逆向物流随机库存策略研究
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摘要
由于回收产品在数量、时间与质量的高度不确定性,以及存在多个可替代的供应源,逆向物流的库存管理相当困难与复杂。签于传统库存优化问题的定量研究的局限性,论文采用马可夫决策过程(MDP)理论在对逆向物流库存系统的动态变化特性分析的基础上对随机库存问题进行定量研究。基于产品回收之后的形态变化,论文提出了逆向物流库存系统的两种基本类型：回收产品直接重用,回收产品再制造。在此基础上,论文将所研究的随机库存优化策略问题扩展至回收产品生命周期。
首先,论文分析了回收产品直接重用的逆向物流库存系统,其中只有一个库存点,假设需求与回收之间是相互独立的,且对回收产品不进行废弃处置。针对单位需求与回收的情况,通过一维连续时间马尔可夫模型证明了库存成本函数与采用(s,Q)的传统“前向物流”库存模型的库存成本函数具有完全相同的结构。然后,针对需求与回收服从一般性随机分布的情况,分别采用贴现成本法与平均成本法证明了逆向物流库存系统的库存量可以被分解为两部分,一部分的动态特性与传统库存系统是相同的,另一部分则是独立的对外订购,此时逆向物流库存系统的最优库存策略是(s,S)库存策略。
由于在一定条件下逆向物流库存模型可以转换成采用(s,S)库存策略的“前向物流”库存模型,因此论文采用了线性搜索法进行数值实验,从回收率、需求率、产品回收过程中信息控制等三方面探讨不同的回收参数对平均库存成本的影响。数值实验结果表明,如果采用合理的库存控制策略,回收率对平均库存成本的影响是相当有限的。只有在回收率非常高的时候,对回收产品进行废弃处理以避免过高的库存量才是有必要的。同时,通过预测与监测等手段加强产品回收信息的控制有助于降低逆向物流库存系统的平均库存成本。
其次,论文分析了回收产品再制造的逆向物流库存系统,其中有两个库存点即回收库存、销售备用库存,假设需求与回收之间是相互独立的,且对回收产品不进行废弃处置。另外假设新产品制造与回收产品再制造共享一个服务台,再制造作业比制造作业具有优先权。论文参照Puterman提出的方法采用马尔可夫决策过程(MDP)建立了库存模型,采用单值化系数进行离散化处理,推导出最优性方程。论文首先研究了贴现成本情况下最优库存策略的结构,然后证明了平均成本情况下的最优库存策略是基于销售备用库存的最优初始库存量的库存策略。
对于最优平均库存成本的求解,论文建立二维连续时间马尔可夫链截断模型,提出了基于矩阵几何法的稳态概率求解算法。为提高运算效率,论文提出了求解最优初始库存量的近似值的三种启发式算法。数值研究表明,在多数情况下,尤其是在缺货成本相对于持有成本不是很高的情况,三种启发式算法都可以得到良好地近似值。启发式2得到最优库存成本比使用完整枚举法可以减少平均约77%的计算时间。最后,论文对求解稳态概率的三种算法进行了计算时间性能的比较。数值实验表明,论文提出的矩阵几何算法是平均速度最快的。
再次,在以上研究的基础上,论文探讨了逆向物流库存系统在回收产品生命周期各个阶段的最优库存策略。论文采用需求率与回收率的不同组合来代表回收产品生命周期的特定阶段,建立了马尔科夫(MDP)库存模型,对各种可能的库存策略进行数值实验以期找到最优库存策略。数值研究发现,在产品生命周期中采用何种库存策略取决于系统的持有成本组合,同时在回收产品生命周期各阶段的需求率和／或回收率发生变化的时候采用“随时变化”库存策略的设置可以有效地降低总库存成本,相对而言,如果采用“单一策略”或“部分变化”库存策略,那么将会发生额外库存成本。在回收产品生命周期各阶段的周期数量大于一个以上的时候,MDP模型所产生的库存策略可以得到近似最优库存成本。同时,随着产品生命周期各个阶段的周期数量的增加,MDP库存策略的成本性能也随之得到提高。论文提出的MDP库存策略的库存成本在大多数情况下明显低于拉式库存策略。
最后,论文对逆向物流随机库存优化问题的研究成果进行了总结,并针对研究过程中的一些假设进行讨论,提出了进一步研究的扩展方向。图28幅,表23个,参考文献169篇。
The highly uncertainty of return products in quantity, time and quality, as well as there are several alternative supply sources, making the reverse logistics inventory management difficult and complex. Signed in the limitations of quantitative research in traditional inventory optimization problem, this dissertation uses the Markov Decision Process (MDP) theory to analyze the dynamic nature of the reverse logistics inventory system and optimal inventory policy.
Based on morphological changes in the product recovery, the dissertation proposes two kinds of the basic type of reverse logistics inventory systems:directly reuse, remanufacture. On the basis, the dissertation will extend stochastic inventory optimization to the return product life cycle.
