易腐品配送中的库存—路径问题研究
|
摘要
鉴于易腐品的特性,对其储存、运输等物流环节进行优化管理,可有效减少变质损耗,实现易腐品的及时配送,具有重要的理论和实际意义。在易腐品配送系统中,库存成本和运输成本占有很大的比重,且相互间具有密切的联系,因而有必要对两者进行集成优化研究,以便提高易腐品配送系统的整体绩效,即研究易腐品配送的库存—路径问题(Inventory-Routing Problem, IRP)。为此,本文从以下两个方面对易腐品配送系统的IRP进行了研究。
首先,考虑了由配送中心和需求点组成的两级配送系统的IRP,把IRP分解为库存问题和路径问题两部分分别求解,最后采用提前配送的方法,对所求解进行迭代调整,以协调库存费、订货费、订购费用与运输费之间的关系,通过配送策略和订货策略的变换的不断迭代从而求得原问题的近似最优解。在制定库存策略时,就需求确定环境下考虑易腐品变质率建立了总成本包括订货费用、订购费用和库存费用在内的库存模型,为不同的需求点求得其最佳配送周期和配送量。算例结果表明,配送周期越短的客户越有可能通过提前配送产生成本节约,而全局调整成本的节约值是依靠尽可能地满足车辆的最大容载量来实现的。
其次,针对易腐品配送中的运输问题,考虑城市路网中不同路段在不同时间段具有不同的行车速度,因此会对车辆的行驶时间造成影响,进而导致车辆在到达各个需求点时的到达时间也会因为跨时段而不同。因而在考虑具体每一天的配送策略时,需考虑时变因素。在此,论文采用了考虑时变因素的跨时段处理模型以及遗传算法,解决时间依赖条件下的VRP。
In view of the characteristics of perishable items, optimizing the management of logistics links like storage and transportation would reduce deterioration effectively and distribute perishable items in time, so the optimal management has significant theoretical and practical meaning.In perishable items distribution system, inventory costs and transportation costs account for a large proportion, and there is a close relationship between inventory and transportation. In order to improve the overall performance, it is necessary to study inventory and transportation from the perspective of integration, that is to study on (Inventory-Routing Problem, IRP) in perishable items distribution system. Then, this paper study on IRP in perishable items distribution system from two aspects as follows.
Firstly, this paper study on IRP in a two-level distribution system which is composed of distribution centers and demand points, and IRP is divided into two sub-problems: inventory-controlling problem and vehicle routing problem. Then a advanced distribution approach is proposed to iterate adjusting on the solution, aimed to coordinate the relationships among inventory holding cost, ordering cost, purchasing cost and shipment cost, then the approximate optimal solution can be obtained by iterating on the solution under different distribution strategy and order policy. In making inventory policy, considering the deterioration rate of perishable items under deterministic demand environment, a inventory model is established, in which the total cost is composed of ordering cost, purchasing cost and inventory holding cost. Based on the model we can get the optimal delivery cycle and quantity for each demand point. The example shows that the shorter delivery cycle, the customers are more likely to make cost saving through advanced delivery, while the cost saving by global adjustment is achieved by meetting the vehicle's maximum load capacity as much as possible.
Secondly, for transportation problem in perishable items distribution system, vehicle speed on different subsections in urban transportation network is varied according to different period of time, which will affect the travelling time and led to different arrival time. So, considering distribution strategy in each day, it is necessary to consider time-varying parameter. In this paper, a time-cross processing model incorporating time-dependent parameter is proposed and a satisfying solution is found for time dependent VRP by using genetic algorithm.
