Vehicle routing problem with partly simultaneous pickup and delivery for the cluster of small and medium enterprises

The transportation service for the cluster of small and medium enterprises (SMEs) is different with traditional vehicle routing problems. In the cluster of SMEs, parts of enterprises are pickup and delivery spots simultaneously, but some enterprises are partly pickup and delivery simultaneously. It is necessary to optimize this transportation service with an effective mathematics and algorithm to reduce transportation costs for manufacturers. However, traditional mathematics models and algorithms are not suitable to solve the vehicle routing problem partly simultaneous pickup and delivery (VRPPSD) because these items mainly focus on the vehicle routing problem with pickup and delivery simultaneously. In this paper, a mathematics operational model is proposed to analyze the transportation service of the cluster companies and to describe transportation processes. A hybrid algorithm which is composed by tabu search, genetic algorithm and local search is used to optimize the operational model. The crossover and mutation contained by genetic algorithm are used to generate neighborhood solutions for tabu search, and the local search is used to improve optimizing solutions. The data of a cluster of SMEs, investigating from Changzhou city, China, are employed to show the validity of our mathematical model and algorithm. The results indicate that our model and hybrid algorithm is effective to solve VRPPSD. In this paper, the satisfied solutions of VRPPSD are found by hybrid algorithm. At the same time, the results also show that carriers with optimal routs can service customers with more profits (increasing 5.6%). The potential saving of transport cost will increase profits of carriers in SMEs. Sensitivity analyses about adjusting service time and rate of new orders are lunched to analyze how these two factors influence the profits of the VRPPSPD in a dynamic case. A bottleneck that influences the profits is found, and there has a shorter service time which could increase gross profits, but not significantly.