Post on 11-Feb-2016
description
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