首先,考虑了由配送中心和需求点组成的两级配送系统的IRP,把IRP分解为库存问题和路径问题两部分分别求解,最后采用提前配送的方法,对所求解进行迭代调整,以协调库存费、订货费、订购费用与运输费之间的关系,通过配送策略和订货策略的变换的不断迭代从而求得原问题的近似最优解。在制定库存策略时,就需求确定环境下考虑易腐品变质率建立了总成本包括订货费用、订购费用和库存费用在内的库存模型,为不同的需求点求得其最佳配送周期和配送量。算例结果表明,配送周期越短的客户越有可能通过提前配送产生成本节约,而全局调整成本的节约值是依靠尽可能地满足车辆的最大容载量来实现的。
其次,针对易腐品配送中的运输问题,考虑城市路网中不同路段在不同时间段具有不同的行车速度,因此会对车辆的行驶时间造成影响,进而导致车辆在到达各个需求点时的到达时间也会因为跨时段而不同。因而在考虑具体每一天的配送策略时,需考虑时变因素。在此,论文采用了考虑时变因素的跨时段处理模型以及遗传算法,解决时间依赖条件下的VRP。
In view of the characteristics of perishable items, optimizing the management of logistics links like storage and transportation would reduce deterioration effectively and distribute perishable items in time, so the optimal management has significant theoretical and practical meaning.In perishable items distribution system, inventory costs and transportation costs account for a large proportion, and there is a close relationship between inventory and transportation. In order to improve the overall performance, it is necessary to study inventory and transportation from the perspective of integration, that is to study on (Inventory-Routing Problem, IRP) in perishable items distribution system. Then, this paper study on IRP in perishable items distribution system from two aspects as follows.
Firstly, this paper study on IRP in a two-level distribution system which is composed of distribution centers and demand points, and IRP is divided into two sub-problems: inventory-controlling problem and vehicle routing problem. Then a advanced distribution approach is proposed to iterate adjusting on the solution, aimed to coordinate the relationships among inventory holding cost, ordering cost, purchasing cost and shipment cost, then the approximate optimal solution can be obtained by iterating on the solution under different distribution strategy and order policy. In making inventory policy, considering the deterioration rate of perishable items under deterministic demand environment, a inventory model is established, in which the total cost is composed of ordering cost, purchasing cost and inventory holding cost. Based on the model we can get the optimal delivery cycle and quantity for each demand point. The example shows that the shorter delivery cycle, the customers are more likely to make cost saving through advanced delivery, while the cost saving by global adjustment is achieved by meetting the vehicle's maximum load capacity as much as possible.
Secondly, for transportation problem in perishable items distribution system, vehicle speed on different subsections in urban transportation network is varied according to different period of time, which will affect the travelling time and led to different arrival time. So, considering distribution strategy in each day, it is necessary to consider time-varying parameter. In this paper, a time-cross processing model incorporating time-dependent parameter is proposed and a satisfying solution is found for time dependent VRP by using genetic algorithm.
引文
[1]Bernard Commere, Controlling the Cold Chain to Ensure Food Hygiene and Quality[J],Bulletin of the IIR,2003,(2).
[2]潜力无限的中国冷链物流市场[OR]. http://info.service.hc360.com/2009/09/ 24114562386.shtml.
[3]T.M.Whitin. Theory of inventory management[M], Princeton University Press,Prineeton, NJ,1957:62-72.
[4]E.Raafat. Survey of literature on continuously deteriorating inventory model[J]. Journal of the Operational Research Soeiety,1991,42:27-37.
[5]S.K.Goyal, B.C. Giri.Recent trends in modeling of deteriorating inventory[J], European Journal of Operational Research,2001,134:1-16.
[6]Shah,Y.K.&Jaiswal,M.C.An order-level inventory model for a system with constant ate of deterioration[J]. Opsearch,1977,14:174-184.
[7]Aggarwal,S.P. A note on an order-level inventory model for a system with Constant rate of deterioration[J]. Opsearch,1978,15:184-187.
[8]G..Padmanabhana,Prem vrath. EOQ models for perishable items under stock dependent selling rate[J], European Journal of Operational Researeh,1995,86(2):281-292.
[9]A.K.Bhunia,M.Maiti. An inventory model of deteriorating items with lot-size dependent replenishment cost and a linear trend in demand[J], Applied Mathematical Modelling, 1999,23:301-308.
[10]A.K.Bhunia,M.Maiti. Deterministic inventory model for deteriorating items with finite rate of replenishment dependent on inventory level [J]. Computers&Operations Research,1998,25(11):997-1006.
[11]S.Mukhopadhyay,R,N.Mukherjee, K.S Chaudhuri. Joint pricing and ordering policy for a deteriorating inventory[J], Computers&Industrial Engineering,2004,47:339-349.
[12]Hui-Ming Wee. Deteriorating inventory model with quantity discount, Pricing and Partial backordering[J]. International Journal of Poduction Economics,1999,59: 511-518.
[13]N.K.Mahapatra. Decision process for multi-objective, multi-item production inventory system via interactive fuzzy satisfyng technique[J]. Computers and Mathematics with Applieations,2005,49:805-821.
