Research On Inventory Routing Game Problem Considering Transportation Outsourcing

With the continuous development of the logistics industry,more and more enterprises are looking for ways to further reduce logistics costs,and collaborative logistics emerges as the times require.More and more enterprises are looking for different forms of cooperation in collaborative logistics.Vendor Managed Inventory(VMI)is a typical example.Although cooperation can bring cost savings,the following problem is how to allocate the system cost to make the cooperation sustainable.Based on this background,this paper proposes the inventory routing game in transportation outsourcing(IRG-TO).In this problem,this paper focuses on designing a new allocation method for IRG-TO to allocate IRP(inventory routing problem)cost.Because the core of the IRG-TO problem does not always exist in this paper,the difficulty of this paper is how to deal with the problem when the core of the cooperative game does not exist,and how to achieve the closest distribution scheme to the core by reducing the collective rationality.Firstly,this paper studies the characteristics of the mode of transportation outsourcing,and establishes a mixed integer linear programming model with the objective of minimizing the total cost including the vehicle cost and inventory cost in an optimization period.Different from the general IRP,the vehicle cost in this paper is only related to the number of vehicles used,instead of the fixed cost plus variable cost accounting method.Considering the characteristics of transportation outsourcing,this paper focuses on adding the constraints of vehicle distance and the number of vehicles used per day in the model.The example in this paper is constructed by modifying the benchmark example of IRP and solved on CPLEX.Because the IRP problem is more complex than the general VRP Problem,it is more difficult to solve on CPLEX,and the efficiency is lower.In this paper,by combing the existing IRP effective inequalities,and combining with the characteristics of this model,a total of 8 groups of effective inequalities are designed and used.Through the test of limited examples,the IRP model can effectively reduce the system cost,and test the effective inequality on cplex12.6.0can effectively speed up the solution speed.In the part of cost allocation,considering the different synergetic effects of three kinds of costs(central warehouse inventory cost,customer inventory cost,vehicle use cost)in IRP system,a separate cost allocation method(scam)is designed.In addition,compared with traditional IRG research,this paper also considers the constraint of customers’ willingness to share additional inventory capacity in IRP,That is to say,when allocating the inventory cost of customers,we should focus on the allocation of additional revenue for some customers who have made sacrifices for the major league.Moreover,considering that some cost allocation schemes may not satisfy the individual rationality condition,this paper designs a group of linear programming constraints,and finds the allocation scheme closest to the core by reducing the collective rationality.However,some of the existing allocation methods have their own characteristics in terms of stability,but once the scale is expanded,the sub alliance will encounter a lot of challenges in reality to obtain and solve the allocation scheme.Based on this,this paper considers improving the traditional proportion method to make the allocation scheme simple and fast,and taking into account certain stability requirements.The traditional proportion method considers the weight design based on the limited customer information when allocating the cost.However,this weight can not well explain the synergy effect behind IRG-TO.Therefore,this paper considers the weight allocation cost based on the marginal contribution of customers.The experimental data show that the marginal contribution based proportion method is more stable than the customer information based proportion method in the allocation of IRP cost.In the aspect of stability analysis,this paper analyzes the change of allocation stability from the perspective of customer and central warehouse,which are customer location distribution and expense balance cycle.Through the comparison of the distribution results of different cases,it is found that the core cases with uniform distribution account for 70%,and the total unstable average value is 4.52%,while the core cases with uneven distribution account for 50%,and the total unstable average value is 11.31%.Therefore,for customers,as far as possible to choose close location of customers to work together can effectively improve the stability of distribution.In addition,from the perspective of central warehouse,the average value of distribution instability is 9.63% under one optimization cycle,while the average value of cost distribution instability is 6.13% under two optimization cycles.Therefore,appropriately extending the expense balance cycle is also one of the effective means to improve the stability of customer distribution.Finally,this paper compares the performance of the allocation method from three dimensions,and the experimental data show that the separation allocation method designed in this paper is better than other methods in terms of core search and stability.The allocation method designed in this paper finds 19 out of 20 core cases,accounting for 95%,and the average allocation instability value is 2.08%.