Mathematical programming and grey wolf optimiser for minimising sum of the total due date assignment, maximum tardiness and delivery costs for a supply chain scheduling problem

This paper focuses on the integration of the three most important and practical decisions in a supply chain, including due date assignment, production scheduling and outbound distribution. The issue under consideration is to minimise the summation of maximum tardiness, and due date assignment and batch delivery costs. To provide solution methods, first, two mathematical programming models including one mixed nonlinear model and one mixed linear model to solve it are presented. After these developments, since the problem is NP-hard and solving real problems on a large scale is virtually impossible, the combinational meta-heuristic algorithm based on Grey Wolf optimiser (GWO) and heuristic algorithm for solving the problem are presented. The GWO is a fast and robust algorithm in which the number of parameters that should be controlled is few. In this study, various computational tests have also been used to evaluate the effectiveness of the development methods - Taguchi method to set the parameters, design of experiments to generate the experiments, and analysis of variance to analyse the results. The computational results show that the combinational meta-heuristic method introduced in this paper puts in a high performance.