First, the dissertation studies the reverse logistics inventory system with return product directly reuse, in which only one inventory point, assuming that demand and return are independent of each other, without disposal of return product. For the unit demand and return, the dissertation construts one-dimensional continuous-time Markov model to prove that the inventory cost function has exactly the same structure as inventory cost function of the traditional inventory model with (s, Q) inventory policy. Then, subject to the general random distribution for demand and return, the dissertation proves the inventory level of the reverse logistics inventory system can be broken down into two parts, the dynamic characteristics of part is the same as the traditional inventory system, the other part is independently the external order, so the optimal inventory policy of reverse logistics inventory system is (s, S) inventory policy.
Because of reverse logistics inventory models can be converted into forward logistics inventory model with (s, S) inventory policy under certain conditions, some traditional inventory optimization algorithms can also be used in the reverse logistics inventory system. The dissertation investigates different recovery parameters affecting the average inventory cost by linear search method proposed by Zheng&Federgruen three areas of demand rate, return rate and product retrun process. The numerical results show that, if we adopt a reasonable inventory control policy, return rate is fairly limited impact on the average inventory cost. Only when return rate is very high, it is necessity to disposal return product in order to avoid excessive inventory levels. At the same time, the dissertation pointed out to control the product return information by means of prediction and monitoring that can reduce the average inventory cost of reverse logistics inventory system.
Second, the dissertation studies the reverse logistics inventory system with return product remanufacture, which has two inventory point of recovery inventory and serviceable inventory. The dissertation assumes that demand and return are independent of each other, without disposal of return product. The dissertation consideres a hybrid production and remanufacturing system where both production and remanufacturing operations are performed by the same single server, and remanufacturing operation has priority. This dissertation construtes the inventory model by Markov Decision Process (MDP), which uses the coefficient of uniformization to discretization, so the optimality equation is derived. This dissertation firstly studies the structure of optimal inventory policy in the discount cost situatio, then proves that the optimal inventory policy is the inventory policy that based on the optimal initial inventory level of serviceable inventory in the average cost situatio.
For the optimal average inventory cost, the dissertation constructs two-dimensional continuous-time Markov chain truncated model, and proposes a solution algorithm based on matrix-geometric methods to solve steady-state probability. In order to improve computational efficiency, the dissertation proposes three heuristic algorithms for solving the approximation of the optimal initial inventory level, in which heuristic1,2are based on the precise formula of the production queuing system with product return, heuristic3is a combination of both. Numerical studies have shown that in most cases, especially in the shortage cost is not very high, all three heuristics can obtain the good approximate value. Heuristics2may reduce approximately77%computing time to obtain the optimal inventory cost than the complete enumeration method. Finally, the dissertation compares the computing time performance of three algorithms for solving steady-state probability. Numerical experiments show that the matrix geometric algorithm proposed by the dissertation has the fastest average speed.
Once again, on the basis of the above studies, the dissertation discusses optimal inventory policy of reverse logistics inventory system in the various stages of the return product life cycle. The dissertation uses the demand rate and the returns-ratio different combination to represent the specific stage of the return product life cycle, establishes a Markov inventory model, carries on the value experiment to find the optimal inventory policy on a variety of possible inventory policies. The results indicate that the optimal inventory policy structures to be used over the return product life cycle depend on the holding cost structure of the system. The optimal parameter values of the inventory policies are sensitive to the changes in demand rate and return rate, and the cost of an inventory policy is sensitive to the changes in its parameters values. Hence, it is recommended to revise the inventory policies over the return product life cycle every time a change in demand rate and/or return rates occurs. Instead of frequently revising the inventory policies over the life cycle, if no revision or only a partial revision is done, then a significant amount of additional cost occurs. The optimal inventory policies based on the MDP model are also good approximations of the optimal policies in a finite-horizon life cycle setting if the life cycle stages are at least a few periods long. Clearly, as the number of periods in which a certain pair of demand rate and return rate is valid increases, the performance of the optimal inventory policy improves.
Finally, the dissertation summarizes the study results of the stochastic inventory optimization problem in reverse logistics, and discusses some assumptions in the course of the study, proposes the extension directiones for further research. The dissertation contains28figures,23table and169references.
