The Inventory Routing Problem:A Distributionally Robust Optimization Approach

In the traditional inventory management,retailers monitor their own inventory level and order goods from the upstream supplier.After the supplier receives the orders from each retailer,it begins to product goods and distributes goods to the retailers.This supply chain system often lacks coordination and cooperation.Vendor Managed Inventory(VMI)mode,as a relatively new operating system,has been successfully implemented in various large enterprises.In the VMI,the supplier which is a centralized decision maker manages the inventory of the retailer,the production and distribution directly.In other words,it decides the order quantity of retailers in each period.Therefore,in VMI,retailers do not need to manage the inventory,and the supplier can make unified planning for the production and distribution of goods by coordinating the goods demand of each retailer.Inventory Routing Problem is the core Problem of implementing VMI mode.In this paper,we mainly study robust inventory routing problem.The classical inventory routing problem is modeled from the perspective of cost minimization.The goal is to minimize the sum of inventory cost and transportation cost.However,in order to get more market share,some enterprises take service level as the primary goal.In this paper,the inventory routing problem is modeled from the perspective of service level.And the service level is affected by the uncertain demand of the retailers in each period.In this paper,we use the VMI system.The supplier decides the order quantity and keeps the inventory level of the retailers within a reasonable range in each period.It shows the service level of the supplier.The goal of the model is to minimum the sum of the requirement violation index(RVI),which accounts for how severely the inventory is violated,within each period.In some cases,the demand is uncertain and the historical data about retailer demand is limited.we assume the demand is distributed in an uncertain set and build a distributionally robust optimization model to handle it.however,the model is difficult to be solved directly.We approximate a nonlinear function with piecewise linear one,and the model is transformed into a mixed integer programming model.Then we provide three algorithms to solve the model(subtour detection algorithm based on integer nodes,subtour detection algorithm based on all nodes,Benders decomposition algorithm).Lastly,we write programs for numerical study,in this part,we study the impact of parameters and compare three algorithms.