy and are designed to flow through from the vendor to the retail stores. Handling of these larger pre packs rather than individual SKUs proves to be cheaper and faster at all touch points in the vendor to retail store supply chain. Although pre packing has proven benefits in terms of easier and cheaper handling, the development of pre pack configurations determining different pre pack compositions is a major challenge. Clubbing together of individual SKUs into larger cases reduces flexibility of the supply chain. If pre packs need to be opened at any point before they reach stores, additional cost and time is incurred. Inefficient decision making regarding pre pack configuration may result in extensive opening up of pre packs and reconfiguration at distribution centers. It may also lead to excess inventory at stores in case whole pre packs containing superfluous SKUs are shipped to the stores. This can potentially negate the efficiency enhancement targeted to be achieved as a result of pre packing. An efficient pre pack decision-making process involves taking multiple decisions throughout the supply chain management cycle, starting right from the demand forecast to initial planned allocation during assortment planning, purchase order generation, as well as allocation performed at the distribution centers. These decisions have to be taken under various degrees of uncertainty regarding the exact SKU Quantity demand foreseen at the stores. Demand forecasts are typically probabilistic, based upon which assortment planning is done and purchase orders are generated. At the time of stocks reaching distribution centers, store demand is much more concrete in nature, with reduced variability. The pre pack decisions taken at different points in the supply chain have to accommodate the probabilistic demand forecast and be robust enough to handle variations in the actual allocation to stores from the distribution centers with respect to planned allocation at the time of assortment plan development. The ultimate objective is to maximize flowthrough in pre pack terms and minimize handling of individual units throughout the supply chain. This involves managing various trade-offs at each point with the objective of enhancing overall supply chain efficiency and reducing the total supply chain costs. We have developed an approach to pre pack optimization that balances the trade-offs at different points in the supply chain using data intensive models. This approach has its roots in various standard operations research problems and their mathematical modeling techniques. It is a modularized approach that focuses on taking the right decisions at the right time in order to arrive at the best solutions that attain targeted objectives. With this approach and with a robust demand forecast, there is scope for a significant improvement in the efficiency of the supply chain using pre packs that are packaged at the vendor shipment point and that flow through the supply chain with minimal handling, straight to the retail outlet servicing store demands. 2

3 Table of Contents 1 INTRODUCTION TO THE PRE PACKING PROCESS PRE PACKING TOUCH POINTS IN THE SUPPLY CHAIN PRE PACKING DECISION LAYERS OF UNCERTAINTY 5 2 FOUNDATIONS OF THE OPTIMIZATION APPROACH PRE PACK DEFINED WHERE DO YOU MAKE THE PRE PACK CONFIGURATION? COMPARATIVE ANALYSIS OF THE TWO APPROACHES 8 3 PRE PACK OPTIMIZATION SOLUTION PRE SEASON ACTIVITIES IN SEASON STEPS 13 4 CONCLUDING REMARKS 16 5 APPENDIX: MATHEMATICAL MODELING PRE PACK TEMPLATE DEFINITION ASSORTMENT OPTIMIZATION ORDER CONFIGURATION INTO PRE PACKS OPTIMIZING ALLOCATION TO STORES 22 6 REFERENCES 24 7 ABOUT THE AUTHORS 25 3

4 1 Introduction to the Pre Packing Process Merchandise is commonly pre packed (or case packed) for easier handling in the supply chain. Pre pack implies a lumping of the assortment into lots of SKU combinations. These lots are then used as the lowest level of packaging hierarchy in the supply chain planning and execution cycle. In apparel and general merchandise retail, a pre pack could contain similar items differentiated by just one aspect, such as size. For instance, a pre pack of shoes could have shoes of the same style and color but different sizes packed in one case. This practice is primarily due to the large variety of SKUs in each style and the low demand for individual SKUs. The advantage of this practice is that there is less data in the pipeline, which leads to lesser handling in the supply chain, which in turn increases flow through efficiency. On the other hand, sending a pre pack to a store could meet the store requirements for some items, while over fulfilling or under fulfilling demand for other items in the pre pack. This leads to a trade-off between flow through efficiency and demand inefficiency in the supply chain. Some retailers compromise on this by repackaging pre packs in their distribution centers or by inter-store transfers. In a scenario where potentially each SKU can have its own demand pattern, the key challenge in pre packing is to group the SKUs so that replenishment for each of them is executed efficiently. This is what pre pack optimization attempts to address. 1.1 Pre Packing Touch Points in the Supply Chain Pre pack sizes are normally decided by the retailer after considering vendor constraints, if any. This decision on the retailer s side is driven by the SKU s sales history and demand patterns. Demand patterns depend on the sophistication of the data capture/forecasting/planning process followed by the retailer leading to variations in the granularity and accuracy of the forecasted data. Some forecasting engines predict weekly sales by store for a category, while others provide daily sales by SKU and store. The consolidated demand pattern drives the planning and ordering Figure 1 Pre Pack Touch Points in the Supply Chain of the assortment that needs to be supplied to an individual store. Pre pack sizes are normally decided when a new vendor comes on board or when a new SKU is launched by an existing vendor. It is our opinion that retailers need to give more thought to the pre pack configuration at this stage in order to minimize inefficiencies in the downstream supply chain. At 4

