Pre Pack Optimization

7/25/2019 Pre Pack Optimization

1/26

Pre Pack OptimizationPre Pack OptimizationPre Pack OptimizationPre Pack Optimization

Increasing Supply Chain EfficiencyIncreasing Supply Chain EfficiencyIncreasing Supply Chain EfficiencyIncreasing Supply Chain Efficiency

Inderlal Singh Chettri

Divyanshu Sharma

RReettaaiillBBuussiinneessssPPrraaccttiiccee

CCooggnniizzaannttTTeecchhnnoollooggyySSoolluuttiioonnss

500 Glenpointe Center West Teaneck, NJ 07666

Visit us at www.cognizant.com


2/26

Pre Pack O timization White Pa e

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 vendorto 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 flow-

through 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 flowthrough the supply chain with minimal handling, straight to the retail outlet servicing store demands.


3/26


Table of Contents

1 INTRODUCTION TO THE PRE PACKING PROCESS 4

1.1 PRE PACKING TOUCH POINTS IN THE SUPPLY CHAIN 41.2 PRE PACKING DECISIONLAYERS OF UNCERTAINTY 5

2 FOUNDATIONS OF THE OPTIMIZATION APPROACH 6

2.1 PRE PACK DEFINED 62.2 WHERE DO YOU MAKE THE PRE PACK CONFIGURATION? 72.3 COMPARATIVEANALYSIS OF THE TWOAPPROACHES 8

3 PRE PACK OPTIMIZATION SOLUTION 9

3.1 PRE SEASONACTIVITIES 103.2 IN SEASON STEPS 13

4 CONCLUDING REMARKS 16

5 APPENDIX: MATHEMATICAL MODELING 17

5.1 PRE PACK TEMPLATE DEFINITION 175.2 ASSORTMENT OPTIMIZATION 18

5.3 ORDER CONFIGURATION INTO PRE PACKS 205.4 OPTIMIZINGALLOCATION TO STORES 22

6 REFERENCES 24

7 ABOUT THE AUTHORS 25


4/26


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 retailers side is driven by the SKUs 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

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 existingvendor. 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

Figure 1 Pre Pack Touch Points in the Supply Chain


5/26


this stage, the overall Store-SKU Demand can be configured into pre pack configurations so that ordering of

individual SKU units is minimized. If its 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 storesbased 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 forecasteddemand 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 tofulfill 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.


6/26


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.

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

Figure 2 Pre Pack Definition

PP-A SKU 1 SKU 2 SKU 3 SKU 4 SKU 5

QTTY a b c d e


7/26


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 willingto 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.

2.2.1 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.

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.

Figure 3 Assortment Plan Matrix

Figure 4 Pre Pack Decision at Ordering Level


8/26


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.

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 packingdecision 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.

Figure 5 Pre Pack Decision at Store Level


9/26


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


10/26

1


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 arere-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

3.1.1 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.

3.1.1.1 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 processat 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


11/26

1


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.

3.1.2 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:

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.

3.1.3 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

Figure 8 Pre Pack Template Definition


12/26

1


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 groupStore 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.

The output of this optimized assortment plan, with mean and variances, forms the input for pre pack

configuration definitions.

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.

Figure 9 Assortment Optimization

Figure 10 Optimized Probabilistic Assortment Plan


13/26

1


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.

3.2.1 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 SKUQuantity 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 suppliers 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

Figure 11 Pre Season Pre Pack Optimization Steps


14/26

1


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 respectto composition, the pre packs may

show some of the following

characteristics:

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 fast-

moving 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 thatare 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

Figure 12 Order Configuration into Pre Packs


15/26

1


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 groupSKU 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 groupSKU group demand at the time of allocation may not vary significantly, butactual 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


16/26

1


The result is the mapping of pre packs to the allocation required.

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 stepare 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 step-

wise approach, this objective is attained.

Figure 15 Store Allocation Mapped in Pre Pack Terms


17/26

1


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 ofthis 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.


18/26

1


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 (X1, X2, 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 (X1, X2, 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 groupStore 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.


19/26

1



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 Qij 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

the minimum stock requirement for the SKU to meet the service levels.