[14]T.Chakrabarty,B.C.Giri,K.S.Chaudhuri.An EOQ model for items with weibull distribution deterioration, shortages and trended demand:an extension of philips model [J]. Computers&Operations Research,1998,25(7-8):649-657.
[15]Prakash L.Abad. Optimal price and ordersize for a reseller under partial backordering [J]. Computers&Operations Research,2001,28:53-65.
[16]Bhaba R.Sarker,A.M.Mjamal,Shaojun Wang. Supply chain models for perishable products under inflation and permissible delay in payment [J].2000,27:59-75.
[17]Chun-Tao Chang. An EOQ model With deteriorating items under inflation when supplier credits linked to order quantity [J]. International Journal of Production Economics,2004,88:307-316.
[18]Kun-Jen Chung, Jui-Jung Liao. The optimal ordering policy in a DCF analysis for deteriorating items when trade credit depends on the order quantity[J]. International journal of production economics,2006,100:116-130.
[19]Kuo-Nan Huang,Jui-JungLiao. A simple method to locate the optimal solution for exponentially deteriorating items under trade credit financing[J]. Computers and Mathematics with Applications.
[20]张冲,戴更新,韩广华,李明.基于信用支付和现金折扣的变质物品库存模型[J].运筹与管理,2007,16(6).
[21]S.KALRAKAM,S.SHANTHI. A Perishable System with Modified Base Stock Policy and Random Supply Quantity [J].2000,39:79-89.
[22]S.Kalpakam,S.Shanthi. A perishable inventory system with modified (S-1,S) Policy and arbitrary proeessing times[J]. Computers&Operations Research,2001,28:453-471.
[23]Eylem Tekin,Ulku Gurler. EmreBerk.Age-based.stock level control policies for a perishable inventory system[J]. European Journal of Operational Research, 2000,134:309-329.
[24]吕大昭.易腐库存中提前时间内的两种需求分布[J].西安工业学院学报,2003,23,(2).
[25]朱广萍.单一易腐变质物品的最优存贮模型[J].宁夏大学学报,2001,22(1).
[26]P.C.Yang,H.M.Wee. A single-vendor and multiple-buyers production-inventory policy for a deterioratingitem[J]. European Journal of Operational Research,2000,134:570-581.
[27]Po-ChungYang, Hui-Ming wee. An integrated multi-lot-size production inventory model for deteriorating item [J]. Computers & Operations Research,2003,30:671-682.
[28]KAR S, BHUNIA A K, MAITIM. Inventory of multi-deteriorating items sold frow two shops under single management with constrains on space and investment[J]. Computer &Operations Research,2001,28:1203-1221.
[29]BHATTACHARYADK. On multi-item inventory [J]. European Journal of Operational Research,2005,162:786-791.
[30]杜少甫,梁裸,张靖江,卢正刚.考虑产品变质的VMI混合补货与发货策略及优化仿真[J].中国管理科学,2007,15(2).
[31]A.Federgruen and P Zipkin. A combined Vehicle routing and inventory allocation Problem[J].Operations Researeh,1984,32(5):1019-1036..
[32]刘立辉,叶春明.库存—路径问题的研究综述[J].工业工程,2009,12(3)：1-6.
[33]赵达,李军.随机需求库存—路径问题研究与展望[J].系统工程,2007,25(8)：39-41.
[34]B.Golden,A.Assad, and R.Dhal.A. A alysis of a large scale vehicle routing problem With an inventoy component[J]. Large scale systems.1984,7(2-3):18-190.
[35]M.Fisher, R.A.Greenfield, Rjaikmuar and.PKedia. Real-time scheduling of bulk delivery fleet:practical application of lagrangean relaxation.[R].The Washingtion School, University of Pennsylvania,Department of Decision Seienees, October 1982.
[36]M.Dror and M.Ball. Inventory routing:Reduction form and annual to a short period problem[J]. Naval Research Logisties,1987,34(6):891-905.
[37]M.Dorr and Larry Levy. A vehicle routing improvement algorithm comparison of agreed and a matching implementation of inventory routing problem[J]. Computer.and Operational Researeh,1986,13(1):33-45.
[38]P.Jaillet, L.Huang.Bard, and M.Dorr. Delivery cost approximations for inventory routing problems in a rolling horizon framework[J]. Transportation Science.2002,36(3)292-300.