5 this stage, the overall Store-SKU Demand can be configured into pre pack configurations so that ordering of individual SKU units is minimized. If it s a new SKU, the best fit demand pattern (same SKU, similar SKU, category level forecasts) can be used for this purpose. The second major touch point in the supply chain relevant to pre packing is at the time of store allocation. Once the pre packs are received from the vendor at the warehouses, they have to be allocated to stores based on the actual store demand for SKUs. In a scenario where store demand cannot be fulfilled in terms of pre packs, there are two choices: to open pre packs and ship individual SKU units or to ship pre packs and allow for overstocking of certain SKUs at stores. Both these have cost implications and the pre packing exercise at this point can be focused on minimizing the overall cost. 1.2 Pre Packing Decision Layers of Uncertainty Over the supply chain, the two major points impacted by pre packing are: 1. Configuring the purchase orders into pre packs so that most of the orders are placed in terms of pre packs and ordering of individual SKU units is minimized. This is done on the basis of forecasted demand months before the SKU reaches the store. 2. Allocating to stores in terms of pre packs so that most of the allocation is in terms of pre packs and opening of pre packs/overstocking due to extra SKUs sent is minimized. This is done on the basis of forecasted demand a couple of days before the stock reaches the store. In an ideal scenario where forecasted demand is the same as actual demand, the pre packing exercise boils down to finding the best fit configurations that minimize ordering in individual units and opening of pre packs. In reality, this is not the case. Actual demand can vary a lot from forecasted demand. This is mainly due to the time difference between ordering and sales. Ordering to vendors may precede store allocations and sales by months, especially if the sourcing is global. Events, unaccounted for by the forecasting model, could occur which could affect the accuracy of the forecast. Forecasting accuracy increases as we come closer to the event. So, to link the two areas impacted by pre packing, we need to consider demand as probabilistic. Creating pre pack configurations in a probabilistic demand scenario involves greater complexity in modeling the business scenario for optimization. Success or failure of the pre pack optimization process, in terms of whether pre packs have to be opened or not, depends on a lot of decision elements in the supply chain, such as: a) Demand Forecasting the forecasting accuracy determines up to what degree the actual demand would vary from the expected demand. With high forecast error, pre packs would have to be opened to fulfill store orders even with accurate initial pre packing. b) Assortment Planning the assortment planning determines what quantity of each SKU is planned to be stocked at different stores. In a scenario where the actual store allocation demand varies greatly from the planned assortment, opening of pre packs would become unavoidable. 5

6 Faced with the above preconditions, the pre packing decision has to consider a probabilistic demand and assortment scenario in most cases. The real challenge then is not just to configure pre packs that are best fits between assortment and store demands, but also to work on a probabilistic assortment and create pre pack configurations that can withstand variations in demand at the time of actual allocation. The pre pack optimization exercise thus needs to model the probabilistic demand and assortment scenario and generate the pre pack configurations. The questions an efficient pre pack optimization framework would answer are: 1. At what point in the supply chain should the decision to configure pre packs be taken? 2. What should be the permissible limits of variation, weight, dimension and value while configuring a pre pack definition? 3. How many pre pack definitions should be used? 4. What should be the composition of each individual pre pack in terms of SKUs it holds and quantities of each SKU? 5. How much of the overall assortment should be configured in terms of pre packs and what percentage should be handled in individual SKU terms? There can be multiple points in the supply chain where individual SKUs demanded can be grouped to form pre packs. It is important to take the right decisions at the right time. The objective is to come up with an optimal number of pre pack configurations and determine the composition of each one. Too large a number of configurations may lead to complications in the supply chain and too less a number may lead to a greater probability of opening of pre packs. A decision has to be made about whether to pack everything in pre packs or handle some individual units as well. The approach towards building the pre pack optimization solution would involve exploring all these questions in greater detail and finding the right answers. 2 Foundations of the Optimization Approach Understanding the basic questions involved leads to comprehension of objectives the solution should attain, as well as the challenges and risks involved. With this foundation, a first principles-based approach can lead to the development of a pre pack optimization model that helps maximize efficiency enhancements and minimize overall supply chain costs. 2.1 Pre Pack Defined A pre pack can be defined as a combination of different SKUs and quantities of each SKU contained within a case of a particular weight/dimension. Figure 2 Pre Pack Definition PP-A SKU 1 SKU 2 SKU 3 SKU 4 SKU 5 QTTY a b c d e In the example, PP-A is a Pre Pack Definition that has SKU 1, 2, 3, 4 and 5 in quantities a, b, c, d and e respectively. An SKU is defined as a style/color/size combination. Theoretically, a pre pack can have SKU combinations of multiple styles/multiple colors/multiple sizes. However, in practice, pre packs have 6