Constraints

1. Total demand for all SKUs for all stores within the group has to be equal to the forecast demand.


20/26

2


F(Qij), 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(Qij) 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(Qij) would have to fall within the tolerance range.

3. Service levels at stores have to be met.

Allocation Qij, the instance of the distribution f(Qij) >= Qij(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(Qij) 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

Qij= demand for SKU I for Store j

Inputs

Qijfor all past periods

Demand forecast = i j(qij) = 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: Dis 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.


21/26

2



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(Qij) 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.

Qij(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 Qij(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 xijis 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 xij 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.


22/26

2


If each pre pack definition PPjhas 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 is the total number of individual units left over after pre pack

configuration, the total cost of handling individual units would be Cu times . 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)

PPj= pre pack definition j, 0 =< j =

Cp)

= total number of individual units handled in the system

Model

Minimize total cost Z = Cp ((over j=1-p) (nj)) + Cu

So that, for all k (k=one store)

((over j=1-p) ((nj)((over i=1-n)(xij)) ) + ((over i=1-n)( I)) = i Dik

Where, Dik= demand for a SKU I for store k

5.4 Optimizing Allocation to Stores

Problem StatementThe 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.


23/26

2



This problem is essentially about the distribution of lot-sized inventory in a single source-multi-sink

distribution scenario. The distribution center acts as the single source, while there can be n number of retail

stores acting as the sink. This is close to a standard OR problem of lot-sizing in a single warehouse multi-

retail inventory scenario. The key difference here is that the problem has to be solved with a pre-

determined set of lots that have been defined in the pre pack template definition and order configuration

stages. The approach here is to simulate these modules and feedback outputs of allocation to the pre pack

configuration modules, so that pre pack configuration outputs are refined to cater to allocation scenarios.

Inputs

1. Total number of different pre packs as well as individual units received from supplier.

There are Nj number of pre packs each of definition PPj that have been received at the distribution

center from supplier. Each PPj contains SKUs I in quantities xij. In addition to them, there are

number of individual units received from supplier which couldnt be packed in pre packs.

2. Demand from each store for each SKU.

Actual allocation demand Qij (deterministic) for each SKU-Store combination at the distributioncenter.

3. Service level to be maintained at each store Qij(sl) is known for each SKU-Store combination.

4. Cost of stocking pre packs and individual units at warehouse and retail store points.

Holding cost of inventory, in pre packs as well as individual units, is known for DCs and stores.

Constraints

1. Allocation has to meet service levels.

Allocation Qij>= Qij(sl)

Objective Function

Minimize the overall cost of stocking in the Warehouse-Store part of the chain, while maintaining a

minimum quantity of stocks at the stores to meet service levels.

Total cost of stocking is equal to the cost of stocking at DC plus the cost of stocking at each store.

Stocking can be done either in pre packs or individual units after breaking of pre packs. The total cost

function is calculated. It needs to be minimized in a way that the minimum in-store allocation for each

SKU-Store combination is equal to or greater than that required for meeting service levels.


24/26

2


6 References

1. Dong, Ling Xiu and Hau L. Lee. Optimal Policies and Approximations for a Serial Multi-EchelonInventory System with Time-Correlated Demand. Operations Research, 2003 INFORMS 51.6 (2003):969980.

2. Gramani, Maria Cristina N. and Paulo M. Franc. The Combined Cutting Stock and Lot-Sizing Problem inIndustrial Processes. European Journal of Operational Research (2005).

3. Lodi, Andrea, Silvano Martello and Michele Monaci. Two-Dimensional Packing Problems: A Survey.European Journal of Operational Research 141 (2002): 241252.

4. Belvaux, Gaetan and Laurence A. Wolsey. Modeling Practical Lot-Sizing Problems as Mixed-IntegerPrograms. Management Science 47.7 (2001): 9931007.

5. Ryzin, Garrett van and Siddharth Mahajan. On the Relationship between Inventory Costs and VarietyBenefits in Retail Assortments. Management Science 45.11 (1999): 14961509.

