Multi-objective optimization for the reliable pollution-routing problem with cross-dock selection using Pareto-based algorithms

Cross-docking practice plays an important role in improving the efficiency of distribution networks, especially, for optimizing supply chain operations. Moreover, transportation route planning, controlling the Greenhouse Gas (GHG) emissions and customer satisfaction constitute the major parts of the supply chain that need to be taken into account integratedly within a common framework. For this purpose, this paper tries to introduce the reliable Pollution-Routing Problem with Cross-dock Selection (PRP-CDS) where the products are processed and transported through at least one cross-dock. To formulate the problem, a Bi-Objective Mixed-Integer Linear Programming (BOMILP) model is developed, where the first objective is to minimize total cost including pollution and routing costs and the second is to maximize supply reliability. Accordingly, sustainable development of the supply chain is addressed. Due to the high complexity of the problem, two well-known meta-heuristic algorithms including Multi-Objective Simulated-annealing Algorithm (MOSA) and Non-dominated Sorting Genetic Algorithm II (NSGA-II) are designed to provide efficient Pareto solutions. Furthermore, the e-constraint method is applied to the model to test its applicability in small-sized problems. The efficiency of the suggested solution techniques is evaluated using different measures and a statistical test. To validate the performance of the proposed methodology, a real case study problem is conducted using the sensitivity analysis of demand parameter. Based on the main findings of the study, it is concluded that the solution techniques can yield high-quality solutions and NSGA-II is considered as the most efficient solution tool, the optimal route planning of the case study problem in delivery and pick-up phases is attained using the best-found Pareto solution and the highest change in the objective function occurs for the total cost value by applying a 20% increase in the demand parameter.