The harmony search for the routing optimization in fourth party logistics with time windows

Recently, fourth party logistics (4PL) is receiving more and more attentions in manufacturing and retail industries. However, the research on the fourth party logistics routing problems (4PLRP) has just begun. In this paper, the mathematical model of the point to point single task path optimization of 4PLRP with time windows (4PLRPTW) is established based on multi-graph. The objective is to find minimum cost routes from the start node to the destination node within the pre-specified time windows. A recently-developed meta-heuristic optimization method, harmony search, is suggested for solving 4PLRPTW. The results of the numerical experiments demonstrate that the harmony search is effective and could find near optimal solution within the reasonable amount of time and computation.