7 SKU combinations of a single style, and many times, even a single color with just different quantities of different sizes. A pre pack can be as large as possible, within the given constraints of dimensions, weight, total value (in price terms), and so on. These constraints are defined on the basis of various factors, such as the maximum weight that can be handled and the maximum value of goods the vendor or retailer is willing to put in a pre pack. 2.2 Where do you make the Pre Pack Configuration? Based on the understanding of pre pack touch points in the supply chain, there can be two approaches to configure pre packs. The first one defines pre packs at the purchase order level and the second one defines pre packs at the store ordering level. In line with the pre pack configuration information flow in the supply chain, these approaches can be categorized as being top down and bottom up approaches The Top Down Approach to Pre Pack Configuration The assortment plan provides planned allocation of SKUs for each store for each period (usually a week). In modeling terms, the assortment plan output for each period (normally a week) can be denoted in terms of the matrix shown in figure 3. This assortment plan drives purchase order generation that results in the flow of SKUs from the top (vendor) down to the store. Pre pack configuration in this case is done on the basis of top down planned allocation for each store and hence is seen as the top down approach. At the time of generation of purchase orders, the assortment plan is configured in terms of pre packs and orders are placed in terms of quantities of each pre pack definition rather than each individual SKU. Figure 4 Pre Pack Decision at Ordering Level Figure 3 Assortment Plan Matrix Creating larger pre pack configurations and having greater quantities and higher number of SKUs ensures greater cost advantages in terms of handling. But larger pre packs reduce flexibility in redistribution at the Distribution Centre (DC) and consequently increase probability of opening or overstocking. Thus, it is necessary to balance divergent goals to ensure that the pre packs created go straight to stores without opening. In the top down approach, even though configuration is done at an aggregate planned allocation level, individual store allocation needs to be considered. 7

8 2.2.2 The Bottom Up Approach to Pre Pack Configuration In another approach that initiates at the individual store allocation level, each store places its demand in terms of configured pre pack definitions rather than SKU quantity terms. In this approach, actual bottom up store orders are configured into pre packs and sent to the ordering level. Hence, this is seen as the bottom up approach to pre pack configuration. Figure 5 Pre Pack Decision at Store Level Each store decides on its own pre pack configurations within the overall preset constraints of weight, dimension or value. The store orders are then placed in terms of defined pre packs and some individual units remaining. At the ordering level, orders are received from each store in terms of store level pre pack configurations as well as individual SKU orders. These are aggregated and purchase orders are generated accordingly. The stocks received from suppliers at distribution centers in this approach are in terms of store level pre pack configurations. Thus the probability of opening of pre packs is minimized to a large extent, unless allocation needs to be drastically different from initial store level demand. 2.3 Comparative Analysis of the Two Approaches The top down and bottom up approaches address the same questions in different ways. While the top down approach handles the question of pre pack configuration on the basis of planned allocation, the bottom up approach points to the actual store demand. These occur at different times in the supply chain management cycle and are pieces of a larger picture. In terms of the rationale for taking the pre packing decision at the procurement/ordering level or at the store level, both approaches have their pros and cons. The decision to configure pre packs at the store level increases the probability of a pre pack passing through to the store because it has been specifically designed for fulfilling a particular store demand. But on the other hand, designing store specific pre packs reduces the flexibility of distribution. Having different pre pack definitions for each store may mean a huge, almost unmanageable number of configurations at the aggregate level. Plus, these pre packs may not be suitable for allocation to any other store in case the store allocation requirement changes. This may also lead to a greater percentage of the overall assortment being ordered in individual units. The top down approach to pre pack configuration resolves some of these issues and creates pre packs based on aggregate demand rather than individual store demand. This may ensure a manageable number of pre packs and lesser individual SKUs in the ordering stage. It may also create more flexibility in allocating pre packs to stores. But the major concern at this stage is the increased probability of pre pack opening at warehouses. 8

9 The rationale behind pre pack configuration is to reduce the SCM costs and increase efficiencies, and it has been observed that handling individual SKUs has an adverse impact on both. The underlying objective behind defining pre pack configurations is to minimize handling of individual units throughout the supply chain. This includes minimizing the individual ordering and breaking of pre packs at any stage in the supply chain to ship individual SKUs. Any optimization that concentrates only on a part of the supply chain rather than the whole supply chain would create disturbances elsewhere. Efficient optimization can happen only when the whole process is observed in its totality. With this in mind, a pre pack configuration process needs to be developed, that combines the best inputs of both approaches and provides a larger picture, integrating all the small pieces. 3 Pre Pack Optimization Solution As discussed, pre pack touch points in the supply chain are distributed across the supply chain and occur at different times. These touch points involve decisions taken under varying degrees of uncertainty of demand. The pre pack optimization solution should make it possible to take the right decisions at the right time in the supply chain, with the purpose of enhancing overall efficiency. The suggested approach involves breaking down the overall problem into components and executing them at various touch points in accordance with the inputs and constraints applicable. Steps have to be taken at various levels to ensure the efficient flow through of pre pack configurations in the supply chain. Figure 6 Solution Approach for Pre Pack Optimization 9

