Abstract Nowadays, product manufacturers commonly establish coordination with members of their distribution channels by making contracts with them. The contract may affect product design to a certain extent. Therefore, manufacturers should consider this in the product planning stage. Some analytical studies have investigated the effect of the contract scheme on the product line strategy. However, how contracts affect the real-world product line design in terms of product attribute settings and consumer choice behaviors is still unclear. Herein, a methodology of incorporating contracts for establishing coordination with distribution channel members into the product line extension is proposed. The Stackelberg game theory is adopted to formulate joint optimization models that involve a manufacturer and a retailer. Four common types of contracts are considered in the models, including wholesale-price (WP), revenue-sharing (RS), quantity-discount (QD), and retail-price-maintenance (RPM) contracts. Then, we adopt a nested bi-level genetic algorithm to identify the joint optimization for the product line extension. A case study of smartphone design is conducted to illustrate the applicability of the proposed methodology; thus, we identify the effects of different contract schemes and their parameter settings on the optimal product design, pricing, market shares, and both-side profits. The case study showed that if a QD parameter is relatively high, the manufacturer should add a lower-quality product in the product line. Meanwhile, an intermediate value of the QD parameter would maximize the manufacturer’s profits and the total profits. An RPM contract leads to a high-quality design for the new product to be launched than other contracts. The novelty of this study is that it incorporates retail contracts into the real-world product line design and builds a joint optimization model to solve it.

中文翻译：

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使用 Stackelberg 游戏和嵌套双层遗传算法将与零售商的合同纳入产品线扩展

摘要 如今，产品制造商通常通过与分销渠道成员签订合同来与其分销渠道成员建立协调。合同可能会在一定程度上影响产品设计。因此，厂商在产品规划阶段就应该考虑到这一点。一些分析研究调查了合同方案对产品线战略的影响。然而，合同如何在产品属性设置和消费者选择行为方面影响现实世界的产品线设计仍不清楚。在此，提出了一种将与分销渠道成员建立协调的合同纳入产品线扩展的方法。采用 Stackelberg 博弈理论来制定涉及制造商和零售商的联合优化模型。模型中考虑了四种常见的合同类型，包括批发价格 (WP)、收入分成 (RS)、数量折扣 (QD) 和零售价格维护 (RPM) 合同。然后，我们采用嵌套的双层遗传算法来识别产品线扩展的联合优化。进行了智能手机设计案例研究，以说明所提出方法的适用性；因此，我们确定了不同合同方案及其参数设置对最优产品设计、定价、市场份额和双方利润的影响。案例研究表明，如果 QD 参数相对较高，制造商应在产品线中添加质量较低的产品。同时，QD 参数的中间值将使制造商的利润和总利润最大化。与其他合同相比，RPM 合同可以为要推出的新产品提供高质量的设计。本研究的新颖之处在于，它将零售合同纳入现实世界的产品线设计，并构建了联合优化模型来解决它。