固定分区法在库存路径联合优化问题中的应用
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摘要
本论文研究来源于国家自然科学基金与新世纪优秀人才支持计划。
库存路径联合优化问题是将库存控制问题和运输问题集成到一系统中,用一个目标函数来刻画。从研究和应用的现状来看,整合优化更有利于提高物流系统的效率和节省费用支出。国外早在上世纪80年代中期就开始研究库存路径问题,在模型和算法方面已有了一些研究,但在国内对库存路径问题的研究很少见。
固定分区法是研究战术层库存路径联合优化问题的一种非常有效的方法。所谓固定分区原则就是预先将客户划分到不同区域中,对每个分区指派一辆车送货。固定分区法中的费用函数有自己独特的结构特性,无论是从建模角度还是从算法设计角度,都使得处理库存路径问题变得简单些。固定分区法的应用非常广泛,不仅可以应用在VMI中,还可以在非一体化供应链中应用。由于在我国大多数情况是供应商与零售商为不同的企业,它们为了追求各自的利润最大化,而不考虑与其它企业的合作。因此研究非一体化的库存路径问题具有更大的实际意义。
总的来说,本文主要做了以下两方面工作:
第一部分分析了在允许缺货的前提下固定分区法在VMI中的应用。为供应商提出了一个配送计划,给出了整个系统的费用函数,以及求解费用函数的算法。
第二部分分析了在不允许缺货的前提下固定分区法在非一体化供应链中的应用。为供应商提出了一个配送计划,给出了整个系统的利润函数,以及求解利润函数的算法。并且为了保证供应商与零售商都可以接受这个计划,提出了一个价格策略,实现了对整个供应链的协调。
Inventory-transportation integrated optimization problem integrates inventory control problem and transportation problem into a system and use a objective function to depiction. From the research and application status, optimization of these two aspects to make for improving logistics system efficiency and saving costs. As early as mid-1980, overseas scholars had begun to study inventory-transportation integrated optimization problem. The model and algorithm had a number of studies, but the studies were rare in the domestic.
FPP is a very effective method to study tactical level of inventory-transportation integrated optimization problem. The so-called FPP is dividing customs into different regions in advance, and assigning a vehicle to each region. Costs functions of FPP have its own unique structure characterization which makes model and algorithm design simpler. FPP has been widely used. It not only can be applied to VMI, but also to the non-integrated supply chain. Owing to the case of suppliers and retailers for different enterprises in our country, they do not take account of cooperating with other enterprises in order to maximize their own profits. Therefore, the studying inventory-transportation integrated optimization problem of non-integrated supply chain has more practical significance.
Overall, this paper has done some research in the following two aspects:
The first part analyses FPP's applying on VMI allowed out of stock. We determine a distribution plan for supplier and give the costs function of the whole system and an algorithm of solving the costs function.
The second part analyses FPP's applying on non-integrated supply chain disallowed out of stock. We determine a distribution plan for supplier and give the profits function of the whole system and an algorithm of solving the profits function. Moreover, in order to ensure that suppler and retailers can accept this plan, we put forward a pricing strategy to realize the whole supply chain coordination.
库存路径联合优化问题是将库存控制问题和运输问题集成到一系统中,用一个目标函数来刻画。从研究和应用的现状来看,整合优化更有利于提高物流系统的效率和节省费用支出。国外早在上世纪80年代中期就开始研究库存路径问题,在模型和算法方面已有了一些研究,但在国内对库存路径问题的研究很少见。
固定分区法是研究战术层库存路径联合优化问题的一种非常有效的方法。所谓固定分区原则就是预先将客户划分到不同区域中,对每个分区指派一辆车送货。固定分区法中的费用函数有自己独特的结构特性,无论是从建模角度还是从算法设计角度,都使得处理库存路径问题变得简单些。固定分区法的应用非常广泛,不仅可以应用在VMI中,还可以在非一体化供应链中应用。由于在我国大多数情况是供应商与零售商为不同的企业,它们为了追求各自的利润最大化,而不考虑与其它企业的合作。因此研究非一体化的库存路径问题具有更大的实际意义。
总的来说,本文主要做了以下两方面工作:
第一部分分析了在允许缺货的前提下固定分区法在VMI中的应用。为供应商提出了一个配送计划,给出了整个系统的费用函数,以及求解费用函数的算法。
第二部分分析了在不允许缺货的前提下固定分区法在非一体化供应链中的应用。为供应商提出了一个配送计划,给出了整个系统的利润函数,以及求解利润函数的算法。并且为了保证供应商与零售商都可以接受这个计划,提出了一个价格策略,实现了对整个供应链的协调。
Inventory-transportation integrated optimization problem integrates inventory control problem and transportation problem into a system and use a objective function to depiction. From the research and application status, optimization of these two aspects to make for improving logistics system efficiency and saving costs. As early as mid-1980, overseas scholars had begun to study inventory-transportation integrated optimization problem. The model and algorithm had a number of studies, but the studies were rare in the domestic.