[39]Webb I.R,Larson R.C. Period and phase of customer replenishment:a new approach to the strategic inventory-routing Problem[J]. EuropeanJournal of Operational Researeh, 1995,85:132-148.
[40]Anily S, Federgruen A. One warehouse multiple retailer systems with vehiele routing costs[J]. Management Science,1990,36(1):92-114.
[41]Guillermo Gall ego and David Simehi-levi. On the effieetiveness of direct shipping strategy of the one warehouse multi-retailer R-systems[J]. Management Scienee,1990,36 (2):240-242.
[42]BramelJ,Simehi-Levid. A location based heuristic of general routing problems[J]. Operations Researeh.1995,43:649-660.
[43]袁庆达.库存运输联合问题[D].西南交通大学博士学位论文,2001.
[44]高梦昭,张文杰,物流成本探析[J].北方交通大学学报,2003,2(3)：12-15
[45]赵达,李军,李妍峰,孙斌锋.随机需求库存—路径问题：研究现状及展望[J].系统工程,2007,25(8)：38-44.
[46]梁蔚.库存与运输系统集成优化研究与应用[D].大连海事大学硕士论文,2002.
[47]赵达.随机需求的库存—路径问题研究[D].西南交通大学硕士论文,2005.
[48]于涛.VMI下库存管理与运输调度整合优化研究[D].同济大学硕士论文,2008.
[49]王莺.基于R-SYSTEM和DR-SYSTEM的存储路径问题研究[D].西南交通大学硕士论文,2004：28-30.
[50]李军,郭耀煌.配送车辆优化调度理论与方法[M].北京：中国物资出版社,2001.
[51]肖增敏,李军.动态网络车辆路径问题：研究现状及展望[J].系统工程.2004,22(7)：68-71.
[52]HillA V, Benton W C. Modelling intra city time-dependent travel speeds for vehicle scheduling problems[J] Journal of the Operational Research Society,1992,43(4): 343-351.
[53]Malandraki C, Daskin M S. Time-dependent vehicle routing problems formulations properties and heuristic algorithms[J]. Transportation Science,1992,26(3).
[54]Malandrakic, Dial R B. A restriced dynamic programming heuristic algorithm for the time dependent traveling salesman problem[J]. European Journal of Operational Research,1996,90:45-55.
[55]Wiel R, JV Sahinidis.NV. Heunstic bounds and test problem generation for the time-dependent traveling salesman problem [J]. Transportation Seience.1995,29 (22):167-183.
[56]Park Y B. A solution of the bicriteria vehicle-scheduling problems with time and area dependent travel speeds[J]. Computer & Industrial Engineering,2000,38:173-187.
[57]Donati A V, Ambardella L M,Casagrande N, MontemanniR Rizzoli. A Time-dependent vehicle routing problem with an ant colony system[R]. Z.Istituto Dalle Molledi Studisull Intelligenza Artificiale IDSIA Galleria, Manno Switzerland.
[58]Donati A.V.Montemanni, R Casagrande N.RizzoliA.E.Ambardella L.M. Time dependent vehicle-routing problem with an multi ant colony system[A].Z Istituto DalleMolledi Studisull Intelligenza Artificiale(IDSIA) Galleria2,6928, Manno Switzerland IDSIA.
[59]Donati A V Montemanni R Casagrande L MRizzoliA E. Integeration of a robust shortest path algorithm with a time-dependent vehicle routing model and applications[A]. International Symposium on Computational Intelligence for Measurement Systems and Applocation,2003:29-31.
[60]Jung S. A genetic algorithm for vehicle routing problem w ith time dependent travel times[J],2000.
[61]Soumia.Gendreau M Potvin J Y. Vehicle dispatching with time-dependent travel times [J]. European Journal of Operational Research,2003,144(2):379-396.
[62]B Hung Shin J Y. Vehicle routeing w ith time windows and time-varying congestion[J]. Journal of the Operational Research Society,1991,42(5):393-400.
[63]郑成武,刘冬梅.时变网络中物流车辆调度问题的研究[J].天津师范大学学报,2007,9.27(3)：76-80.
[64]王正国,工红卫,刘会新.双目标时变速度车辆路径问题的模型及算法[J].华中科技大学学报(自然科学版).2005,12：94-97.
