Optimal Pricing, Warranty, and Quality Level Decisions in a Competing Dual-channel Supply Chain

Document Type : Research Paper


1 Associate Prof., Faculty of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran.

2 MSc. Student, Faculty of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran.


Objective: The globalization of the economy and the improvement of data innovation has caused the supply-oriented market to alter to the demand-oriented market. Furthermore, organizations ought to prioritize the desires of clients to proceed and survive in the competitive market, which requires the presence of supply chain management. Considering the wide assortment of products and today's competitive market, choosing the correct strategies to provide the required services according to a few primary components such as price, quality level, and the warranty period is one of the most concerns of company managers and dealers. This study sought to consider the increase in the profit of each part of the chain along with providing appropriate services and keeping up product quality, extracting and applying suitable implementation strategies. It also tried to present pricing strategies in a two-echelon supply chain comprised of one manufacturer and two competing retailers, with warranty period, quality, and price-dependent demands.
Methods: The strategies presented and discussed in this research have several implications; in addition; their improvements are practical. The profit functions of the manufacturer and the retailers were maximized under centralized and decentralized approaches. Mathematical models were developed in four distinctive cases (i) two non-cooperative frameworks, (ii) a channel-cooperative framework, and (iii) a global-cooperative framework. The producer intended to maximize his benefit by setting a diverse wholesale price for each of the retailers and the length of the common warranty period. On the other hand, retailers maximized their profit by setting the selling price for consumers. This can be explained through the models related to general cooperation strategies, cooperation within the channel, and non-cooperation (Stackelberg of the leading producer and Stackelberg of the leader retailers), furthermore; the profit function of each case and its formula is presented.
Results: For each case, the values of the main decision variables and the profit of each member of the supply chain were calculated and appeared in a numerical case. Moreover, the total profit was compared with each other through two solution methods i.e., the Mathematica computer program and the Championship Algorithm in sports leagues (LCA). The championship algorithm in sports leagues was presented as a population-based algorithm for worldwide search in continuous space and inspired by sports competitions within the real world. During this algorithm, distinctive solutions that can be given to a problem were compared and each one was improved based on its suitability, last; a solution close to the optimum was selected.
Conclusion: A research gap was recognized by studying the research conducted within the field of pricing, warranty, and product quality using the game theory approach. On the other hand, the models were developed by considering all decision variables at the same time as well as between a manufacturer and two competitive retailers deciding on the retail price to maximize their profit. In this regard, four models of Stackelberg manufacturer leader, Stackelberg retailer leader, participation within the channel, and overall cooperation were considered. In all models, the LCA algorithm resulted in better answers compared with Mathematica software. In this study by investigating four techniques, we realized that the best reply can be achieved through the cooperation strategy which is more profitable than the others. Finally, sensitivity analyses were also performed on various model parameters.