10 The supply chain objective, in a non-pre pack scenario, is to service the store demand on time and at the lowest cost, based on the desired service levels to be achieved at each store. Store demand is serviced by the flow of the assortment SKUs through the supply chain. The aim of pre pack optimization is to service store demand, as far as possible, using pre packs. Thus, the spectrum of the solution building approach ranges from decisions taken regarding service levels for stores, to decisions involving demand forecasting and assortment optimization, order configuration, as well as allocation optimization. All these processes are re-considered and configured with a view towards introducing pre pack configurations and using pre packs rather than individual SKUs as the lowest unit of the packaging hierarchy. There are steps that happen prior to the start of the season and span across more than a single season. These are the planning elements as well as broad levels of agreement that need to be set up between the retailers and suppliers, as well as broad parameters of demand fulfillment, such as service levels. Some steps need to be taken during the seasonal cycle. Using a step-by-step approach to taking decisions, this approach achieves the larger objective integrating the smaller pieces. The steps are classified into two major segments of Pre Season and In Season Activities. 3.1 Pre Season Activities Defining Service Levels the Fundamental Step The process of servicing store demand starts from defining the service levels the level and the degree up to which store demand would be fulfilled through the supply chain. Service levels are defined based on the balancing act between the cost of overstocking and the cost of shortage. While excess inventory has its own adverse impact on ROI, stock outs mean lost sales and may also translate to loss of brand and store image. A balanced service level attains the right Fill Rate (demand met/expected demand) and increases the probability of no stock out, keeping in view the criticality of the SKU to the store image, as well as the speed at which it moves off the shelf. In an ideal scenario, there should be a distinct service level set for each Store-SKU combination. But in practice, service levels for stores are generally defined for Store-SKU group combinations, or even more broadly, at the store level The Service Level Classification Matrix At the store level, SKUs can be classified based on the speed of their movement off the shelf as well as the criticality of their demand. Once SKUs are classified into each segment of this matrix, service levels can be set for each segment. These service levels and the classification matrix affect the pre pack optimization process at every subsequent step. Collectively, these service levels can be represented by a service set for each store. This service level set would have a number of service levels for each SKU segment for the store. With pre packing, pre packs rather than Figure 7 Service Level Classification Matrix 10

11 SKUs are the lowest level of packaging hierarchy. At this stage, the pre pack decision element is to define rules so that SKUs with similar or complementary demand patterns are packed together. Decisions involve whether or not to configure fast-moving SKUs with slow-moving SKUs or critical SKUs with non-critical SKUs, and so on. These decisions and the rules formulated would provide ways to slice this matrix and prepare segment groupings as an input to pre pack configuration. This would ensure that consistency is maintained in the pre packed supply chain from the service level point of view. Furthermore, this matrix provides pointers to understand the criticality of the whole pre packing process itself. For example, while taking a decision regarding allocating a fast moving critical SKU, there can be some degree of excess inventory maintained. Similarly, while allocating slow moving non-critical SKUs, some stock outs may be tolerated. Ultimately, this matrix-based classification provides the fundamental strategic input on each SKU that governs pre pack decisions taken throughout the supply chain Pre Pack Template Definition The pre pack configuration exercise can be broken into two parts: determining different sizes for pre packs and determining the composition of each pre pack definition. Both steps are taken in a retailer-supplier collaborative environment, where mutually agreed fundamental pre pack properties, such as weight and dimension of the carton, and regulations on pre pack composition are set. In most cases, it is important to set the carton sizes (weight and permissible number of SKUs) before determining the composition. In this context, a template is defined as the capacity of a carton that is used to pack in individual units (SKUs) of mutually agreed style/color/size variations. The Optimization Model for Pre Pack Template Definition involves: Figure 8 Pre Pack Template Definition Based on past data on store demands as well as flow through of individual units into the supply chain, clubbing together, or lot-sizing of SKUs in different quantity groups can be arrived at, resulting in an optimal number of cartons and optimal carton capacities. This lot-sizing needs to fulfill the boundary conditions of maximum permissible weight of a lot packed in a carton and the dimension constraints Assortment Plan Optimization Assortment plans determine the width and depth of the assortment to be carried catering to the cross section of consumer demand. They also determine planned allocation of SKUs to stores. Assortment plans are normally based on probabilistic demand scenarios and in cases where actual allocation is widely 11

