Study On Solving The Location Routing Problem With Stochastic Demands Based On Simulated Annealing Algorithm

With the rapid development of the social economy, the market competition is becoming increasingly fierce. The key for an enterprise to establish its competitive advantage is turning from saving raw materials and improving labor productivity to establishing an efficient logistics system. In today's increasingly globalized economy, as an important part of the third type of profit and the tertiary industry, the modern logistics is receiving more and more attention.As the basic element of the logistics operation, the location selecting of the logistics center is very important to be optimized and studied, and the study for this issue is location allocation problem (LAP); while as an important part of logistics system, the vehicle routing problem also has a great impact on the cost of the logistics systems, the problem to consider and optimize the two aspects is the location routing problem (LRP). The LRP solves the logistics system problem in an integrated version, so it can reduce the total cost of logistics systems greatly.This paper studies the location routing problem with stochastic demands (LRPSD), which is an extension of the above location routing problem. In this problem, the demand of the customer is not known precisely in advance but is described by an identical probability distribution. The uncertainty of the demand and the capacity constraint on the vehicle may result in a route failure when serving a certain customer for a vehicle, so the vehicle must return to the depot to load (or unload) and then resume service to the remaining customers. An upper bound for the times of the route failure and the mathematical model with vehicle fixed cost and facility cost are set up for this problem.Because of the NP-hard attribute of the problem, the simulated annealing (SA) algorithm is developed, and the C++ and matlab program are designed to realise the algorithm for solving the problem. The data for testing the problem is transformed from the international standard Solomon 25 customers test data for vehicle routing problem. In the process of solving the problem, the space filling curves and the simulated annealing algorithm is used to solve the location allocation problem, and then the simulated annealing algorithm is used to solve the vehicle routing problem with stochastic demands, and at last the output of the latter is used as an input of the location phase to optimize the selection of the facility and achieve the final optimal solution of this problem finally.In this paper, the statistical analysis of the results of each step is done, and the results show that: for the location routing problem with stochastic demands in a certain scale, the method for solving it is fast, accuracy and stable, so it proves that the method for solving the location routing problem with stochastic demands is feasible and effective. Finally, the supplementary explanation for the problem extends the applicability of the problem to common problems, which has the vital significance to the apply research and practice of logistics system integration theory under the actual environment.