A BI-OBJECTIVE MATHEMATICAL MODEL FOR INVENTORY-DISTRIBUTION-ROUTING PROBLEM UNDER RISK POOLING EFFECT: ROBUST META-HEURISTICS APPROACH

In this paper, a bi-objective model is proposed to study LocationRouting-Inventory (LRI) problem considering risk pooling and soft time window. The first objective function aims to minimize the costs of establishing Distribution Centers (DCs), transportation, ordering, and inventory holding; the second one minimizes the earliness and lateness of vehicles. Considering the large-scale instances of this problem is NP-Hard, three meta-heuristic algorithms, such as NSGA-II, MOPSO, and Pareto Envelope-based Selection Algorithm (PESA)-II, are proposed. These algorithms are compared, and NSGA-II outperforms the other algorithms. Afterward, the proposed NSGA-II is compared with the exact method. The computational results show that the exact method only outperforms this algorithm with around 6% gap in the first objective function on average. Eventually, a sensitivity analysis has been conducted with respect to the number of DCs and vehicles. This shows that total costs, and total earliness and lateness increase and decrease in both cases, respectively.