A composite contract for coordinating a supply chain with sales effort-dependent fuzzy demand
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ORIGINAL ARTICLE
A composite contract for coordinating a supply chain with sales effort‑dependent fuzzy demand Xiaobin Wang1 · Zhibing Liu2 · Huiru Chen2 Received: 12 April 2016 / Accepted: 26 December 2017 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract In this paper, we study the coordination problem for a supply chain composed of one supplier and one retailer when the demand is a fuzzy variable that is dependent on sales effort. We find that neither a buyback contract nor a promotion costsharing contract can coordinate the supply chain in this setting. Furthermore, we design a composite contract by combining a buyback contract with a promotion cost-sharing contract to coordinate the supply chain and analyze the coordination conditions. We also draw a performance comparison of the designed composite contract and the price-only contract for the profit maximization of the supply chain and present some extensions. Finally, the main theoretical results and the effectiveness of the designed composite contract are illustrated with numerical examples. We show that the production cost and sensitivity parameter of effort cost have negative impacts on the expected profits of the supplier, the retailer and the entire supply chain, whereas basic demand and the sensitivity parameter of demand stimulation have positive impacts on their profits. Keywords Fuzzy variable · Buyback contract · Promotion cost-sharing contract · Coordination
1 Introduction In this age of heavy business, coordination between upstream and downstream firms in a supply chain has drawn an increasing amount of attention. For example, Ehring [13] shows that the cooperation between Walmart and Proctor & Gamble (P&G) in the market can reduce operating expenses and increase the total profit of the two firms. Furthermore, many researchers and practitioners suggest that good relationships among partners should be a supply chain’s lifeblood, especially in a globalized, scale-driven industry. In fact, if each member of a supply chain maximizes only its own profit, the total supply chain performance may be poor, i.e., double marginalization may occur. Therefore, coordination between upstream and downstream members becomes an essential strategic issue. Moreover, supply chain coordination depends on an upstream or downstream member offering a set of appropriate contracts to another member * Zhibing Liu [email protected] 1
School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, China
College of Mathematics and Physics, Huanggang Normal University, Hubei 438000, China
2
such that members have incentives to take optimal actions for the entire supply chain. Recent literature has thoroughly explored supply chain contracts as a possible mechanism for achieving coordination, with examples including buyback [35], revenue sharing [23, 24], quantity discount [53], promotion cost-sharing contracts [27], price and quantity discount [20, 21, 61], sales rebate [11, 22] and delay in payments
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