12 different from the assortment plan, opening pre packs becomes unavoidable. The assortment plan is such a critical input for pre pack optimization that it becomes almost inevitable to optimize the assortment as a step towards developing the pre pack optimization solution in cases where the assortment plan input has not been optimized beforehand. In the pre pack optimization process, the decisions on depth and breadth of the assortment are generally not considered and the planned allocation is optimized. Demand forecasts are usually made for groups of SKUs projected to be sold in certain quantities through a group of stores. A typical demand forecast would predict that X number of shoes of a particular style would be sold in the 20 stores that sell these shoes in a certain city. Assortment optimization involves taking the overall SKU group Store group level demand forecast and disaggregating this to an SKU-Store based periodic plan. The overall demand is broken up using past demand patterns of individual SKUs at each store. Optimization is constrained by overall demand forecast figures and the fulfillment of service levels at each store. In a probabilistic demand scenario, this SKU-Store assortment plan needs to follow probabilistic distribution. Figure 9 Assortment Optimization The output of this optimized assortment plan, with mean and variances, forms the input for pre pack configuration definitions. Figure 10 Optimized Probabilistic Assortment Plan Development of an optimized assortment plan, along with service levels and pre pack template definitions, fulfills the pre season activity set for pre pack optimization. These steps form the foundation for the subsequent in season steps. 12

13 Figure 11 Pre Season Pre Pack Optimization Steps 3.2 In Season Steps After the pre season steps are developed, the two steps of configuring the purchase order into pre packs and allocating pre packs from distribution centers to stores are performed Order Configuration in Pre Packs Purchase orders are raised against the open-to-buy derived from the assortment plan. In pre packing, these orders consisting of an SKU Quantity assortment plan for each vendor have to be configured in terms of pre packs rather than individual SKU-Quantities. In a scenario in which the vendor is ready to ship as soon as the order is received, the purchase order raised needs to specify the pre pack configurations. But in a scenario where there is a significant time lag between the instant the order is received and the moment the vendor starts shipment, the initial order can be sent in terms of aggregate SKU-Quantity, and pre pack definitions can be sent just before the packing stage starts at the supplier s point. This would ensure that the pre pack decision is taken as close to the actual demand as possible. As an output of this model, the assortment plan is clubbed into pre pack configurations and after this point, pre packs become the lowest level of packaging hierarchy. The pre pack configurations map the whole assortment plan and fit into the Store-SKU-Quantity demands. The key element in this step is to determine 13

14 the composition of each individual pre pack and the total number of such pre packs used. The size of every pre pack would be equal to one of the pre pack sizes defined in the pre pack template. With respect to composition, the pre packs may show some of the following characteristics: Figure 12 Order Configuration into Pre Packs A particular pre pack may contain SKUs required for a particular store or a group of stores. Packing together of SKUs that are meant for different stores increases the chance of opening. Pre packs may contain SKUs of a particular style, size or color. Generally, SKUs are characterized first by style and then by size and color. Even if there are no constraints due to pre pack template definition, pre pack configurations may have SKUs that differ in color and size, but belong to the same style. Fast-moving SKUs may be clubbed together or in some pre packs, there could be a number of fastmoving SKUs together with a few slow-moving SKUs. Slow-moving non-critical SKUs may not be clubbed together in pre packs, as this may create excess inventory in stores. An important decision taken at this point is whether to ship everything in pre packs or ship some individual units that are left out after pre packing. There may be cases in which pre pack configurations are not able to completely map the assortment plan and some individual SKUs remain. In such a scenario, either the remaining SKUs can be sent individually or the assortment plan modified a little bit so that an integral number of pre packs closest to the assortment plan are shipped. In most cases, for ease of operations, the assortment plan is modified a little bit to allow all shipment to happen in integral pre pack numbers. Another option may be to hold back the individual SKUs to be shipped in the next period. In cases where shipments are frequent due to slow-moving or non-critical SKUs, this option requires serious consideration. Figure 13 Pre Packs Mapped on Assortment Plan 14

15 3.2.2 Pre Pack Allocation to Stores When the pre packs reach the distribution centers, demand from stores is closest to the actual consumer demand. The accuracy of the assortment plan is tested at this instant. If the assortment plan is totally accurate, allocation is the same as the assortment plan, and this is a straight flow through process. But the assortment plan being probabilistic, in most cases, actual store allocation from distribution centers differs from the assortment plan. This variance introduces complexities at two levels. The overall Store group SKU group demand at the time of allocation may differ from the demand forecast. If this deviation is significant, either excess inventory or shortages are inevitable, whether pre packing is done or not. Inaccurate demand forecast is an input which causes a major portion of excess inventory or shortages, and thus the pre pack optimization process needs to have as accurate a demand forecast as possible. Using pre packs, some inaccuracies in forecast can be smoothened, but the utility of pre pack optimization in a widely inaccurate demand forecast scenario is compromised to a great extent. The overall Store group SKU group demand at the time of allocation may not vary significantly, but actual SKU-Store allocation may be widely different from the assortment plan output. This is a result of inaccurate assortment planning something which requires regrouping of SKUs at distribution centers and revised allocation. Using an un-optimized assortment plan as an input to pre packing may necessitate the opening of pre packs for reallocation of SKUs, in case the plan is way off target. The utility of assortment optimization lays in the fact that it goes a long way in reducing variances in the assortment plan to allocation figures. With an optimized assortment plan used as input for pre pack configurations, reallocation at the level of entire pre packs rather than individual SKUs becomes much more feasible. The decision at this level is to allocate the pre pack stocks received according to the deterministic store allocation demand. The best situation is when all store demands can be fulfilled in an integral number of pre packs. If this is not the case, a decision may be taken to hold back entire pre packs at distribution centers and ship lesser SKUs to stores than demanded, or to ship entire pre packs to stores with more SKUs than demanded. The third option is to open pre packs and ship individual units. Stocking/allocation decisions are based on the cost of opening pre packs, handling individual units, holding stock at a warehouse, as well as overstocking/under stocking at retail stores. Figure 14 Pre Pack Allocation to Stores 15

