随机需求下联合选址-库存模型研究

Study on Joint Location-Inventory Model under Stochastic Demand

研究了一类具有季节性需求特性的商品的联合选址-库存模型。在传统的无容量限制的固定费用设施选址问题中考虑了分销中心的运作库存和安全库存的影响,以及规模经济效应和风险分摊效应,同时考虑了季节性商品未来需求的不确定性,将订货决策作为模型的决策变量,建立了一类随机需求下以期望销售收益最大化为目标函数的联合选址-库存模型,拓展了已有的联合选址-库存模型。该模型是一个混合整数规划问题,给出了求解该问题的基于拉格朗日松弛算法的两阶段算法,最后通过随机生成四组不同规模的数值算例,得到的计算结果表明拉格朗日松弛算法可以有效地求解该问题。

A class of joint location-inventory models for products with seasonal selling property is investigated in this paper. Based on the traditional uncapacitated fixed charge facility location problem, the working inventory cost and the safety stock cost in the distribution centers, as well as the impacts or scale of economy and risk pooling, are considered. Considering the uncertainty of future demand with seasonal products, this paper treats the replenishment decisions as exogenous decision variables, and develops a joint locationinventory model aiming at the maximization of expected revenue. The proposed model extends the existed joint location-inventory models. As the proposed model is a mixed integer programming problem, a twophrase solution procedure based on Lagarangian relaxation algorithm is developed to solve this problem. At last, four groups of numerical examples which are generated stochastically are given and the solution results show that the proposed Lagrangian relaxation approach can solve the problem effectively.