Integrated production-inventory-routing problem incorporating greenness consideration: A mathematical model and heuristic solver

This research focuses on the integrated production-inventory-routing planning (PIRP) problem, which persuades necessary decisions to study the supply chains (SCs). Previous research studies confirm that corporations coping with production, inventory, and routing problems, can remarkably decrease the total costs and meet the customers' demands efficaciously. Currently, because of severe obligations, corporations must consider environmental factors and cost optimization in their activities. Accordingly, in this article, a green PIRP (GPIRP) is addressed using mixed-integer linear programming (MILP), which simultaneously takes into account the economic and social decisions of the SCs. Furthermore, because the SCs routing-oriented problems belong to the NP-hard categories, we propose a two-phase heuristic solution method; in the first phase, the inventory and production decisions are determined using MILP formulation. The second phase seeks to find optimal vehicle routing and transportation decisions using a genetic algorithm (GA). Two main deals leading to this paper's unique position are to develop a bi-objective MILP model for the GPIRP and present a novel hybrid two-phase heuristic solution method that sequentially utilizes the CPLEX solver and the proposed GA. To validate the computational performance of the proposed solution method, we conduct a case study from the Ahvaz Sugar Refinery Company in Iran to demonstrate the advantages of the formulated model. Moreover, we handle sensitivity analyses to study the effectiveness of the suggested method for the large-sized examples