[65]王正国,刘振元,王红卫.适应性禁忌搜索算法求解带回程的时变速度车辆路径问题[J].计算机集成制造系统,2006,12(9)：1453-1458
[66]李妍峰.时变网络环境下车辆调度问题的研究[D].西南交通大学博士论文.2008：35-39.
[67]张岩,贺国光.一类新的动态车辆调度问题的建模与算法[J].控制工程.2007,5：562-565.
[68]肖增敏.动态网络车辆路径问题研究[D].西南交通大学硕士学位论文,2005：35-39.
[69]王莺.基于R-SYETEM和DR-SYSTEM的存储路径问题研究[D].西南交通大学硕士学位论文,2004：28-38.
[70]周凯.随机时间定位—运输路线安排问题研究[D].中南大学硕士学位论文,2005：33-39.
[71]辛宗丽.随机需求下的血液的订货策略研究[D].西南交通大学硕士学位论文,2005：31-35.
[72]雷英杰.MATLAB遗传算法工具箱及应用[M].西安电子科技大学出版社.
[73]李汝仙.易腐品库存控制研究[D].北京交通大学硕士学位论文,2009：28-29.
[2]潜力无限的中国冷链物流市场[OR]. http://info.service.hc360.com/2009/09/ 24114562386.shtml.
[3]T.M.Whitin. Theory of inventory management[M], Princeton University Press,Prineeton, NJ,1957:62-72.
[4]E.Raafat. Survey of literature on continuously deteriorating inventory model[J]. Journal of the Operational Research Soeiety,1991,42:27-37.
[5]S.K.Goyal, B.C. Giri.Recent trends in modeling of deteriorating inventory[J], European Journal of Operational Research,2001,134:1-16.
[6]Shah,Y.K.&Jaiswal,M.C.An order-level inventory model for a system with constant ate of deterioration[J]. Opsearch,1977,14:174-184.
[7]Aggarwal,S.P. A note on an order-level inventory model for a system with Constant rate of deterioration[J]. Opsearch,1978,15:184-187.
[8]G..Padmanabhana,Prem vrath. EOQ models for perishable items under stock dependent selling rate[J], European Journal of Operational Researeh,1995,86(2):281-292.
[9]A.K.Bhunia,M.Maiti. An inventory model of deteriorating items with lot-size dependent replenishment cost and a linear trend in demand[J], Applied Mathematical Modelling, 1999,23:301-308.
[10]A.K.Bhunia,M.Maiti. Deterministic inventory model for deteriorating items with finite rate of replenishment dependent on inventory level [J]. Computers&Operations Research,1998,25(11):997-1006.
[11]S.Mukhopadhyay,R,N.Mukherjee, K.S Chaudhuri. Joint pricing and ordering policy for a deteriorating inventory[J], Computers&Industrial Engineering,2004,47:339-349.
[12]Hui-Ming Wee. Deteriorating inventory model with quantity discount, Pricing and Partial backordering[J]. International Journal of Poduction Economics,1999,59: 511-518.
[13]N.K.Mahapatra. Decision process for multi-objective, multi-item production inventory system via interactive fuzzy satisfyng technique[J]. Computers and Mathematics with Applieations,2005,49:805-821.
[14]T.Chakrabarty,B.C.Giri,K.S.Chaudhuri.An EOQ model for items with weibull distribution deterioration, shortages and trended demand:an extension of philips model [J]. Computers&Operations Research,1998,25(7-8):649-657.
[15]Prakash L.Abad. Optimal price and ordersize for a reseller under partial backordering [J]. Computers&Operations Research,2001,28:53-65.
[16]Bhaba R.Sarker,A.M.Mjamal,Shaojun Wang. Supply chain models for perishable products under inflation and permissible delay in payment [J].2000,27:59-75.
[17]Chun-Tao Chang. An EOQ model With deteriorating items under inflation when supplier credits linked to order quantity [J]. International Journal of Production Economics,2004,88:307-316.
[18]Kun-Jen Chung, Jui-Jung Liao. The optimal ordering policy in a DCF analysis for deteriorating items when trade credit depends on the order quantity[J]. International journal of production economics,2006,100:116-130.
[19]Kuo-Nan Huang,Jui-JungLiao. A simple method to locate the optimal solution for exponentially deteriorating items under trade credit financing[J]. Computers and Mathematics with Applications.
