Integrated production-distribution planning with make-to-order production system considering Stackelberg competition and discount for a Furniture Company

Nowadays, in the competitive global market, increasing market share is the main objective of the most manufacturers, however, customization, service speed, customer satisfaction, and environmental problems are vital factors that manufacturers ought to consider to expand their market share.so, the supply chain management can be applied as a proper approach to optimize these factors in whole supply chain to benefit the supply chain members. in this way, the current paper addresses an integrated production and distribution model with combination of stackelberg competition and make-to-order production system in different periods. in addition, this model wants to investigate how discounts impact the chain's profits with presence of competition and make-to-order production system. this study uses a modified non-dominated sorting genetic algorithm ii (nsga-ii) approach to solve the medium and large cases model because of the np-hardness feature. additionally, the model is applied to furniture company to demonstrate its efficacy and validity and results are provided. according to the obtained results, the modified algorithm has better performance in solving model in medium and large-scale cases. the proposed model would be beneficial to increase network efficiency by integrating productiondistribution planning.