Incorporating contracts with retailer into product line extension using Stackelberg game and nested bi-level genetic algorithms

C. K. Kwong, Yi Xia, C. Y. Chan, W. H. Ip

Research output: Journal article publicationJournal articleAcademic researchpeer-review

10 Citations (Scopus)


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.

Original languageEnglish
Article number106976
JournalComputers and Industrial Engineering
Publication statusPublished - Jan 2021


  • Bi-level optimization
  • Coordination contracts
  • Nested bi-level genetic algorithm
  • Product line design
  • Stackelberg game

ASJC Scopus subject areas

  • General Computer Science
  • General Engineering


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