Abstract: Facility location, inventory control and vehicle routes scheduling are critical and highly related problems in logistics system. The decision makers need to optimize the three problems integrated and comprehensively. We formulate a stochastic Location-Inventory-Routing Problem(LIRP) model using continuous review(Q, r)inventory policy in two level supply chain distribution systems, consisting of one supplier, a set of retailers and a single type of product. Restructuring the non-linear mixed integer programming LIRP model into a set covering model, an approximate optimum solution is obtained using column generation. To realize the “integrated optimization”, Brand-and-Price algorithm is applied to improve the initial solution. At last, based on the several instances generated randomly with sizes ranging from 10 to 160 retailers, the proposed approach is tested and evaluated. The computational results show the proposed approach can resolve this complex problem efficiently.

Key words: logistics engineering, location-inventory-routing problem, column generation algorithm, logistics system

摘要： 设施选址、库存控制和车辆路径安排是物流系统优化中的三个关键问题,三者之间存在相互依赖的关系,应该根据这种关系来相应地进行综合优化与管理物流活动。以典型的单一生产基地、单一产品、采用不断审查的(Q, r)库存策略的供应链二级分销网络为研究对象,建立了一个随机型选址-库存-路径问题优化模型;在将非线性混合整数规划转化为线性整数集合覆盖模型的基础上,采用列生成算法来获得一个近似最优解,再用分支定价法对初始解进行改进,以实现对整个问题“完全集成”的优化。最后,用随机生成的方式,产生了10至160个客户的计算实例,分析了运输费用和库存费用对总成本的影响,算法运算时间表明本文给出的算法能较快地求解这一复杂问题。

关键词: 物流工程, 选址-库存-路径问题, 列生成算法, 物流网络