固定分区策略下SDIRP问题周期性最优策略及其算法

Periodic Optimal Strategy and Algorithm of Stochastic Demand IRP Under Fixed Partition Policy

随机需求库存-路径问题(Stochastic Demand Inventory Routing Problem,SDIRP)是典型的NP难题,也是实施供应商管理库存策略过程中的关键所在。文章通过引入固定分区策略(Fixed Partition Policy,FPP),将SDIRP分解为若干个独立的子问题,并采用拉格朗日对偶理论以及次梯度算法确定最优的客户分区。在此基础上证明了各子问题的最优周期性策略由分区内各客户的(T,S)库存策略以及相应的最优旅行商路径构成,进而给出了客户需求服从泊松分布时求解最优(T,S)策略各参数的方程组,并设计了求解算法。最后,通过数值算例讨论了上述策略以及算法对于解决SDIRP的有效性。

The Stochastic Demand Inventory Routing Problem（ SDIRP） is a kind of typical NP-hard problem. It is also crucial to implementing Vendor Managed Inventory（VMI）strategy. This paper decomposes SDIRP into several independent sub-problems by introducing the Fixed Partition Policy（FPP） and determines the optimal partitions of customers with application of Lagrangian Duality theory and subgradient algorithm. It further proves the optimal periodic replenishment policy for customers in each sub-problem consists of customers＇ （T, S）policy in each partition and the corresponding optimal traveling salesman route. And thus equation sets and corresponding algorithm are given to derive parameters for the optimal（ T, S）policy when customers＇ demand follows Poisson distribution. Finally, a numerical example is presented to confirm the efficiency of the above policy and algorithm.