Abstract
In this work, mathematical models are formulated in order to investigate the effect of the additional order on the expected total profit of a two-stage supply chain. A multi-period buyback contract between a supplier and a retailer under the demand uncertainty is considered. Under the contract, an advance order is submitted to the supplier in advance when the demand is unknown, and an additional order can be made at the beginning of each period after the previous period demand is realized. The impact of the coordination on the supply chain’s expected total profit is also considered. The results show that the additional order does not always increases the supply chain profit. The additional order increases the supply chain profit only when both the retailer and supplier are coordinated. Under the decentralized system with the buyback contract, the retailer tends to order less in an advance order to reduce the risk. This leads to the higher cost due the additional order after the demand is realized. As a result, it is lowers the supply chain profit. Moreover, the sensitivity analysis is performed using numerical studies in order to observe the behavior of the expected total profit of the supply chain.
Highlights
Mathematical models are constructed with the expected total profit of the supply chain under the uncertainty demand for a multi-period buyback contract between one supplier and one retailer
Quantities cannot be written explicitly in the closed form for the advance order only, we provide the optimal order conditions as shown in Theorems 1 and 2, which are concerned with the advance ordering policies under the decentralized and the centralized systems, respectively
Mathematical models models have have been been formuformulated with the expected total profit of the supply chain
Summary
Every company in the supply chain needs to achieve its own goal, which is to satisfy the customer’s demand while maximizing profit or minimizing costs. The order with a regular price is submitted during the selling season He and Zhao analyzed the behavior of an APD contract for a selling season and found that the APD with a revenue sharing contract could coordinate the supply chain with both supply and demand uncertainties as well as achieve flexible profit allocation [7]. This work studies a multi-period buyback contract between a supplier and a retailer under the demand uncertainty in order to investigate the effect of the additional order on the supply chain’s expected total profit. They have not obtained the advance quantities for a multi-period contract [10] He and Zhao considered the advance-purchase discount contract allowing two order opportunities under the uncertainty of supply and demand for a single period only [7].
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