FPP is a very effective method to study tactical level of inventory-transportation integrated optimization problem. The so-called FPP is dividing customs into different regions in advance, and assigning a vehicle to each region. Costs functions of FPP have its own unique structure characterization which makes model and algorithm design simpler. FPP has been widely used. It not only can be applied to VMI, but also to the non-integrated supply chain. Owing to the case of suppliers and retailers for different enterprises in our country, they do not take account of cooperating with other enterprises in order to maximize their own profits. Therefore, the studying inventory-transportation integrated optimization problem of non-integrated supply chain has more practical significance.
Overall, this paper has done some research in the following two aspects:
The first part analyses FPP's applying on VMI allowed out of stock. We determine a distribution plan for supplier and give the costs function of the whole system and an algorithm of solving the costs function.
The second part analyses FPP's applying on non-integrated supply chain disallowed out of stock. We determine a distribution plan for supplier and give the profits function of the whole system and an algorithm of solving the profits function. Moreover, in order to ensure that suppler and retailers can accept this plan, we put forward a pricing strategy to realize the whole supply chain coordination.
引文
[1]Burns L.D,Hall R.W.,Blumenfeld D.E.et al.Distribution strategies that minimize transportation and inventory costs[J].Operations Research.1985,33:469-490.
[2]Baita F.,Ukovich W.,et al..Dynamic routing and inventory problem:a review[J].Transportation Research.1998,32(8):585-598.
[3]Anily S.,Federgruen A..One Warehouse Mutiple Retailer Systems with Vehicle Routing Costs[J].Management Science.1990,1(36):92-114.
[4]Anily S.,Federgruen A..Structured Partitioning Problems[J].Operations Research.1990,2(15):268-285.
[5]Anily S..The general multi-retailer EOQ problem with vehicle routing costs[J].European Jounal of Operations Research.1994,79:451-473.
[6]Anily S.,Federgruen A..A Class Of Euclidean Routing Problems With General Route Cost Functions[J].Mathematics of Operations Research.1990,2(15):268-285.
[7]Robin Roundy.98%-Effective Integer-Ratio Lot-Sizing for One-Warehouse Multi-Retailer Systems[J].Management Science.1985,11(31):1416-1430.
[8]Shoshana Anily,Julien Bramel.An asymptotic 98.5%-effective lower bound on fixed partition policies for the inventory-routing problem[J].Discrete Applied Mathmatics.2004,145:22-39.
[9]Qiu-Hong Zhao,Shou-Yang Wang,K.K.Lai.A partition approach to the inventory/routing problem[J].European Journal of Operation Research.2007,177:786-802.
[10]Lap Mui Ann Chan,Awi Federguren,David Simchi-Levi.Probabilistic Analyses And Practical Algorithms For Inventory-Routing Models[J].Operations Research.1998,1(46):96-106.
[11]Novaes A.G.N,Cursi J.E.S.,Graciolli O.D..A continuous approach to the design of physical distribution systems[J].Computers & Operations Research.2000,27:877-893.
[12]袁庆达.随机库存-运输联合优化问题研究[D].成都;西南交通大学交通运输规划与管理系,2001:1-11.
[13]郭耀煌,李军.车辆优化调度[M].成都科技大学出版社,1994.
[14]刘丽文,袁佳瑞.VMI环境下的库存与发货模型研究[J].中国管理科学,2003,5(11):31-36.
[15]牛永亮,王金妹.物流配送车辆路线求解算法[J].交通运输工程学报,2006,2(6):83-87.
[16]Hall R.W..Comment on one warehouse multiple retailer system with vehicle routing costs[J].Management Science.1991,37:1416-1497.
[17]Bramel J.,Simic-Levi D.A location based heuristic for general routing problems[J].Operation Research.1995,43:649-660.
