Single-Manufacturer Multi-Retailer Supply Chain Models with Discrete Stochastic Demand

Yaqing Xu, Jiang Zhang, Zihao Chen and Yihua Wei
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Yaqing Xu: School of Economics and Management, Xidian University, Xi’an 710071, China
Jiang Zhang: Robert B. Willumstad School of Business, Adelphi University, Garden City, NY 11530, USA
Zihao Chen: School of Economics and Management, Xidian University, Xi’an 710071, China
Yihua Wei: School of Management, Shanghai University, Shanghai 200444, China

Sustainability, 2021, vol. 13, issue 15, 1-13

Abstract: Although there are highly discrete stochastic demands in practical supply chain problems, they are seldom considered in the research on supply chain systems, especially the single-manufacturer multi-retailer supply chain systems. There are no significant differences between continuous and discrete demand supply chain models, but the solutions for discrete random demand models are more challenging and difficult. This paper studies a supply chain system of a single manufacturer and multiple retailers with discrete stochastic demands. Each retailer faces a random discrete demand, and the manufacturer utilizes different wholesale prices to influence each retailer’s ordering decision. Both Make-To-Order and Make-To-Stock scenarios are considered. For each scenario, the corresponding Stackelberg game model is constructed respectively. By proving a series of theorems, we transfer the solution of the game model into non-linear integer programming model, which can be easily solved by a dynamic programming method. However, with the increase in the number of retailers and the production capacity of manufacturers, the computational complexity of dynamic programming drastically increases due to the Dimension Barrier. Therefore, the Fast Fourier Transform (FFT) approach is introduced, which significantly reduces the computational complexity of solving the supply chain model.

Keywords: decentralized supply chain; multiple retailers; discrete demand; Fast Fourier Transform (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2021
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