A bi-objective two-echelon pollution routing problem with simultaneous pickup and delivery under multiple time windows constraint

Abstract

Pollution emitted by a vehicle can be checked by reducing the distance traveled and through operational adjustments. Optimized route and simultaneous pickup and delivery in a vehicle routing problem (VRP) can achieve the same. This paper investigates a two-echelon pollution routing problem with simultaneous pickup and delivery by considering multiple time windows (2E-PRPSPD-MTW) for customers’ visit. The first echelon consists of depots and intermediate depots (called satellites), whereas the second echelon consists of the satellites and customers. Two fleets (one for each echelon) of heterogeneous vehicles accomplish pickup and delivery operations. The 2E-PRPSPD-MTW is developed in a bi-objective framework, focusing on minimization of both travel time and fuel consumption. The proposed bi-objective 2E-PRPSPD-MTW is an NP-hard problem. So, in order to optimize it, multi-objective variable neighborhood search (MOVNS) is modified and used. In this process, six operators are proposed in order to improve the neighborhood structure. The suggested operators explore the entire solution space to find the near optimal solution. With the aim of providing much richer insights, the efficacy of the proposed method and mathematical formulation is demonstrated through numerical experiment for a number of instances varying from small to large scale.