[20]张冲,戴更新,韩广华,李明.基于信用支付和现金折扣的变质物品库存模型[J].运筹与管理,2007,16(6).
[21]S.KALRAKAM,S.SHANTHI. A Perishable System with Modified Base Stock Policy and Random Supply Quantity [J].2000,39:79-89.
[22]S.Kalpakam,S.Shanthi. A perishable inventory system with modified (S-1,S) Policy and arbitrary proeessing times[J]. Computers&Operations Research,2001,28:453-471.
[23]Eylem Tekin,Ulku Gurler. EmreBerk.Age-based.stock level control policies for a perishable inventory system[J]. European Journal of Operational Research, 2000,134:309-329.
[24]吕大昭.易腐库存中提前时间内的两种需求分布[J].西安工业学院学报,2003,23,(2).
[25]朱广萍.单一易腐变质物品的最优存贮模型[J].宁夏大学学报,2001,22(1).
[26]P.C.Yang,H.M.Wee. A single-vendor and multiple-buyers production-inventory policy for a deterioratingitem[J]. European Journal of Operational Research,2000,134:570-581.
[27]Po-ChungYang, Hui-Ming wee. An integrated multi-lot-size production inventory model for deteriorating item [J]. Computers & Operations Research,2003,30:671-682.
[28]KAR S, BHUNIA A K, MAITIM. Inventory of multi-deteriorating items sold frow two shops under single management with constrains on space and investment[J]. Computer &Operations Research,2001,28:1203-1221.
[29]BHATTACHARYADK. On multi-item inventory [J]. European Journal of Operational Research,2005,162:786-791.
[30]杜少甫,梁裸,张靖江,卢正刚.考虑产品变质的VMI混合补货与发货策略及优化仿真[J].中国管理科学,2007,15(2).
[31]A.Federgruen and P Zipkin. A combined Vehicle routing and inventory allocation Problem[J].Operations Researeh,1984,32(5):1019-1036..
[32]刘立辉,叶春明.库存—路径问题的研究综述[J].工业工程,2009,12(3)：1-6.
[33]赵达,李军.随机需求库存—路径问题研究与展望[J].系统工程,2007,25(8)：39-41.
[34]B.Golden,A.Assad, and R.Dhal.A. A alysis of a large scale vehicle routing problem With an inventoy component[J]. Large scale systems.1984,7(2-3):18-190.
[35]M.Fisher, R.A.Greenfield, Rjaikmuar and.PKedia. Real-time scheduling of bulk delivery fleet:practical application of lagrangean relaxation.[R].The Washingtion School, University of Pennsylvania,Department of Decision Seienees, October 1982.
[36]M.Dror and M.Ball. Inventory routing:Reduction form and annual to a short period problem[J]. Naval Research Logisties,1987,34(6):891-905.
[37]M.Dorr and Larry Levy. A vehicle routing improvement algorithm comparison of agreed and a matching implementation of inventory routing problem[J]. Computer.and Operational Researeh,1986,13(1):33-45.
[38]P.Jaillet, L.Huang.Bard, and M.Dorr. Delivery cost approximations for inventory routing problems in a rolling horizon framework[J]. Transportation Science.2002,36(3)292-300.
[39]Webb I.R,Larson R.C. Period and phase of customer replenishment:a new approach to the strategic inventory-routing Problem[J]. EuropeanJournal of Operational Researeh, 1995,85:132-148.
[40]Anily S, Federgruen A. One warehouse multiple retailer systems with vehiele routing costs[J]. Management Science,1990,36(1):92-114.
[41]Guillermo Gall ego and David Simehi-levi. On the effieetiveness of direct shipping strategy of the one warehouse multi-retailer R-systems[J]. Management Scienee,1990,36 (2):240-242.
[42]BramelJ,Simehi-Levid. A location based heuristic of general routing problems[J]. Operations Researeh.1995,43:649-660.
[43]袁庆达.库存运输联合问题[D].西南交通大学博士学位论文,2001.
[44]高梦昭,张文杰,物流成本探析[J].北方交通大学学报,2003,2(3)：12-15
[45]赵达,李军,李妍峰,孙斌锋.随机需求库存—路径问题：研究现状及展望[J].系统工程,2007,25(8)：38-44.