首先,论文分析了回收产品直接重用的逆向物流库存系统,其中只有一个库存点,假设需求与回收之间是相互独立的,且对回收产品不进行废弃处置。针对单位需求与回收的情况,通过一维连续时间马尔可夫模型证明了库存成本函数与采用(s,Q)的传统“前向物流”库存模型的库存成本函数具有完全相同的结构。然后,针对需求与回收服从一般性随机分布的情况,分别采用贴现成本法与平均成本法证明了逆向物流库存系统的库存量可以被分解为两部分,一部分的动态特性与传统库存系统是相同的,另一部分则是独立的对外订购,此时逆向物流库存系统的最优库存策略是(s,S)库存策略。
由于在一定条件下逆向物流库存模型可以转换成采用(s,S)库存策略的“前向物流”库存模型,因此论文采用了线性搜索法进行数值实验,从回收率、需求率、产品回收过程中信息控制等三方面探讨不同的回收参数对平均库存成本的影响。数值实验结果表明,如果采用合理的库存控制策略,回收率对平均库存成本的影响是相当有限的。只有在回收率非常高的时候,对回收产品进行废弃处理以避免过高的库存量才是有必要的。同时,通过预测与监测等手段加强产品回收信息的控制有助于降低逆向物流库存系统的平均库存成本。
其次,论文分析了回收产品再制造的逆向物流库存系统,其中有两个库存点即回收库存、销售备用库存,假设需求与回收之间是相互独立的,且对回收产品不进行废弃处置。另外假设新产品制造与回收产品再制造共享一个服务台,再制造作业比制造作业具有优先权。论文参照Puterman提出的方法采用马尔可夫决策过程(MDP)建立了库存模型,采用单值化系数进行离散化处理,推导出最优性方程。论文首先研究了贴现成本情况下最优库存策略的结构,然后证明了平均成本情况下的最优库存策略是基于销售备用库存的最优初始库存量的库存策略。
对于最优平均库存成本的求解,论文建立二维连续时间马尔可夫链截断模型,提出了基于矩阵几何法的稳态概率求解算法。为提高运算效率,论文提出了求解最优初始库存量的近似值的三种启发式算法。数值研究表明,在多数情况下,尤其是在缺货成本相对于持有成本不是很高的情况,三种启发式算法都可以得到良好地近似值。启发式2得到最优库存成本比使用完整枚举法可以减少平均约77%的计算时间。最后,论文对求解稳态概率的三种算法进行了计算时间性能的比较。数值实验表明,论文提出的矩阵几何算法是平均速度最快的。
再次,在以上研究的基础上,论文探讨了逆向物流库存系统在回收产品生命周期各个阶段的最优库存策略。论文采用需求率与回收率的不同组合来代表回收产品生命周期的特定阶段,建立了马尔科夫(MDP)库存模型,对各种可能的库存策略进行数值实验以期找到最优库存策略。数值研究发现,在产品生命周期中采用何种库存策略取决于系统的持有成本组合,同时在回收产品生命周期各阶段的需求率和／或回收率发生变化的时候采用“随时变化”库存策略的设置可以有效地降低总库存成本,相对而言,如果采用“单一策略”或“部分变化”库存策略,那么将会发生额外库存成本。在回收产品生命周期各阶段的周期数量大于一个以上的时候,MDP模型所产生的库存策略可以得到近似最优库存成本。同时,随着产品生命周期各个阶段的周期数量的增加,MDP库存策略的成本性能也随之得到提高。论文提出的MDP库存策略的库存成本在大多数情况下明显低于拉式库存策略。
最后,论文对逆向物流随机库存优化问题的研究成果进行了总结,并针对研究过程中的一些假设进行讨论,提出了进一步研究的扩展方向。图28幅,表23个,参考文献169篇。
The highly uncertainty of return products in quantity, time and quality, as well as there are several alternative supply sources, making the reverse logistics inventory management difficult and complex. Signed in the limitations of quantitative research in traditional inventory optimization problem, this dissertation uses the Markov Decision Process (MDP) theory to analyze the dynamic nature of the reverse logistics inventory system and optimal inventory policy.
Based on morphological changes in the product recovery, the dissertation proposes two kinds of the basic type of reverse logistics inventory systems:directly reuse, remanufacture. On the basis, the dissertation will extend stochastic inventory optimization to the return product life cycle.
First, the dissertation studies the reverse logistics inventory system with return product directly reuse, in which only one inventory point, assuming that demand and return are independent of each other, without disposal of return product. For the unit demand and return, the dissertation construts one-dimensional continuous-time Markov model to prove that the inventory cost function has exactly the same structure as inventory cost function of the traditional inventory model with (s, Q) inventory policy. Then, subject to the general random distribution for demand and return, the dissertation proves the inventory level of the reverse logistics inventory system can be broken down into two parts, the dynamic characteristics of part is the same as the traditional inventory system, the other part is independently the external order, so the optimal inventory policy of reverse logistics inventory system is (s, S) inventory policy.
Because of reverse logistics inventory models can be converted into forward logistics inventory model with (s, S) inventory policy under certain conditions, some traditional inventory optimization algorithms can also be used in the reverse logistics inventory system. The dissertation investigates different recovery parameters affecting the average inventory cost by linear search method proposed by Zheng&Federgruen three areas of demand rate, return rate and product retrun process. The numerical results show that, if we adopt a reasonable inventory control policy, return rate is fairly limited impact on the average inventory cost. Only when return rate is very high, it is necessity to disposal return product in order to avoid excessive inventory levels. At the same time, the dissertation pointed out to control the product return information by means of prediction and monitoring that can reduce the average inventory cost of reverse logistics inventory system.
Second, the dissertation studies the reverse logistics inventory system with return product remanufacture, which has two inventory point of recovery inventory and serviceable inventory. The dissertation assumes that demand and return are independent of each other, without disposal of return product. The dissertation consideres a hybrid production and remanufacturing system where both production and remanufacturing operations are performed by the same single server, and remanufacturing operation has priority. This dissertation construtes the inventory model by Markov Decision Process (MDP), which uses the coefficient of uniformization to discretization, so the optimality equation is derived. This dissertation firstly studies the structure of optimal inventory policy in the discount cost situatio, then proves that the optimal inventory policy is the inventory policy that based on the optimal initial inventory level of serviceable inventory in the average cost situatio.