[18]Gallego D.,Simchi-Levi D..On the effectiveness of direct shipping strategy for the one-warehouse multi-retailer R-systems[J].Management Science.1990,36:240-243.
[19]Hall R.W,A note on bounds for direct shipping cost[J].Management Science.1992,38,1212.
[20]Hall R.W..Determing vehicle dispatch frequency when shipping frequency differs from suppliers[J].Transportation Research.1985,19B:421-431.
[21]Maxwell W.L.,Muckstadt J.A..Establishing consistent and realistic reorder intervals in production-distribution systems[J].Operations Research.1985,30B:163-188.
[22]Jackson P.L.,Maxwell W.L.,Muckstadt J.A..Determining optimal reorder intervals in capacitated production-distribution systems[J].Management Science.1988,34:938-958.
[23]Muckstadt J.A.,Roundy R.O..Analysis of multistage production systems [J].Handbooks in Operations Research and Management Science.1993,4:59-131.
[24]Viswanathan S.,Mathur K..Integrating routing and inventory decisions in one warehouse multiretailer miltiproduct distribution system[J].Management Science.1997,43:294-312.
[25]Herer Y.,Roundy R..Heuristics for a one-warehouse multiretailer distribution problem with performance bounds[J].Operation Research.1997,45:102-115.
[26]Speranza M.G.,Ukovich W..Minimizing transportation and inventory costs for several products on a single link[J].Operations Research.1994,42:879-894
[27]Federgruen J.M.,Prastacos G.,Zipkin P..An allocation and distribution model for perishable products[J].Operations Research.1986,34:75-82.
[28]Dror M.,Trudeau P..Inventory routing operational design[J].Jounal of Business Logistics.1988,9:165-183.
[29]Dror M.,Trudeau P..Cash flow optimization in delivery scheduling [J].European Journal of Operational Research.1996,88:504-515.
[30]郭耀煌,范莉莉.货运调度的一种启发式算法[J].系统工程.1989,1.
[31]赵庆芝,叶晴园.需求随时间变化的动态库存模型的经济分析[J].哈尔滨师范大学自然科学学报.1997,13(4):37-45.
[32]王海滋,黄渝祥.随机状态下的基本经济定购批量模型[J].系统工程理论方法应用.1997,6(4):5-9.
[33]徐天亮.物流热不会成为泡沫[J].中国物资流通.2001,18:15-17.
[34]鲁晓春,詹荷生.关于配送中心重心法选址的研究[J].北方交通大学学报,2000,6(24):108-110.
[35]Daganzo.C.F.Logistics System analysis[J].Springer-Varleg.1996.
[36]冯春松,王军宇.TSP问题的一种改进遗传算法[J].武汉理工大学学报,2006,4(28).116-118.
[37]吴升,王钦敏.基于改进遗传算法的多约束VRP求解[J].测绘科学技术学报,2006,6(23)396-399.
[38]李静芳,马士华.如何成功运用供应商管理库存[J].物流技术.2001,(6):17-201.
[39]黄洁纲.存贮论原理及其应用[M].上海科学技术文献出版社,1984.
[2]Baita F.,Ukovich W.,et al..Dynamic routing and inventory problem:a review[J].Transportation Research.1998,32(8):585-598.
[3]Anily S.,Federgruen A..One Warehouse Mutiple Retailer Systems with Vehicle Routing Costs[J].Management Science.1990,1(36):92-114.
[4]Anily S.,Federgruen A..Structured Partitioning Problems[J].Operations Research.1990,2(15):268-285.
[5]Anily S..The general multi-retailer EOQ problem with vehicle routing costs[J].European Jounal of Operations Research.1994,79:451-473.
[6]Anily S.,Federgruen A..A Class Of Euclidean Routing Problems With General Route Cost Functions[J].Mathematics of Operations Research.1990,2(15):268-285.
[7]Robin Roundy.98%-Effective Integer-Ratio Lot-Sizing for One-Warehouse Multi-Retailer Systems[J].Management Science.1985,11(31):1416-1430.
[8]Shoshana Anily,Julien Bramel.An asymptotic 98.5%-effective lower bound on fixed partition policies for the inventory-routing problem[J].Discrete Applied Mathmatics.2004,145:22-39.