Main Subjects

Aghazadeh, H. & Maleki, H. (2020). Developing a Conceptual Framework of Buyer-Supplier Relationship Quality in the Supply Chain and Prioritizing its key Components: A Meta-Synthesis Method. Industrial Management Journal, 12(4), 578-608. doi: 10.22059/imj.2021.311129.1007785. (in Persian)
Banihashemi, S. A. & Haji Molana, S. M. (2017). Analyzing Bullwhip Effect Sensitivity in a Four-level Supply Chain Using Average Moving Method to Forecast the Demand. Industrial Management Journal, 9(1), 43-58. doi: 10.22059/imj.2017.223681.1007173. (in Persian)
Chakraborty, T., Chauhan, S. S. & Ouhimmou, M. (2019). Cost-sharing mechanism for product quality improvement in a supply chain under competition. International Journal of Production Economics, 208, 566-587.
Chien, Y. H., Zhang, Z. G., Wang, J. & Sheu, S. H. (2020). A note on optimizing practical product warranty via linear pricing. Quality Technology & Quantitative Management, 17(2), 234-253.
Choi, T., Taleizadeh, A. & Yue, X. (2020). Game theory applications in production research in the sharing and circular economy era, International Journal of Production Research, 58(1), 118-127.
Dai, Y., Zhou, S. X., Xu, Y. (2012). Competitive and collaborative quality and warranty management in supply chain. Production and Operations management, 21(1), 129–144.
Dos Santos, R. R. & Guarnieri, P. (2020). Social gains for artisanal agroindustrial producers induced by cooperation and collaboration in agri-food supply chain. Social Responsibility Journal, 17(8), 1131-1149.
Fang, Y. & Shou, B. (2015). Managing supply uncertainty under supply chain Cournot competition. European Journal of Operational Research, 243(1), 156-176.
Farrokhi, M. A. & Rasti-Barzoki, M. (2016). Pricing in a Two-Echelon Supply Chain with Manufacturers’ Competing to Seizing the Market in the Make-to-Order Environment by Using Game Theory. Journal of Industrial Engineering Research in Production Systems, 3(6), 207-219. (in Persian)
Husseinzadeh Kashan, A. H. (2009, December). League championship algorithm: a new algorithm for numerical function optimization. 2009 international conference of soft computing and pattern recognition (pp. 43-48). IEEE
Husseinzadeh Kashan, A. H., Karimiyan, S., Karimiyan, M. & Kashan, M. H. (2012, November). A modified League Championship Algorithm for numerical function optimization via artificial modeling of the “between two halves analysis”. In The 6th international conference on soft computing and intelligent systems, and the 13th international symposium on advanced intelligence systems (pp. 1944-1949). IEEE.
Husseinzadeh Kashan, A., Jalili, S. & Karimiyan, S. (2018). Optimum structural design with discrete variables using league championship algorithm. Civil engineering infrastructures journal, 51(2), 253-275.
Husseinzadeh Kashan, A., Jalili, S. & Karimiyan, S. (2019). Premier league championship algorithm: A multi-population-based algorithm and its application on structural design optimization. In Socio-cultural inspired metaheuristics (pp. 215-240). Springer, Singapore.
Khorshidvand, B., Soleimani, H., Sibdari, S. & Esfahani, M. M. S. (2021). Developing a two-stage model for a sustainable closed-loop supply chain with pricing and advertising decisions. Journal of Cleaner Production, 309, 127165.
Kirmani, A., Rao, A. R. (2000). No pain, no gain: a critical review of the literature on signaling unobservable quality. Journal of Marketing 64 (2), 66-79.
Li, D. & Nagurney, A. (2015). A general multitiered supply chain network model of quality competition with suppliers. International Journal of Production Economics, 170, 336-356.
Li, P., Rao, C., Goh, M. and Yang, Z. )2021(. Pricing strategies and profit coordination under a double echelon green supply chain. Journal of Cleaner Production, 278, 123694.
Li, Q., Sun, H., Zhang, H., Li, W. & Ouyang, M. (2020). Design investment and advertising decisions in direct-sales closed-loop supply chains. Journal of Cleaner Production, 250, 119552.
Liu, B., Shen, L., Xu, J. & Zhao, X. (2020). A complimentary extended warranty: Profit analysis and pricing strategy. International Journal of Production Economics, 229, 107860.
