Consider a two-tier supply chain with one manufacturer and one retailer who interact in a single selling season. The manufacturer sells a product to the retailer, who in turn sells in the market. Demand E is uncertain with cumulative distribution function F (·) and probability density function f (·). Since the production lead time is much longer than the selling season, the retailer must place a single order before demand is realized and cannot replenish her inventory during the season. The retailer sells the product at an exogenous and fixed retail price r. The manufacturer produces the product at a unit cost of c. The manufacturer uses a linear sales rebate contract and determines the following contract terms: For each unit ordered, he charges the retailer a wholesale price w, and for each unit sold, he pays the retailer a rebate s. Assume that the product has zero salvage value at the end of the season, and the inventory holding cost during the season is negligible. Characterize the condition on (w, s) such that the sales rebate contract coordinates the supply chain. Is this coordinating contract implementable? Show your steps and reasoning.
Consider a two-tier supply chain with one manufacturer and one retailer who interact in a single selling season. The manufacturer sells a product to the retailer, who in turn sells in the market. Demand E is uncertain with cumulative distribution function F (·) and probability density function f (·). Since the production lead time is much longer than the selling season, the retailer must place a single order before demand is realized and cannot replenish her inventory during the season. The retailer sells the product at an exogenous and fixed retail price r. The manufacturer produces the product at a unit cost of c. The manufacturer uses a linear sales rebate contract and determines the following contract terms: For each unit ordered, he charges the retailer a wholesale price w, and for each unit sold, he pays the retailer a rebate s. Assume that the product has zero salvage value at the end of the season, and the inventory holding cost during the season is negligible. Characterize the condition on (w, s) such that the sales rebate contract coordinates the supply chain. Is this coordinating contract implementable? Show your steps and reasoning.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter11: Simulation Models
Section: Chapter Questions
Problem 47P
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Question
Consider a two-tier supply chain with one manufacturer and one retailer who
interact in a single selling season. The manufacturer sells a product to the retailer, who in
interact in a single selling season. The manufacturer sells a product to the retailer, who in
turn sells in the market. Demand E is uncertain with cumulative distribution function F (·)
and probability density function f (·). Since the production lead time is much longer than
the selling season, the retailer must place a single order before demand is realized and cannot
replenish her inventory during the season. The retailer sells the product at an exogenous
and fixed retail price r. The manufacturer produces the product at a unit cost of c. The
manufacturer uses a linear sales rebate contract and determines the following contract terms:
For each unit ordered, he charges the retailer a wholesale price w, and for each unit sold, he
pays the retailer a rebate s. Assume that the product has zero salvage value at the end of
the season, and the inventory holding cost during the season is negligible. Characterize the
condition on (w, s) such that the sales rebate contract coordinates the supply chain. Is this
coordinating contract implementable? Show your steps and reasoning.
and probability density function f (·). Since the production lead time is much longer than
the selling season, the retailer must place a single order before demand is realized and cannot
replenish her inventory during the season. The retailer sells the product at an exogenous
and fixed retail price r. The manufacturer produces the product at a unit cost of c. The
manufacturer uses a linear sales rebate contract and determines the following contract terms:
For each unit ordered, he charges the retailer a wholesale price w, and for each unit sold, he
pays the retailer a rebate s. Assume that the product has zero salvage value at the end of
the season, and the inventory holding cost during the season is negligible. Characterize the
condition on (w, s) such that the sales rebate contract coordinates the supply chain. Is this
coordinating contract implementable? Show your steps and reasoning.
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