An Optimization Of Inventory And Routing Problems Based On Lagrangian Relaxation Approach

Inventory and transportation are the two most important links in the logistics system,in the total cost of logistics system in the largest proportion,between these two aspects of interests exist paradox phenomenon,must take it as a whole.To optimize the inventory routing problem(inventory routing problem,referred to as IRP)is a hot research problem international transportation and operational research,the problem is a typical NP-hard problem solving complexity greatly,at the same time,inventory and transportation and relates to the real life in all walks of life,study the deterministic demand of(a distribution center corresponding to multiple customers)inventory routing problem,the transportation cost(related to distribution volume and the distance of vehicle transport related costs)and customer shortage cost as the optimization goal,thus effectively reducing the total cost of the system,so that customer satisfaction significantly enhance the main content.As follows:The first chapter is the introduction part.A large number of domestic and international literatures are reviewed in this chapter.From the research background and significance,research status,research content and technical flow chart were analyzed.The second chapter is the relevant theoretical basis of inventory routing problem.It introduces the definition of inventory routing problem the classification of inventory routing problem,research on the characteristics of inventory routing problem(the research object,decision-making target,cost factors and limiting factors),compare the inventory routing problem with vehicle routing problem,summarizes the inventory strategy and distribution strategy of inventory routing problems.The third chapter establishes the mathematical model of inventory routing problem.The hypothesis and related symbols defined in this model,the inventory routing problem is described,and then set up a single cycle to determine the needs of inventory routing problem mathematical model.The fourth chapter design algorithm.Considering the inventory routing problem is a NP-hard problem,analyzes on the algorithm selection,the final design of Lagrange relaxation algorithm.Lagrange relaxation algorithm theory were described,and the subgradient algorithm for the design of Lagrange.The fifth chapter presents numerical examples.With a small scale example and a larger scale of the real example of the mathematical model and Lagrange relaxation algorithm was verified.The results verified the rationality of the algorithm and the validity and feasibility of the model.The sixth chapter is summary and prospect.The whole research contents of the dissertation are a summary of the thesis and the future direction of development and research trends are prospected.