16 The result is the mapping of pre packs to the allocation required. Figure 15 Store Allocation Mapped in Pre Pack Terms 4 Concluding Remarks The intent of pre pack optimization is to eliminate handling of individual SKUs throughout the supply chain. In the pre packing context, individual units may appear at the time of ordering or at the time of shipment from vendors to distribution centers, or at the time of opening of pre packs to allocate SKUs for fulfilling store demands. These touch points in the supply chain require various decisions to be taken so that overall handling of individual units is minimized. In the modularized, step-by-step approach taken to achieve this purpose, there is an effort to answer the right questions at the right time in the supply chain, so that the efficiency of the overall process is enhanced. These modules appear as independent pieces but are actually part of a unified picture because the fundamental assumptions, inputs and constraints used at each step are the same. Through simulation of each module and feedback of one module output to another, the optimization outputs coming out of each module are refined in order to give enhanced benefits. Furthermore, the underlying objective in developing all these modules is to eliminate individual SKUs from the supply chain and use pre packs as the lowest level of packaging hierarchy. By a systematic and stepwise approach, this objective is attained. 16

17 5 Appendix: Mathematical Modeling The optimization models developed for the whole process of pre pack optimization have been based on an understanding of theoretical Operations Research problems, and their adaptation for the modeling tasks at hand. While pre pack optimization modeling for an individual industry and business case would have its own characteristics, all the models would inherently follow a similar fundamental approach. The objective of this section is to illustrate that fundamental mathematical approach towards pre pack optimization. 5.1 Pre Pack Template Definition Problem Statement A template is defined as the capacity of a carton that is used to pack SKUs. At this level, all SKUs of a particular style are considered identical. Past data for allocation made to different stores for each style and for order sizes placed to vendors for each style is available. Individual units of a style have to be grouped into cartons of different capacities. Thus, most of the units can be packed in the cartons. The objective of this exercise is to find out the optimum carton sizes for each vendor within which the pre packs to be ordered can be defined. Theoretical Reference This problem is similar to a number of Operations Research problems, such as lot-sizing in a multi-echelon inventory system, as well as a multidimensional bin-packing problem. In essence, both template definition and order configuration optimization modules work with similar theoretical references. The overall decision of determining the size of pre packs and composition is broken up. Template definition focuses on determining sizes, while order configuration determines composition. Thus, template definition turns out to be a special and simplified case of a three- dimensional bin-packing problem, where the objective is to determine a minimum number of bin sizes in which smaller three-dimensional rectangular boxes can be fit. There are also elements of the multi-echelon lot-sizing problems in this case, as the bins (or pre packs) have to fulfill the past demand data of each store at a disaggregate level, that is, without opening the bins. Modeling Constructs Inputs 1. Supplier/retailer agreement on style/color/size variety permissible for each pre pack. It is assumed that a template is defined for all styles supplied by the vendor. Vendor V produces styles Style 1 Style 2 Style n. It is assumed that a single set of pre pack sizes has to be developed for all styles produced by vendor V. 2. Past data on order sizes and allocation. It is assumed that data is available on the past y number of years for order sizes placed and allocation to individual stores. For vendor V, there is data on quantities ordered in each order in the past y years. 17

