Abstract: Bundling refers to the marketing strategy of offering two or more products or services as a specially priced package. It is widely adopted by manufacturers and retailers, as it reduces production and transaction costs, captures more consumer surplus, achieves economies of scale, and raises entry barriers for competing firms.
This paper aims to investigate how a monopolistic firm determines the composition and pricing of multiple bundles. Component suppliers provide the retailer with m categories of components, each containing n products of distinct quality levels. The retailer selects appropriate products from the upstream component portfolio to bundle and sells to heterogeneous consumers, with the goal of maximizing profits. In this paper, we assume that each bundle must include exactly one component from each category, that is, the m categories of components are assembled in a 1∶1∶…∶1 ratio, resulting in a total of n^m technically feasible bundled products available for the retailer to choose from. Considering that consumers exhibit heterogeneous perceived quality toward bundled products, this paper explores the retailer’s optimal bundle design and pricing strategies under two scenarios: super-additive perceived quality and sub-additive perceived quality.
The customer’s demand across different bundles is developed based on the utility maximization theory, and a mixed integer non-linear program is proposed to solve this problem. Firstly, a two-step solution approach is developed to obtain the optimal decisions of the retailer: in the first stage, the optimal prices can be obtained based on the assumption that the composition and assortment of bundles are known; in the second stage, the optimal composition and assortment of bundles can be recognised using the optimal price generated in the first step. Secondly, we propose an efficient algorithm to solve the problem based on the optimal properties. Finally, the validity of the algorithm is tested and the effect of perceived quality and consumer quality valuation on the retailer’s decisions is examined by numerical analysis.
The results reveal the following key findings: (1)The optimal assortment of bundles consists of the Pareto frontier of all feasible bundles, and the components constituting the optimal bundles also lie on their respective Pareto frontiers. Additionally, the optimal set of bundles depends only on the cost/perceived quality ratios of the bundles and is independent of the distribution of consumers’ valuation for quality. (2)The optimal prices of bundles, the retailer’s market share and profits are all monotonically decreasing functions of b. Specifically, when most consumers in the market have a low marginal valuation for quality, the retailer will reduce the selling price to stimulate consumption. However, this price reduction does not lead to an increase in market share. Under the dual impact of declining marginal revenue and reduced demand, the retailer’s profits decrease. (3)The optimal prices of bundles and the retailer’s profits both increase in α, which implies that when consumers have a higher perceived quality, the retailer can appropriately raise product prices to capture more consumer surplus.
The above conclusions provide the following practical implications for retailers in bundle design and pricing: (1)In making pricing decisions, retailers should take into account not only the cost and quality of the bundles but also the distribution of consumers’ quality valuation. (2)In the design of bundles, replacing dominated components with dominant ones can either improve the qualities of the bundles or reduce their costs, thereby increasing profits. (3)For retailers, the key to securing stable future returns lies in enhancing consumers’ perceived quality of their products rather than continuously expanding the scale of their product lines.
Notably, to the best of our knowledge, this is the first study to provide practitioners with optimization approaches for the design and pricing of vertically differentiated bundles. However, this research has certain limitations that are worth noting. For instance, consumers may engage in dynamic substitution if their first-choice bundle is out of stock. Therefore, a promising direction for future research is to solve the problem of optimal composition and prices of multiple bundles under stockout-based substitution.

Key words: vertically differentiated products, bundle design, pricing, mixed non-linear integer program

摘要： 研究垄断零售商在满足技术约束条件下的垂直差异化产品的捆绑设计和定价问题。基于效用最大化理论构建了捆绑产品的需求函数,以期望利润最大化为目标构建了解决零售商捆绑设计和定价问题的非线性整数规划模型。首先根据模型的特点设计了两阶段求解法以获取零售商的最优决策,然后利用捆绑产品最优集的性质设计了凸增包络算法以解决零售商的捆绑设计和定价联合决策问题,最后通过数值分析的方法,验证了模型和算法的可行性,并研究了顾客单位质量估值分布和感知质量对零售商的最优决策的影响。结果表明,零售商的捆绑产品最优集由所有满足技术约束的捆绑产品的Pareto前沿构成,且构成最优捆绑产品的组件产品均位于该类组件产品的Pareto前沿上;此外,捆绑产品的最优价格及零售商的利润随着顾客感知质量和单位质量估值的增加而增加。

关键词: 垂直差异化产品, 捆绑设计, 定价, 非线性整数规划