Lu, Z. & Shang, J. (2019). Warranty mechanism for pre-owned tech products: Collaboration between E-tailers and online warranty provider. International journal of production economics, 211, 119-131.
Mirhabibi, S. D. Farsijani, H., Modiri, M., khalili Damghani, K. (2018). Explaining the role of Integrated Supply Chain on Attainment of World Class Manufacturing in Electronic domestic Appliance Industries. Industrial Management Journal, 10(1), 101-120. doi: 10.22059/imj.2018.247134.1007355. (in Persian)
Mohaghar, F., Jolai, F. & Heydari, J. (2020). Modeling a Four Echelon Omni-Channel Supply Chain for Seasonal Product under Stochastic Demand. Industrial Management Journal, 12(2), 206-235. doi: 10.22059/imj.2020.306753.1007759. (in Persian)
Mojibian, F. & Khadivar, A. (2016). Product Pricing Model in Industrial Clusters Using Game Theory Approach (Case Study: Stone Cluster in Tehran). Industrial Management Journal, 8(2), 263-286. doi: 10.22059/imj.2016.60658. (in Persian)
Myerson, R. B. (1997). Game theory: analysis of conflict. Harvard university press.
Nasrollahi, M. & Asgharizadeh, E. (2016). Estimating warranty costs for the manufacturer and buyer based on a new Pro-Rata Warranty policy. Industrial Management Journal, 8(1), 97-112. doi: 10.22059/imj.2016.59601. (in Persian)
Niwas, R. & Garg, H. (2018). An approach for analyzing the reliability and profit of an industrial system based on the cost free warranty policy. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(5), 1-9.
Sadeghi Moghadam, M. R., Taghizadeh Yazdi, M. R. & Noferesti, R. (2022). Designing a Humanitarian Supply Chain Coordination Model for Housing Reconstruction after Floods: An Agent-Based Simulation. Industrial Management Journal, 13(3), 467-491. doi: 10.22059/imj.2021.324747.1007848 (in Persian)
Sadeghi, R., Taleizadeh, A. A., Chan, F. T. & Heydari, J. (2019). Coordinating and pricing decisions in two competitive reverse supply chains with different channel structures. International Journal of Production Research, 57(9), 2601-2625.
Seyyedi, S. H., Amiri, M. & Yousefi Hanoomarvar, A. (2016). Designing a framework for determining the optimal strategy combination on SWOT analysis by fuzzy net present value and game theory. Industrial Management Journal, 8(3), 405-422. doi: 10.22059/imj.2016.61713. (in Persian)
Szmerekovsky, J. G. & Zhang, J. (2009). Pricing and two-tier advertising with one manufacturer and one retailer, European Journal of Operational Research,192(3), 904-917.
Wang, X., Li, L. & Xie, M. (2020(. An unpunctual preventive maintenance policy under two-dimensional warranty. European Journal of Operational Research, 282 (1), 304–318.
Wang, X., Zhao, X., Liu, B., (2020). Design and pricing of extended warranty menus based on the multinomial logit choice model. European Journal of Operational Research, 287 (1), 237–250.
Whitefield, R. I., Duffy, A. H. B. (2012). Extended revenue forecasting within a service industry. International Journal of Production Economics, 141 (2), 505-518.
Wu, Ch. Ch., Chou, Ch. Y., Huang, Ch. (2009). Optimal price, warranty length and production rate for free replacement policy in the static demand market. Omega-The International Journal of Management Science, (37), 29–39.
Wu, S. (2013). A review on coarse warranty data and analysis. Reliability Engineering & System Safety, 114, 1-11. 
Wu, S. (2014). Warranty return policies for products with unknown claim causes and their optimisation. International Journal of Production Economics, 156, 52-61.
Wu, S., Coolen, F. P. & Liu, B. (2017). Optimization of maintenance policy under parameter uncertainty using portfolio theory. IISE Transactions, 49(7), 711-721.
Xie, J. & Wei, J.C. (2009). Coordinating advertising and pricing in a manufacturer–retailer channel. European Journal of Operational Research, 197(2), 785–791.
Xie, J., Neyret, A. (2009). Co-op advertising and pricing models in manufacturer– retailer supply chains. Computers & Industrial Engineering, 56 (4), 1375–1385.
Yazdian, S. A., Shahanaghi, K. & Makui, A. (2016). Joint optimisation of price, warranty and recovery planning in remanufacturing of used products under linear and non-linear demand, return and cost functions. International Journal of Systems Science, 47(5), 1155-1175.