18 For all styles manufactured by vendor V, there is data on quantities of each style allocated to each store for the past y number of years. Constraints 1. It is assumed that the maximum number of templates that can be defined is fixed. For a particular vendor V, there can be only p numbers of template sizes defined. 2. There is a cap on the maximum number of units in a particular pre pack template. This is based on the fact that any pre pack capacity cannot be too large, as handling it would be impossible. Let us assume that for a particular vendor V, a pre pack template cannot contain more that r number of individual units. Objective Function The number of different pre pack sizes has to be optimized so that the sizes are a best fit with the past allocation to each store as well as the order sizes for each style. Define different sizes X (X 1, X 2, a maximum of p sizes) so that a. The past allocation demand from stores for the style group shipped by vendor V is fulfilled in the sizes defined to the maximum level. b. Past order sizes can be grouped into the sizes defined to the maximum level. c. In both cases, the total number of individual units remaining after grouping into sizes defined has to be minimized. Desired Output A set of pre pack sizes for each vendor X (X 1, X 2, a maximum of p sizes) Assumptions 1. The first level of assumptions is that all the inputs defined above are available and constraints are provided in quantitative terms. 2. Each individual unit (a pair of shoes in its own box) is of the same dimensions. 3. It is assumed that all styles manufactured by a vendor can be packed into one carton. If that is not the case, carton sizes specific to those styles which can be packed in one carton size would have to be developed. 5.2 Assortment Optimization Problem Statement There is a weekly demand forecast for a particular style for a particular group of stores. Each style can be disaggregated in terms of color and size SKUs. The SKU group Store group demand forecast has to be disaggregated in terms of probabilistic SKU-Store forecast based on past data available from stores on their SKU sales as well as their service level requirements. 18

19 Theoretical Reference Assortment Optimization is a developed field of Operations Research, with various streams of thought being published. One stream focuses on the problem of an optimal assortment that produces the best fit with consumer demands. It attempts to determine the assortment depth and breadth catering to as much variety in consumer demand as possible. For the purposes of this document, it is assumed that decisions on breadth and depth of assortment have already been carried out, and that the focus is on the distribution of the overall demand into SKU-Store combinations, developing the assortment matrix as discussed. This is essentially a variation of the curve-fitting problem in which data extrapolation is done to fit the curves developed based on past data. From demand forecast, the aggregate projected probabilistic demand functions of a group of SKUs to be sold through a group of stores are calculated. Based on past SKU sales data from each store, the SKU demand curves for each store can be constructed. The approach is then to fit the SKU probabilistic demand functions into each of the Store-SKU demand curves, so that the aggregate SKU demand equals what is forecasted. Inputs 1. Weekly Demand Forecast a. Assumption: Style A can have n number of color/size variations. Thus the forecast would be for SKU group A that has n number of SKUs. The SKU group A denotes all the color-size variations ( n number) for the Style A. SKU group n contains all SKUs with Style A colors and sizes may vary within that style, giving n number of SKUs. b. Assumption: The forecast is for s number of stores. s number of stores can be in one channel or area for which the forecast is made. Forecast for n SKUs for s stores = f (D), where f (D) may be a probabilistic function obeying a given distribution. It is assumed here that this demand would follow normal distribution with mean D and Std. Deviation d. This demand can be readily assumed to follow some other distribution function and the equations derived would change accordingly. 2. Past data on allocation of each SKU/similar SKUs for each store. a. For each SKU among the n SKUs for which the demand forecast has been made, past sales data from each store (from the s number of stores) is available. 3. The service levels to be maintained at each store are provided. Based on the demand distribution (whether it follows normal distribution or some other one), the minimum stock requirement for a particular service level can be calculated. Let us assume Q ij is the stock of SKU i (which can vary within the n number of SKUs in the group) for Store j (which can vary within the s number of stores in the group). Thus Q ij (sl) is Constraints the minimum stock requirement for the SKU to meet the service levels. 1. Total demand for all SKUs for all stores within the group has to be equal to the forecast demand. 19

20 F(Q ij ), the planned stock of SKU I for store J is a probabilistic quantity having the same probabilistic distribution as the demand f(d). Sum of all f(q ij ) distributions would be equal to f(d) distribution. 2. Demand for each SKU-Store combination falls within the range of demand projections done on the basis of past SKU-Store allocation data. Time Series analysis of past demand for each SKU-Store combination-analysis of base, trend and seasonality would provide demand curves demand = f(time) for all SKU-Store combinations. These demand curves would have a tolerance level of ± T. The probabilistic demand functions for future demand for each SKU-Store combination-f(q ij ) would have to fall within the tolerance range. 3. Service levels at stores have to be met. Allocation Q ij, the instance of the distribution f(q ij ) >= Q ij (sl) for all stores and SKUs. Objective Function Determine optimal quantity of each SKU to be kept in each store to be able to fulfill the service levels. Determine the probabilistic functions f(q ij ) for all SKUs and stores within the group so that service levels are met and the sum of all the individual distributions is equal to the demand function f(d). Mathematical Model Number of stores in the store group for which the demand forecast is available = s Number of SKUs in the SKU group for which the demand forecast is available = n Q ij = demand for SKU I for Store j Inputs Q ij for all past periods Demand forecast = Σi Σj(q i j) = D (D is a probabilistic demand and all the equations have to be expressed in terms of probabilistic demand) Service levels for each store within the group Model Determine qij for all I = 1-n and j = 1-s So that: D is fulfilled and service levels are met 5.3 Order Configuration into Pre Packs Problem Statement A number of SKUs of a particular style have been ordered from vendor V. The probabilistic allocation of each SKU for each store is available. The cost of handling pre packs and the cost of handling individual units is known. The cost of handling of individual units is very large compared to the cost of handling pre packs. Pre packs should be defined so that most of the flow of items happens in terms of pre pack units and handling of individual units is minimized. A pre pack definition would mean selecting a combination of 1 to n number of SKUs for a particular style and selecting quantities for each SKU so that the total number of units in the definitions equals one of the pre pack sizes defined in the template. 20

