This study explores the problem of optimally dynamic joint decisions: replenishment quantity, retail price and depletion time, in a vertically decentralized single-retailer and single-supplier supply chain over a dynamic multi-period planning horizon, subject to multivariate demand function and deteriorating goods with shortages allowed and with no consideration of fixed costs. This research uses a calculus-based formulation coupled with dynamic programming techniques to solve the channel-wide profit maximization under price-only contract and consignment contract respectively. The analysis reveals that the consignment contract can significantly achieve higher channel-wide profit than the price-only contract for the dynamic decentralized channel.
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Liang‐Tu Chen (2017) studied this question.
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