[46]梁蔚.库存与运输系统集成优化研究与应用[D].大连海事大学硕士论文,2002.
[47]赵达.随机需求的库存—路径问题研究[D].西南交通大学硕士论文,2005.
[48]于涛.VMI下库存管理与运输调度整合优化研究[D].同济大学硕士论文,2008.
[49]王莺.基于R-SYSTEM和DR-SYSTEM的存储路径问题研究[D].西南交通大学硕士论文,2004：28-30.
[50]李军,郭耀煌.配送车辆优化调度理论与方法[M].北京：中国物资出版社,2001.
[51]肖增敏,李军.动态网络车辆路径问题：研究现状及展望[J].系统工程.2004,22(7)：68-71.
[52]HillA V, Benton W C. Modelling intra city time-dependent travel speeds for vehicle scheduling problems[J] Journal of the Operational Research Society,1992,43(4): 343-351.
[53]Malandraki C, Daskin M S. Time-dependent vehicle routing problems formulations properties and heuristic algorithms[J]. Transportation Science,1992,26(3).
[54]Malandrakic, Dial R B. A restriced dynamic programming heuristic algorithm for the time dependent traveling salesman problem[J]. European Journal of Operational Research,1996,90:45-55.
[55]Wiel R, JV Sahinidis.NV. Heunstic bounds and test problem generation for the time-dependent traveling salesman problem [J]. Transportation Seience.1995,29 (22):167-183.
[56]Park Y B. A solution of the bicriteria vehicle-scheduling problems with time and area dependent travel speeds[J]. Computer & Industrial Engineering,2000,38:173-187.
[57]Donati A V, Ambardella L M,Casagrande N, MontemanniR Rizzoli. A Time-dependent vehicle routing problem with an ant colony system[R]. Z.Istituto Dalle Molledi Studisull Intelligenza Artificiale IDSIA Galleria, Manno Switzerland.
[58]Donati A.V.Montemanni, R Casagrande N.RizzoliA.E.Ambardella L.M. Time dependent vehicle-routing problem with an multi ant colony system[A].Z Istituto DalleMolledi Studisull Intelligenza Artificiale(IDSIA) Galleria2,6928, Manno Switzerland IDSIA.
[59]Donati A V Montemanni R Casagrande L MRizzoliA E. Integeration of a robust shortest path algorithm with a time-dependent vehicle routing model and applications[A]. International Symposium on Computational Intelligence for Measurement Systems and Applocation,2003:29-31.
[60]Jung S. A genetic algorithm for vehicle routing problem w ith time dependent travel times[J],2000.
[61]Soumia.Gendreau M Potvin J Y. Vehicle dispatching with time-dependent travel times [J]. European Journal of Operational Research,2003,144(2):379-396.
[62]B Hung Shin J Y. Vehicle routeing w ith time windows and time-varying congestion[J]. Journal of the Operational Research Society,1991,42(5):393-400.
[63]郑成武,刘冬梅.时变网络中物流车辆调度问题的研究[J].天津师范大学学报,2007,9.27(3)：76-80.
[64]王正国,工红卫,刘会新.双目标时变速度车辆路径问题的模型及算法[J].华中科技大学学报(自然科学版).2005,12：94-97.
[65]王正国,刘振元,王红卫.适应性禁忌搜索算法求解带回程的时变速度车辆路径问题[J].计算机集成制造系统,2006,12(9)：1453-1458
[66]李妍峰.时变网络环境下车辆调度问题的研究[D].西南交通大学博士论文.2008：35-39.
[67]张岩,贺国光.一类新的动态车辆调度问题的建模与算法[J].控制工程.2007,5：562-565.
[68]肖增敏.动态网络车辆路径问题研究[D].西南交通大学硕士学位论文,2005：35-39.
[69]王莺.基于R-SYETEM和DR-SYSTEM的存储路径问题研究[D].西南交通大学硕士学位论文,2004：28-38.
[70]周凯.随机时间定位—运输路线安排问题研究[D].中南大学硕士学位论文,2005：33-39.
[71]辛宗丽.随机需求下的血液的订货策略研究[D].西南交通大学硕士学位论文,2005：31-35.
[72]雷英杰.MATLAB遗传算法工具箱及应用[M].西安电子科技大学出版社.
[73]李汝仙.易腐品库存控制研究[D].北京交通大学硕士学位论文,2009：28-29.