For the optimal average inventory cost, the dissertation constructs two-dimensional continuous-time Markov chain truncated model, and proposes a solution algorithm based on matrix-geometric methods to solve steady-state probability. In order to improve computational efficiency, the dissertation proposes three heuristic algorithms for solving the approximation of the optimal initial inventory level, in which heuristic1,2are based on the precise formula of the production queuing system with product return, heuristic3is a combination of both. Numerical studies have shown that in most cases, especially in the shortage cost is not very high, all three heuristics can obtain the good approximate value. Heuristics2may reduce approximately77%computing time to obtain the optimal inventory cost than the complete enumeration method. Finally, the dissertation compares the computing time performance of three algorithms for solving steady-state probability. Numerical experiments show that the matrix geometric algorithm proposed by the dissertation has the fastest average speed.
Once again, on the basis of the above studies, the dissertation discusses optimal inventory policy of reverse logistics inventory system in the various stages of the return product life cycle. The dissertation uses the demand rate and the returns-ratio different combination to represent the specific stage of the return product life cycle, establishes a Markov inventory model, carries on the value experiment to find the optimal inventory policy on a variety of possible inventory policies. The results indicate that the optimal inventory policy structures to be used over the return product life cycle depend on the holding cost structure of the system. The optimal parameter values of the inventory policies are sensitive to the changes in demand rate and return rate, and the cost of an inventory policy is sensitive to the changes in its parameters values. Hence, it is recommended to revise the inventory policies over the return product life cycle every time a change in demand rate and/or return rates occurs. Instead of frequently revising the inventory policies over the life cycle, if no revision or only a partial revision is done, then a significant amount of additional cost occurs. The optimal inventory policies based on the MDP model are also good approximations of the optimal policies in a finite-horizon life cycle setting if the life cycle stages are at least a few periods long. Clearly, as the number of periods in which a certain pair of demand rate and return rate is valid increases, the performance of the optimal inventory policy improves.
Finally, the dissertation summarizes the study results of the stochastic inventory optimization problem in reverse logistics, and discusses some assumptions in the course of the study, proposes the extension directiones for further research. The dissertation contains28figures,23table and169references.
引文
[1]Stock J R. Reverse Logistics. Council of Logistics Management[R]. Oak Brook, IL,1992,5-6.
[2]孙华丽,吕帅儿,薛耀锋.逆向物流研究现状综述与展望[J].科技管理研究,2011(2)：127-129.
[3]Fleischmann M, Bloemhof-Ruwaard J M, Dekker R, Van der Laan E, Van Nunen J A E E, Van Wassenhove L N. Quantitative models for reverse logistics:A review[J]. European Journal of Operational Research,1997,85(4):103-107.
[4]Thierry M, Salomon M, Van Nunen J, Van Wassenhove L N. Strategic issues in product recovery management[J]. California Management Review,1995,37(5): 114-135.
[5]Carter C R, Ellram L M. Reverse logistics:A review of the literature and framework for future investigation[J]. Journal of Business Logistics,1998,48(1): 85-101.
[6]Carr S, Duenyas I. Optimal admission control and sequencing in a make-to-stock/ maketo-order production system[J]. Operations Research,2000,48(4):709-720.
[7]Dobos I, Richter K. The integer EOQ repair and waste disposal model-further analysis[J]. Central European Journal of Operations Research,2000,22(8):173-194.
[8]周垂日,梁樑,许传永,查勇.逆向物流研究的新进展：文献综述[J].科研管理,2007,28(3)：123-131.
[9]Barros L, Riley M, David B. Special millennium issue of the EJOR:A global view of industrial logistics [J]. European Journal of Operation Research,2001,129(2): 231-234.
[10]宋守许.面向家电产品的逆向物流关键技术研究：[博士学位论文].合肥：合肥工业大学,2007.
[11]Mahadevan B, Pyke D F, Fleischmann M. Periodic review, push inventory policies for remanufacturing[J]. European Journal of Operational Research,2003, 151(6):536-551.
[12]Sarkis J, Darnall N, Nehman G, Priest J. The role of supply chain management within the industrial ecosystem [R]. International Symposium on Electronics and the Environment, Orlando, FL,1995,229-234.
[13]Guide Jr. Scheduling using drumfbuer-rope in a remanufacturing environment[J]. International Journal of Production Research,1996,34(4):1081-1091.
[14]Daugherty P J, Autry C W, Ellinger A.E. Reverse logistics:The relationship between resource commitment and program performance[J]. Journal of Business Logistics,2001,22(1):107-123.
[15]Krumwiede D, Dennis W, Sheu C. A model for reverse logistics entry by thirdparty providers[J]. Omega,2002,30(8):325-333.
[16]董景峰.面向逆向物流的供应链规划问题研究：[博士学位论文].哈尔滨：哈尔滨工业大学,2008.
[17]Stock J R. Development and Implementation of Reverse Logistics Program[M]. Council of Logistics Management, Oak Brook, IL,1998.
[18]Rogers D S, Tibben-Lembke R S. Going Backwards:Reverse Logistics Trends and Practices[M]. Reverse Logistics Executive Council, Pittsburgh, PA,1999.