[9]Qiu-Hong Zhao,Shou-Yang Wang,K.K.Lai.A partition approach to the inventory/routing problem[J].European Journal of Operation Research.2007,177:786-802.
[10]Lap Mui Ann Chan,Awi Federguren,David Simchi-Levi.Probabilistic Analyses And Practical Algorithms For Inventory-Routing Models[J].Operations Research.1998,1(46):96-106.
[11]Novaes A.G.N,Cursi J.E.S.,Graciolli O.D..A continuous approach to the design of physical distribution systems[J].Computers & Operations Research.2000,27:877-893.
[12]袁庆达.随机库存-运输联合优化问题研究[D].成都;西南交通大学交通运输规划与管理系,2001:1-11.
[13]郭耀煌,李军.车辆优化调度[M].成都科技大学出版社,1994.
[14]刘丽文,袁佳瑞.VMI环境下的库存与发货模型研究[J].中国管理科学,2003,5(11):31-36.
[15]牛永亮,王金妹.物流配送车辆路线求解算法[J].交通运输工程学报,2006,2(6):83-87.
[16]Hall R.W..Comment on one warehouse multiple retailer system with vehicle routing costs[J].Management Science.1991,37:1416-1497.
[17]Bramel J.,Simic-Levi D.A location based heuristic for general routing problems[J].Operation Research.1995,43:649-660.
[18]Gallego D.,Simchi-Levi D..On the effectiveness of direct shipping strategy for the one-warehouse multi-retailer R-systems[J].Management Science.1990,36:240-243.
[19]Hall R.W,A note on bounds for direct shipping cost[J].Management Science.1992,38,1212.
[20]Hall R.W..Determing vehicle dispatch frequency when shipping frequency differs from suppliers[J].Transportation Research.1985,19B:421-431.
[21]Maxwell W.L.,Muckstadt J.A..Establishing consistent and realistic reorder intervals in production-distribution systems[J].Operations Research.1985,30B:163-188.
[22]Jackson P.L.,Maxwell W.L.,Muckstadt J.A..Determining optimal reorder intervals in capacitated production-distribution systems[J].Management Science.1988,34:938-958.
[23]Muckstadt J.A.,Roundy R.O..Analysis of multistage production systems [J].Handbooks in Operations Research and Management Science.1993,4:59-131.
[24]Viswanathan S.,Mathur K..Integrating routing and inventory decisions in one warehouse multiretailer miltiproduct distribution system[J].Management Science.1997,43:294-312.
[25]Herer Y.,Roundy R..Heuristics for a one-warehouse multiretailer distribution problem with performance bounds[J].Operation Research.1997,45:102-115.
[26]Speranza M.G.,Ukovich W..Minimizing transportation and inventory costs for several products on a single link[J].Operations Research.1994,42:879-894
[27]Federgruen J.M.,Prastacos G.,Zipkin P..An allocation and distribution model for perishable products[J].Operations Research.1986,34:75-82.
[28]Dror M.,Trudeau P..Inventory routing operational design[J].Jounal of Business Logistics.1988,9:165-183.
[29]Dror M.,Trudeau P..Cash flow optimization in delivery scheduling [J].European Journal of Operational Research.1996,88:504-515.
[30]郭耀煌,范莉莉.货运调度的一种启发式算法[J].系统工程.1989,1.
[31]赵庆芝,叶晴园.需求随时间变化的动态库存模型的经济分析[J].哈尔滨师范大学自然科学学报.1997,13(4):37-45.
[32]王海滋,黄渝祥.随机状态下的基本经济定购批量模型[J].系统工程理论方法应用.1997,6(4):5-9.
[33]徐天亮.物流热不会成为泡沫[J].中国物资流通.2001,18:15-17.
[34]鲁晓春,詹荷生.关于配送中心重心法选址的研究[J].北方交通大学学报,2000,6(24):108-110.
[35]Daganzo.C.F.Logistics System analysis[J].Springer-Varleg.1996.
[36]冯春松,王军宇.TSP问题的一种改进遗传算法[J].武汉理工大学学报,2006,4(28).116-118.
[37]吴升,王钦敏.基于改进遗传算法的多约束VRP求解[J].测绘科学技术学报,2006,6(23)396-399.
[38]李静芳,马士华.如何成功运用供应商管理库存[J].物流技术.2001,(6):17-201.
[39]黄洁纲.存贮论原理及其应用[M].上海科学技术文献出版社,1984.