Backup Agreements in Fashion Buying-The Value of Upstream

FlexibilityEppen and Iyer (1997)

Presented By:Hakan Umit

21 April 2003

Address Backup Agreements between a catalog company and manufacturers

Present a systematic action to provide upstream sourcing flexibility

Scope

A Backup Agreement is…

commitment of the catalog company for a certain number of units to be purchased for the season long before the it starts

Characteristics of the System

The manufacturer holds back a constant fraction of the commitment and delivers the remaining units before the start of the fashion season

The catalog company can order up to this backup quantity for the original purchase cost and receive quick delivery but will pay a penalty cost for any backup of the units it does not buy

Problems Associated with the System

Long lead times High levels of uncertainty Role of returns Limited opportunities to adjust buying

decisions

Decisions to be made by customers

Commitment quantity Number of units to be taken from the

backup

This paper provides…

Theoretical and Applied Results:Stochastic dynamic programming model for

the backup agreementParallel retrospective study that compares the

performance of a catalog company and proposed model’s results

Extensive test results to evaluate the impact of changes in contract conditions

The Process Flow

: commitment for the season : percentage of units of y to be hold by the

manufacturer : penalty cost to be paid by the customer if

it does not take from backup : cost of a unit product to the catalog co. : price of a unit product at the catalog co.

: Random demand in P-I : Unit holding cost in P-I : Unit cost for unsatisfied demand : Percentage of returned sales in P-I : Percentage of that arrives in time to

satisfy demand for P-II

Period-I Period-II

units are delivered for a cost of c per unit

units are held at the manufacturer

Product is offered for a price of r per unit

Random demand, , occurs

Two weeks

v(sales) returned uv(sales) arrive on time to satisfy demand in P-II

units on hand and 1 units in returns

or

0 units on hand and returned units

Net Revenue:

The Demand Process

Demand is assumed to be generated by pure demand processes

A pure demand process provides a probability distribution of demand for P-I, P-II and for the season

Which pure demand process will generate the demands is uncertain, thus prior probabilities are assigned to these processes by the buyer

Defining the Demand Model consists of two steps..

1. Specify a set of pure demand processes

2. Select a set of prior probabilities at the start of 1st period that each pure demand processes will be the ones that actually produces the demand

Cumulative Demand Distributions

Probability Density Functions

Let P1i be the prior probability for pure demand process i

The Dynamic Programming Model f1(0): optimal expected profit for the two period

problem assuming that 0 items are on hand at the beginning of P-I. Then

1110

1201 )(),()1()0( dyfcyMaxf y

Maximum Expected Profit in P-II if y items are committed

Density function of demand in P-I

G1(y)

The Maximization Problem for is: Where,

Conditional Density for ,the demand in period 2 given

21

Results

A Retrospective Parallel Test

Data Set of CATCO (for years 1990-1993)Sales estimates when purchase decisions

were made the quantity ordered the actual demand during the year the purchase cost and selling price the return and cancel ratesbackup agreements

The Demand Process:

Demand was segregated into intervals then a histogram was plotted: the data fell into 4 nonoverlapping regions

In each of these regions the data were generated by random draws from a negative binomial distribution

Specific model was developed for the pure processes that consists of 4 negative binomial distributions

The Demand Process:From smaller through greater expected

demand, the processes are referred as Dogs, Crawlers, Walkers and Runners

Planned classification by the buyer are used to create priors for the items

Retrospective Study

Optimal value of y is determined Amount to be taken from backup is not

available, therefore given a value of the model evaluates and uses an order-up-to policy to choose this amount

Expected profit, Expected purchases are determined

Results

Buyers at Catco took advantage of the backup opportunity to improve their net profit

The model improved expected profit to $50,433 Expected dollar-weighted cancel rate decreased Revenues increased Purchases decreased Sales to the outlet store decreased

The Impact of b and on Expected Profit

Because it is cheaper to buy an item and have it on hand than it is to pay the penalty for not taking it from backup.

The Impact of b and on Commitment

If it is unlikely that we run out in the first period using the commitment that is optimal when no backup is available, then the optimal commitment with backup is greater than the optimal commitment when no backup is offered

The Impact of Commitment on Expected Profit

The Impact of the Structure of Demand on the Value of Backup Contracts

The Impact on the Manufacturer

Conclusions

Backup is an important practice in merchandising of fashion goods that can benefit both the retailer and the manufacturer

A retrospective parallel test established the potential impact of the model at Catco

Adjusting the order commitment in response to the offered can have significant impact on the expected profit

Thank You