21 Theoretical Reference This module handles the second part of the overall pre packing problem of determining the composition of each pre pack configuration for which sizes are determined by the template definition. This problem also finds references in a variety of Operations Research problems such as three-dimensional cutting stock problems, lot-sizing in a multi-echelon inventory situation, as well as cutting stock problems for cutting a large two-to-three dimensional sheet in smaller pieces, so that waste leftovers from the large sheet are minimized. This problem also finds similarities with the lot-sizing and batch-ordering problems in probabilistic/deterministic demand scenarios, where orders have to be configured into batches for an overall probabilistic or deterministic demand. The fundamental objective in our situation is to configure an overall assortment into smaller blocks of distinct SKUs that can be ordered as lots or batches and that can flow through the multi-echelon supply chain without getting opened. The modeling for the fulfillment of this objective takes best practices from all the modeling exercises mentioned. Modeling Constructs Inputs 1. Probabilistic demand for each SKU for each store from the assortment plan. F(Q ij ) is known for each SKU-Store combination for SKUs. 2. Total order placed for each SKU aggregated for all stores. For the vendor V, total orders placed for each SKU shipped is known. 3. Cost of handling of pre packs and handling of individual units. Let us assume a uniform cost Cp of handling all individual units packed into pre packs, and a uniform cost Cu of handling all individual units handled individually. These costs are summation of all costs throughout the process for pre packs as well as individual units. It is assumed that Cu is much larger than Cp. 4. Service levels to be maintained at each store. Q ij (sl) for all SKU-Store combinations is known. Constraints 1. Demand for each store has to be fulfilled within the permissible service levels. The total demand for a particular store, summed over all SKUs and for all vendors, has to be fulfilled so that Q ij (sl) for all SKUs within the store is fulfilled. 2. The sizes of pre packs defined can only be among the ones given in the templates. If x ij is the number of units of SKU I stocked in pre pack j, then for a particular pre pack definition j, the sum of individual units of all SKUs present in it has to be equal to one of the pre pack sizes as developed in the template module X (X1, X2, a maximum of p sizes). 3. The sum of quantities of a particular SKU aggregated over all pre pack definitions configured in the order have to be equal to the total order quantity of that SKU. If x ij is the number of units of SKU I stocked in pre pack j, then for a particular SKU I, the total number of units packed into all pre packs of different combinations has to be equal to the quantity ordered for the SKU. Objective Function Minimize overall cost of handling inventory by maximizing ordering and shipment in pre packs. 21

22 If each pre pack definition PP j has Nj number of units in the configured order, the total cost of handling of all pre packs would be Cp times the total number of individual units packed in pre packs of all definitions for the order. If δ is the total number of individual units left over after pre pack configuration, the total cost of handling individual units would be Cu times δ. The objective is to minimize the total cost of handling. While doing so, the lower cost Cp would ensure that most units are handled in pre packs and opening of pre packs to handle individual units is minimized. Mathematical Model Inputs X, where X is an element of the set of pre pack sizes (capacities available) P = number of different pre pack definitions (a decision variable) PP j = pre pack definition j, 0 =< j =<P (total number of pre pack definitions can be P) X ij = number of units of SKU i in PP j 0 =< X ij =<X (minimum number of items of a particular SKU in a particular pre pack can be zero, meaning that SKU is not defined within that pre pack. Maximum number can be equal to the pre pack size, meaning only that SKU is defined for that pre pack) Nj = number of pre packs of j type in an order (an order can have many units of the same pre pack definition. Nj signifies the number of each pre pack definition that the order to be configured would contain) Cp = cost of handling of pre packs Cu = cost of handling of individual units (Cu>>Cp) = total number of individual units handled in the system Model Minimize total cost Z = Cp (Σ(over j=1-p) (n j )) + Cu So that, for all k (k=one store) (Σ (over j=1-p) ((nj)(σ(over i=1-n)(x ij )) ) + (Σ(over i=1-n)( I)) = Σi D ik Where, D ik = demand for a SKU I for store k 5.4 Optimizing Allocation to Stores Problem Statement The supplier has sent stocks in pre pack definitions sent during ordering. The cost of stocking pre packs as well as the cost of stocking individual units at the store and at the warehouse is known. A pre-determined service level fixed for each of the stores needs to be maintained. At this stage, the actual deterministic demand for each SKU for each store is available. The allocation of stocks to each store has to be decided upon, to maintain service levels while minimizing the handling of individual units. 22