6. Pentico, David W. The Discrete Two-Dimensional Assortment Problem. Operations Research 36.2(1988).

7. Martel, Alain. A Probabilistic Assortment Problem. Management Science 15.2 (1977).

8. Schwarz, Leroy B. A Simple Continuous Review Deterministic One-Warehouse N-Retailer Inventory

Problem. Management Science 19.5 (1973).

9. Roundy, Robin. 98% Effective Integer Ratio Lot-Sizing for One-Warehouse Multi-Retailer Systems.

Management Science 31.11 (1985).

10.Lodi, Andrea, Silvano Martello and Vigo Daniele. Heuristic Algorithms for the Three-Dimensional Bin-

Packing Problem. European Journal of Operational Research 141 (2002): 410420.

11.Elmaghraby, Salaii E. and Vishwas Y. Bawle. Optimization of Batch Ordering under DeterministicVariable Demand. Management Science 18.9 (1972).


25/26

2


7 About the Authors

Inderlal Singh Chettri

Inderlal Singh Chettri is a Consulting Manager with Cognizant Retail Business Consulting Practice. He hasmore than twelve years of work experience in consulting and sales and marketing. In Cognizant, Inder

manages the retail consulting practice in Calcutta. He is actively involved in providing domain inputs to

clients as well as client teams. He has also led a number of consulting assignments, such as Business

Impact Analysis and Vendor Product Evaluation. Prior to Cognizant, Inder was a business consultant in the

retail domain with Infosys Technologies and Kurt Salmon Associates. Inder is a post graduate (PGDM) from

the Indian Institute of ManagementCalcutta and a graduate (B.Tech) from the Indian Institute of

TechnologyKharagpur.

Inder can be reached at [email protected]

Divyanshu Sharma

Divyanshu Sharma is a Senior Business Analyst with Cognizant Retail Business Practice. He has more than

two years of consulting experience in the Retail and Supply Chain. At Cognizant, Divyanshu has been

involved in projects ranging from Business Process Mapping to Merchandise Management and UCCnet for

major grocery and general merchandise clients. He has also been involved in Price Optimization and

Domain Training. Prior to Cognizant, he worked with i2 Technologies implementing i2 retail products for its

clients. Divyanshu is a post graduate (PGDM - MBA) from the Indian Institute of ManagementCalcutta and

a graduate from National Institute of Technology Bihar.

Divyanshu can be reached at [email protected]

About Cognizant:

Cognizant (NASDAQ: CTSH) is a leading provider of IT services. Focused on delivering strategicinformation technology solutions that address the complex business needs of its clients, Cognizant

provides applications management, development, integration, and re-engineering, infrastructuremanagement, business process outsourcing, and a number of related services such as enterpriseconsulting, technology architecture, program management, and change management through its

onsite/offshore outsourcing model.

Cognizant's more than 19,000 employees are committed to partnerships that sustain long-term, proven

value for customers by delivering high-quality, cost-effective solutions through its development centersin India and onsite client teams. Cognizant maintains P-CMM and SEI-CMM Level 5 assessments from an

independent third-party assessor, was recently named Forbes' Best Small Company in America for thesecond consecutive year, and ranked among the top information technology companies inBusinessWeek's Hot Growth Companies. Further information about Cognizant can be found athttp://www.cognizant.com.


26/26

2


Contact Details:

Cognizant Technology Solutions500 Glen Pointe Center West

Teaneck, NJ 07666

Ph: 201-801-0233

Fax: 201-801-0243Toll Free: 1-888-937-3277

E-mail: [email protected]

United KingdomPh: 44 -(0) 207 321 4888

Fax: 44 - (0) 207 321 4890


GermanyPh: (069) 66 04 450

Fax: (069) 66 04 542


Software Development Centers

KolkataPh: 91-33-23573211, 23573211, 23573213

Fax: 91-33-23573591, 23574281

E-Mail: [email protected]

ChennaiPh: 91-44-8113063, 8116033

Fax: 91-44-8112622, 8112507

E-mail:[email protected]

Visit us @ www.cognizant.com

Pre Pack Optimization

Documents

Transcript of Pre Pack Optimization