Level-based multi-objective particle swarm optimizer for integrated production scheduling and vehicle routing decision with inventory holding, delivery, and tardiness costs

Integrated optimisation of production scheduling and distribution decision is necessary for reducing the whole cost of the supply chain in the make-to-order business environment. This paper studies a new integrated production scheduling and vehicle routing problem (IPSVRP) with inventory holding, delivery, and tardiness costs. The considered IPSVRP is modelled as a triple-objective optimisation problem, where the first objective aims to obtain the minimal total holding cost in the inventory, the second one attempts to achieve the minimal total travelling cost, and the third one tries to acquire the minimal total tardiness cost. To obtain a set of diverse non-dominated solutions in the Pareto-optimal front of the problem, we first derive several key structural properties used to provide necessary conditions for any solution to be Pareto-optimal through theoretical investigation. Based on the derived structural properties, a level-based multi-objective particle swarm optimizer (LMPSO) is subsequently designed. The performance of LMPSO is analysed by conducting a set of experiments, and its superiority is verified through comparing with other optimisation algorithms. Moreover, the convergence behaviour of LMPSO is also investigated, and the experimental results prove that it has the ability to achieve a set of non-dominated solutions proximity to the true Pareto front.