Modeling the Distribution and Production Game in the Green Production Routing Problem, Using Bi-Level Fuzzy Goal Programming Approach

The main purpose of this paper was to provide a mathematical model of the production routing problem by applying environmental protection policies. The target company consists of two independent departments of production and distribution. These subsets are managed locally, and the two-way communication between them forms a Stackelberg game. The first subset (distribution company) is the first level decision maker and determines the route for vehicles and the amount of product transfer to each customer. The distribution company pursues two goals, minimizing costs of distribution, maintenance, and vehicle emissions. As the limited production capacity prevents the manufacturer from meeting all the demands of the distribution sector, the distribution company can procure products from the subsidiary manufacturing company or provide alternative products by paying more from other manufacturers, so in this case, it will receive compensation from the manufacturer. At a lower level, the second subset (manufacturer) schedules production with the aim of minimizing production and maintenance costs. Finally, the multi-objective bi-level problem-solving algorithm is described and developed based on the bi-level fuzzy goal programming approach. Based on numerical analysis results, the utility of final decisions regarding both the distributor and manufacturer perspective is sensitive to the cost of alternative products and also compensation. In order to improve the agreement between the first and second level decision-makers, the proposed algorithm considers tolerances that can be adjusted to achieve more executive plans. Numerical results show that the answers of the bi-level fuzzy goal programming method are equal or very close to the worst answer.