A self-adaptive Gaussian mutation-based arithmetic optimiser algorithm for integrated production scheduling and vehicle routing problem in the distributed manufacturing environment

In response to the challenges posed by economic globalisation and increasing customer demands, enterprises are compelled to adapt and refine their production models and operational objectives, which motivates this paper to address the integrated production scheduling and vehicle routing problem in the distributed manufacturing environment (IPSVRP-DME). The objective is to simultaneously minimise both total energy consumption and total earliness/tardiness. Initially, a mixed integer programming model is proposed to address small-scale problems using Gurobi. Considering the NP-hardness of the problem, a novel Self-adapted Gaussian Mutation-based Arithmetic Optimiser Algorithm (SGMAOA) is developed to handle medium-scale and large-scale instances. To address the complexity of decision-making, an innovative two-level encoding method that encompasses four decision dimensions is introduced. Additionally, an incremental repair strategy is devised to rectify infeasible solutions caused by unreasonable delivery batching, while a time relaxation strategy is proposed to further enhance service levels without compromising energy consumption. Comparative experiments are conducted to demonstrate the effectiveness of SGMAOA, which is benchmarked against five prominent metaheuristics. In addition, a specific example is applied for the discussion of managerial applications and to illustrate the practicality of the proposed model and solution method.