Multi-objective modeling of production and pollution routing problem with time window: A self-learning particle swarm optimization approach

•Integration of two issues of vehicle routing problem, namely, production routing and pollution routing.•Multi-period multi-vehicle production and pollution routing problem with time window is formulated.•Multi-objective formulation with the objectives of minimization of cost and minimization of carbon emissions.•SLPSO algorithm is enhanced in multi-objective framework.•Comparison of the proposed algorithm with NSGA-II through a case study. Production routing and pollution routing problems are two important issues of vehicle routing problem (VRP) of the supply chain planning system. Both determine an optimum path for the vehicle, in addition, production routing problem (PRP) deals with production and distribution whereas pollution routing problem deals with carbon footprint. In this paper, we develop a VRP that simultaneously considers production and pollution routing problems with time window (PPRP-TW). The proposed PPRP-TW is a NP-hard problem concentrating to optimize the routing problem over the periods. A fleet of identical capacitated vehicles leave from a production plant to a set of customers scattered in different locations. The transportation part of PPRP-TW is concerned with carbon footprint. Thus, a multi-objective multi-vehicle PPRP-TW (MMPPRP-TW) is formulated with two objectives: minimization of the total operational cost and minimization of the total emissions (equivalently, minimization of the fuel consumption). A hybrid Self-Learning Particle Swarm Optimization (SLPSO) algorithm in multi-objective framework is proposed to solve the MMPPRP-TW. To establish superior computational efficiency of hybrid SLPSO algorithm, a comparison with the well-known Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is performed.