Vehicle Routing in a Multi-product Supply Chain using Populated Simulated Annealing Algorithm

This paper aims to examine the scheduling of vehicles in a multi-product supply chain regarding to the mutual relationship between the transportation and the manufacturing units. The integration level in the supply chain consists of a manufacturer and its first tier suppliers, which are linked by a transportation fleet. The problem is determining orders allocation to the suppliers, orders production sequence at the suppliers, orders allocation to the vehicles, and orders transportation priority, in order to minimize the sum of orders delivery time. This issue has not been discussed in the literature, so far. At first, the mathematical model of the problem is presented, then the NP-Hardness of the problem is demonstrated. For solving the problem, a new combination of genetic algorithm and simulated annealing algorithm, named as Populated Simulated Annealing algorithm (PSA) is proposed. For verifying the PSA, its results are compared to results of simulated annealing algorithm (SA) and developed version of DGA algorithm, proposed for the nearest problem in the literature to our problem. Furthermore, relaxing some hypothesis, the results of PSA are compared to DGA results. All of the comparisons show that PSA is more efficient than the other algorithms. Finally, comparison of PSA with exact solution for small size problems demonstrates its proper efficiency.