Prioritized K-mean clustering hybrid GA for discounted fixed charge transportation problems

The problem of allocating different types of vehicles for transporting a set of products in an existing transportation network, to minimize the total transportation costs, is considered. The distribution network involves a heterogeneous fleet of vehicles each with the given capacity and with a variable transportation cost and a fixed cost with a discounting mechanism. Due to nonlinearity of the discounting mechanism, a nonlinear mathematical programming model is developed. A prioritized K-mean clustering encoding is introduced to designate the distribution depots distances, their demands, and the vehicles' capacity. Using this priority clustering, a heuristic routine is developed by which heavy capacity vehicles are assigned to the longer distance depots. Then the proposed heuristic is incorporated into a new GA to construct a hybrid GA. Through an extensive computational experiment, first the algorithm parameters are tuned using “factorial experimental designs”, and then the efficiency of the proposed algorithm is compared with the powerful package of the CPLEX solver (OPL 12.3.0.1 Model) and two existing algorithms. The results are revealed that the proposed algorithm can provide superior solutions with the minimal computational effort.