[19]de Koster R B M, de Brito M P, Van de Vendel M A. How to organise return handling:an exploratory study with nine retailer warehouses[J]. International Journal of Retail & Distribution Management,2002,30(4):407-421.
[20]de Brito M P, Dekker R. Modelling product returns in inventory control-exploring the validity of general assumptions [J]. International Journal of Production Economics,2003,81-82(6):225-241.
[21]刘永清.逆向物流系统研究评述[J].经济学动态,2009(5)：119-123.
[22]Van der Laan E A, Salomon M. Production planning and inventory control with remanufacturing and disposal[J]. European Journal of Operational Research,1997, 102(3):264-278.
[23]刘健敏.我国废旧家电逆向物流回收机制探讨[J].物流科技,2008(8)：26-28.
[24]Guide V D R, Van Wassenhove L N. The evolution of closed-loop supply chain research[J].Operations Research,2009,57(4):10-28.
[25]郝梅玲,黄敬前,高刚.逆向物流库存控制模型与逆向供应链管理库存理论综述[J].物流科技,2005,28(3)：78-80.
[26]周海波.供应链模式下制造企业库存控制与管理的研究：[博士学位论文].上海：同济大学,2008.
[27]孟丽君.易逝品逆向物流的库存控制及车辆路径问题的优化研究：[博士学位论文].杭州：浙江大学,2009.
[28]Srivastava S K. Green supply-chain management:A state-of-the-art literature review[J]. International Journal of Management Reviews,2007,9(2):53-70.
[29]Wang J. A fuzzy project scheduling approach to minimize schedule risk for product development[J]. Fuzzy Set and System,2002,127(3):99-116.
[30]许博,吴敏.部分可观察马尔可夫决策过程研究进展[J].计算机工程与设计,2007,28(9)：147-152.
[31]刘克.实用马尔可夫决策过程[M].北京：清华大学出版社,2004,20-52.
[32]Puterman M L. Markov Decision Processes:Discrete Stochastic Dynamic Programming[M]. John Wiley and Sons:Hoboken, New Jersey,1994.
[33]Feng C, Suresh P. A Periodic Review Inventory Model with Demand Influenced by Promotion Decisions[J]. Management Science,1999,45(11):327-343.
[34]Bans T, Kamil Y. Markov chain test for time dependence and homogeneity:An analytical and empirical evaluation[J]. European Journal of Operational Research, 2002,137(5):524-543.
[35]Hansen E A, Bernstein D S, Zilberstein S. Dynamic Programming for Partially Observable Stochastic Games[J]. AAAI,2004,709-715.
[36]Becker R, Zilberstein S, Lesser V, Goldman C. Solving transition independent decentralized markov decision processes [J], Journal of Artificial Intelligence Research,2004,22(3):423-455.
[37]Thomas D, Shieu-Hong L. Decomposition Techniques for Planning in Stochastic Domains[J]. IJCAI 1995,18(5):1121-1129.
[38]廖金福主编.库存管理入门[M].广东经济出版社,2004.
[39]Fogarty D, Blackstone J, Hoffmann T. Production and Inventory Management[M]. South-Western,1991.
[40]Davis R A, Markland R E, Vickery S K. Operations Management 2nd[M]. OhiO: South-Western College Publishing,1998.
[41]Simchi-Levi D, Kaminsky P, Simchi-Levi E. Designing and managing the supple chain:concepts, strategies, and case studies[M]. Singapore:McGraw-Hill,2000.
[42]隋明刚.闭环供应链库存优化研究：[博士学位论文].上海：同济大学,2008.
[43]周海波.供应链模式下制造企业库存控制与管理的研究：[博士学位论文].上海：同济大学,2008.
[44]梁金萍.现代物流学(第3版)[M].东北财经大学出版社,2011.
[45]Silver E A, Peterson R. Decision Systems for Inventory Management and Production Planning[M]. New York, John Wiley,1985.
[46]Srivastava S K. Green supply-chain management:A state-of-the-art literature review[J]. International Journal of Management Reviews,2007,22(9):53-80.
[47]Silver E A. Operations research in inventory management:A review and critique[J]. Operations Research,1981,29(4):628-645.
[48]Raafat F. Survey of literature on continuously deteriorating inventory models[J]. Journal of the Operational Research Society,1991,42(1):27-37.
[49]de Koster M B M, Van de Vendel M. Effcient return handling in the retail:A comparison[R]. Working paper, Erasmus University Rotterdam, The Netherlands, 1999.
[50]Sunil C, Peter M. Supply Chain Management:Strategy, Planning and Operations Third Edition (3nd ed.)[M]. NY:Pearson Custom Publishing,2007.
[51]Lee H L. Effective Inventory and Service Management through Product and Process Redesign[J]. Operations Research,1996,44(1):151-159.
[52]Scarf H. The optimality of (S, s) policies in the dynamic inventory problem. Mathematical Method in the Social Science[M]. Stanford University Press,1960.
[53]Zohurl Kabir A B M, Al-Olayan A S. A stocking policy for spare part provisioning under age based preventive replacemen[J]. European Journal of Operational Research,1996,90(4):171-181.
