Mathematical programming and solution approaches for minimizing tardiness and transportation costs in the supply chain scheduling problem

A new integrated supply chain scheduling and vehicle routing problem is developed here. The objective is to minimize the total weighted tardiness and transportation costs, with respect to fixed costs of vehicles and travelling costs of the network. The problem is strong NP-Hard. A mixed integer linear programming and two solution approaches, where one exact procedure based on Branch-and-Bound (B&B) algorithm, and one meta heuristic genetic algorithm (GA) are proposed to solve this problem. Computational experiments are run for both small and large-scale analyses. The results of small-scale analysis indicate that the proposed B&B algorithm provides a more efficient performance, with respect to both number of optimally-solved problems and run times, in comparison with that of the CPLEX software. The results indicate the capability of meta-heuristic GA, in solving real-life large-scale problems in an efficient manner.