Abstract
This paper studies a single-period supply chain with a buy-back contract under a Stackelberg game model, in which the supplier (leader) decides on the wholesale price, and the retailer (follower) responds to determine the retail price and the order quantity. We analytically investigate the decentralized retailer’s optimal decision. Our results demonstrate that the retailer has a unique optimal simultaneous decision on the retail price and the order quantity, under a mild restriction on the demand distribution. Moreover, as it can be shown that the decentralized supply chain facing price-sensitive random demand cannot be coordinated with buy-back contract, we propose a scheme for the system to achieve Pareto-improvement. Theoretical analysis suggests that there exists a unique Pareto-equilibrium for the supply chain. In particular, when the Pareto-equilibrium is reached, the supply chain is coordinated. Numerical experiments confirm our results.
Highlights
Buy-back contracts have become very prevalent in many industries; see [1] for some practical examples
Pasternack [2] suggests that in a singleperiod supply chain with an exogenously set retail price, channel coordination can be achieved under the buy-back contract where the supplier compensates the retailer with a partial refund for unsold items
We investigate the decision making of each member of a single-period supply chain with a buy-back contract under a Stackelberg game, where the supplier, as the leader, determines the wholesale price to the retailer, while the retailer, as the follower, responds to decide the retail price and the number of units to purchase from the supplier
Summary
Buy-back contracts have become very prevalent in many industries; see [1] for some practical examples. Emmons and Gilbert [9] investigate the properties of each member’s optimal decision in a single-period supply chain under a buy-back contract, by assuming that the demand has a linear and multiplicative form and follows uniform distribution. Arcelus et al [12] introduce to the buy-back model the existence of a secondary market where the supplier can sell the leftover items at a price exceeding the salvage value They investigate the optimal policy of each member in the supply chain with different demand forms and present closed-form solutions for the decentralized retailer’s decision.
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