[54]Das C. Explicit formulas for the order size and reorder point in certain inventory problems[J]. Naval Research Logistics,1976,22(9):25-30.
[55]Matheus P, Gelders L. The (R, Q) inventory policy subject to a compound Poisson demand pattern[J]. International Journal of Production Economics,2000, 68(4):307-317.
[56]Verrijdt J H C M, de Kok A G. Distribution planning for a divergent depotless two-echelon network under service constraints [J]. European Journal of Operational Research,1996,89(5):341-354.
[57]Ramasesh R V, Ord J K, Hayya C, Pan A. Slove versus dual sourcing in stochastic lead-time (s, Q) inventory models[J]. management science,1991,37(4): 428-443.
[58]Schrady D A. A deterministic inventory model for repairable items[J]. Naval Research Logistics Quarterly,1967,14(3):391-398.
[59]Stock J R. The 7 Deadly Sins of Reverse Logistics[J]. Material Handling Management,2001,56(3):5-12.
[60]Fleischmann M, Bloemhof-Ruwaard M, Dekker R, Van der Lann E. Quantitative models for reverse logistics:Areview[J]. European Journal of Operational Research,1997,103(2):1-17.
[61]谢家平,黄雪琪,赵忠.逆向物流系统中的库存成本分析[J].江西财经大学学报,2008(1)：9-14.
[62]Tibben-Lembke R S. (1999). The impact of reverse logistics on the total cost of ownership[J]. Journal of Marketing:Theory and Practice.1999,32(7):51-60.
[63]Petrovic D, Roy R, Petrovic R. Modelling and simulation of a supply chain in an uncertain environment[J]. European Journal of Operational Research,1998,109(2): 299-309.
[64]戴菁.逆向物流网络设计与库存控制模型述评[J].商业经济与管理,2004,11(157)：22-24
[65]Fleischmann M, Kuik R. On optimal inventory control with independent stochastic item returns[J]. European Journal of Operational Research,2003,1511 25-37.
[66]Mahadevan B, Pyke D F, Fleischmann M. Periodic review, push inventory policies for remanufacturing[J]. European Journal of Operational Research,2003, 151(6):536-551.
[67]赵晓敏,帅萍,林英晖.产品再生系统的供应链管理研究进展[J].管理工程学报,2009(1)：128-138.
[68]程晋石,裴九芳.考虑修复成本的逆向物流多级库存优化研究[J].成组技术与生产现代化,2009,26(1)：19-22.
[69]岳辉,钟学燕,叶怀珍.逆向物流库存问题的研究现状及展望[J].商场现代化,2005(11)：209-211.
[70]Guide J. Production planning and control for remanufacturing:Industry practice and research needs[J]. Journal of Operations Management,2000,18(3):467-483.
[71]Stock J R. The 7 Deadly Sins of Reverse Logistics[J]. Material Handling Management,2001,56(3):5-12.
[72]Rubio S, Chamorro A, Miranda F J. Characteristics of the research on reverse logistics (1995-2005)[J]. International Journal of Production Research,2008, 46(4):1099-1120.
[73]Richter K. An EOQ repair and waste disposal model[C]. Igls/Innsbruck, Austria:In Proceedings of the Eighth International Working Seminar on Production Economics,1994,83-91.
[74]Teunter R H. Economic ordering quantities for remanufacturable item inventory systems [R]. Working Paper 31/98, University of Magdeburg, Germany,1998.
[75]刘备林,陈娜.闭环供应链双源库存控制策略模型研究[J].哈尔滨商业大学 学报自然科学版,2006,22(1)：140-143.
[76]王斌.单周期产品逆向物流库存控制问题研究[J].徐州建筑职业技术学院学报,2007,7(4)：41-45.
[77]Mabini M C, Pintelon L M, Gelders L F. EOQ type formulations for controlling repairable inventories[J]. International Journal of Production Economics,1992, 28(3):21-33.
[78]Penev K D, de Ron A J. Determination of a disassembly strategy [J]. International Journal of Production Research,1996,34(2):495-506.
[79]Richter K. The EOQ repair and waste disposal model with variable setup numbers[J]. European Journal of Operational Research,1996,95 (2):313-324.
[80]Richter K. The EOQ repair and waste disposal model with variable set-up numbers[J]. European Journal of Operational Research,1996a,96(3):313-324.
[81]Richter K. The extended EOQ repair and waste disposal model[J]. International Journal of Production Economics,1996b,45(4):443-447.
[82]Richter K. Pure and mixed strategies for the EOQ repair and waste disposal problem[J]. OR Spektrum,1997,19(5):123-129.
[83]Teunter R. Economic ordering quantities for recoverable item inventory systems[J]. Naval Research Logistics,2001,48(5):484-95.
[84]Fleischmann M, Kuik R. On optimal inventory control with independent stochastic item returns[J]. European Journal of Operational Research,2003,151(3): 25-37.
[85]Dobos I, Richter K. A production/recycling model with quality consideration[J]. International Journal of Production Economics,2006,104(2):571-579.
[86]卢荣花,宁宣熙,谢忠赞.逆向物流确定型库存控制策略研究[J].价值工程,2007(5)：101-105.
[87]陈阳,龙芳.含逆向物流的电子产品生产企业库存控制研究[J].商场现代化,2008(2)：137-138.
[88]陶琴,倪明.逆向物流累积批量处理库存控制模型[J].当代经济,2009(2)：152-153.
[89]方春河,周晶洁.允许退货的多品种多级库存系统库存控制研究[J].物流技术,2009,28(6)：70-71.
[90]张姣.供应链环境下含逆向物流的库存控制问题研究[J].商场现代化,2011(5)：45-46.
[91]Wagner H M, Whitin T M. Dynamic version of the economic lot size model[J]. Management Science,1958,5(2):212-219.
[92]Simpson V P. Optimum solution structure for a repairable inventory problem[J]. Operations Research,1978,26(2):270-281.
[93]Beltran J L, Krass D. Dynamic lot sizing with returning items and disposals[R]. Working paper, University of Toronto, Faculty of Management, Toronto. Canada, 1997.
[94]Richter K, Sombrutzki M. Remanufacturing planning by reverse Wagner/Whitin models [J]. European Journal of Operational Research,2000,121(1):304-315.
[95]Richter K, Weber J. The reverse Wagner/Whitin modell with variable manufacturing and remanufacturing cost[J]. Int. J. of Production Economics,2001, 71(3):447-456.
[96]Richter K, Dobos I. Production-inventory control in an EOQ-type reverse logistics system[J]. Supply Chain Management and Reverse Logistics, Springer Verlag,2004,67(14):139-160.
[97]赵道致,詹燕,霍艳芳.累积批量处理的逆向物流最优库存控制研究[J].系统工程理论与实践,2007(4)：67-71.
[98]朱慧敏,王丽萍,戴海容.基于概率分布约束的逆向物流多周期库存模型[J].浙江工业大学学报,2008,36(5)：504-508.
[99]彭维,胡媛.含逆向物流的销售商库存控制研究[J].价值工程,2008(10)：75-78.
[100]Nahmias S, Rivera H. A deterministic model for a repairable item inventory system with a finite repair rate[J]. International Journal of Production Research, 1979,17(2):215-221.
[101]Silver E A, Pyke D F, Peterson R. Inventory Management and Production Planning and Scheduling.3rd edition [M]. John Wiley & Sons, New York,1998.
[102]Bayindir Z P, Erkip N. A model to evaluate inventory costs in a remanufacturing environment. International Journal of Production Economics,2003,81-82(2): 567-607.
[103]Minner S, Kleber R. Optimal Control of Production and Remanufacturing in a Simple Recovery Model with Linear Cost Functions[J]. OR Spektrum,2001,23(2): 3-24.
[104]Muckstadt J A, Isaac M H. An analysis of single item inventory systems with returns[J]. Naval Research Logistics Quarterly,1981,28(4):237-254.
[105]Van der Laan E, Dekker R, Salomon M. Product remanufacturing and disposal:A numerical comparison of alternative control strategies[J]. International Journal Of Production Economics,1996,45(1-3):489-498.
[106]黄祖庆,达庆利.一个允许退货的库存控制策略模型[J].东南大学学报(自然科学版),2003,33(6)：792-795.
[107]黄祖庆,达庆利.基于逆向物流定期和定量处理的最优库存控制策略研究[J].东南大学学报(自然科学版),2005,35(2)：302-307.
[108]杨杰,周磊山,孟羽中,刘佳.包含逆向物流的供应链库存控制问题研究[J].北京交通大学学报(社会科学版),2006(5)2：15-18.
[109]李常洪,石磊.一次逆向物流循环的库存控制模型探讨[J].物流技术,2009,28(10)：65-68.
[110]操露,韩瑞珠.基于多产品的动态回收系统库存优化研究[J].武汉理工大学学报·信息与管理工程版,2010,32(2)：311-344.
[111]Fleischmann M, Bloemhof-Ruwaard J M, Dekker R, Van der Laan E A, Van Nunen J A E E, Van Wassenhove L N. Quantitative models for reverse logistics:A review[J]. European Journal of Operational Research,1997a,103(3):1-17.
[112]Simpson V P. An ordering model for recoverable stock items [J]. AIIE Transactions,1970,2(4):315-320.
[113]Whisler W D. A stochastic inventory model for rented equipment[J]. Management Science,1967,13(9):640-647.
[114]Thompson G L, Sethi S P. Turnpike Horizons for Production Planning[J]. Management Science,1980,26(4):229-241.
[115]Cohen M A, Nahmias S, Pierskalla W P. A dynamic inventory system with recycling[J]. Naval Research Logistics Quarterly,1980,27(2):289-296.
[116]Kelle P, Silver E A. Purchasing policy of new containers considering the random returns of previously issued containers[J]. HE Transactions,1989,21(4): 349-354.
[117]Beltran J L, Krass D, Beyer D, Sridhar R. Stochastic inventory models with returns and delivery commitments[R]. Working paper, University of Toronto, Faculty of Management, Toronto, Canada,1997.
[118]Buchanan D J, Abad P L. Optimal policy for a periodic review returnable inventory system[J]. HE Transactions,1998,30(2):1049-1055.
[119]Inderfurth K. Simple optimal replenishment and disposal policies for a product recovery system with leadtimes[J]. OR Spektrum,1997,19(2):111-122.
[120]Veinott A F. On the optimality of (s; S) inventory policies:New conditions and a new proof[J]. SIAM Journal of Applied Mathematics,1966,14(5):1067-1083.
[121]Van der Laan E A, Salomon M. Production planning and inventory control with remanufacturing and disposal[J]. European Journal of Operational Research,1997, 102(4):264-278.
[122]Van der Laan E, Salomon M, Dekker R. An investigation of lead-time effects in manufacturing/remanufacturing systems under simple PUSH and PULL control strategies[J]. European Journal of Operational Research,1999 a,115(1):195-214.
[123]Kiesmuller GP. A new approach for controlling a hybrid stochastic manufacturing/remanufacturing system with inventories and different leadtimes[J]. European Journal of Operational Research,2003,147(1):62-71.
[124]Kiesmuller GP, Minner S. Simple expressions for finding recovery system inventory control parameter values[J]. Journal of the Operational Research Society, 2003,54(3):83-88.
[125]Guide V D R, Van Wassenhove L N. The evolution of closed-loop supply chain research[J]. Operations Research,2009,57(3):10-18.
[126]乔新妮,毛海军,李旭宏,何杰.基于提前期非零时的再制造逆向物流库存控制策略研究[J].中国制造业信息化,2007,36(3)：17-21.
[127]董景峰,周燕,许恒勤.面向内外部逆向物流的库存控制模型[J].计算机集成制造系统,2010,16(1)：64-69.
[128]Wassenhove L N. Quantitative models for reverse logistics:A review[J]. European Journal of Operational Research,1997,103(2):1-7.
[129]Gupta S M, Ilgin M A. Environmentally conscious manufacturing and product recovery (ECMPRO):A review of the state of the art[J]. Journal of Environmental Management,2010,91(2):563-591.
[130]Inderfurth K, Van der Laan E. Leadtime effects and policy improvement for stochastic inventory control with remanufacturing[J]. International Journal of Production Economics,2001,71(1-3):381-390.
[131]Inderfurth K. Optimal policies in hybrid manufacturing/remanufacturing systems with product substitution[J]. International Journal of Production Economics, 2004,90(3):325-434.
[132]江玮蟠.基于定期处理的多品种逆向物流库存控制研究.数学的实践与认识,2010,40(6)：46-53.
[133]江玮璠,李文.基于蒙特卡罗的逆向物流库存控制研究.南昌工程学院学报,2010,29(3)：51-54.
[134]Heyman D P. Optimal disposal policies for a single-item inventory system with returns[J]. Naval Research Logistics Quarterly,1977,24(2):385-405.
[135]Sennott L I. Average cost optimal stationary policies in infinite state markov decision processes with unbounded costs[J]. Operations Research,1989,37(4): 626-633.
[136]Koh S G, Hwang H, Sohn K, Ko C. An optimal ordering and recovery policy for reusable items[J]. Computers & Industrial Engineering,2002,43(2)59-73.
[137]Nenes G, Panagiotidou S, Dekker R. Inventory control policies for inspection and remanufacturing of returns:A case study [J]. International Journal of Production Economics,2010,125(2):300-312.
[138]Chang K H, Lu Y S. Queueing analysis on a single-station make-to-stock/make-to-order inventory-production system[J]. Applied Mathematical Modelling,2010,34(3):978-991.
[139]Van der Laan E A, Dekker R, Salomon M. Product remanufacturing and disposal:A numerical comparison of alternative control strategies [J]. International Journal of Production Economics,1996b,45(1):489-498.
[140]Van der Laan E, Salomon M. Production planning and inventory control with remanufacturing and disposal[J]. European Journal of Operational Research,1997, 102(2):264-278.
[141]Van der Laan E A, Salomon M, Dekker R. Leadtime effects in push and pull controlled manufacturing/remanufacturing systems[J].European Journal of Operational Research,1999a,115(1):195-214.
[142]Fleischmann M, Kuik R, Dekker R. Controlling inventories with stochastic item returns:A basic model[J]. European Journal of Operational Research,2002,138(6): 63-75.
[143]Fleischmann M, Kuik R. On Optimal inventory control with independent stochastic item returns[J]. European Journal of Operational Research,2003,151 (4): 25-37.
[144]Teunter R, Bayindir Z P, Van den Heuvel W. Dynamic lot sizing with product returns and remanufacturing[J]. International Journal of Production Research,2006, 44(4):377-400.
[145]谢家平,黄雪琪,赵忠.逆向物流系统中的库存成本分析[J].江西财经大学学报,2008(1)：9-14.
[146]欧阳惠卿,朱向阳.一种面向逆向物流的库存控制策略[J].上海交通大学学 报,2010,44(3)：369-372.
[147]陈玲丽.缺货的模糊需求回收物流库存控制模型及算法[J].系统管理学报,2010,19(1)：104-107.
[148]李常洪,马佳,石磊.二次循环下逆向物流库存控制模型探讨[J].物流科技,2011(3)：38-41.
[149]Yuan X M, Cheung K L. Modeling returns of merchandise in an inventory system[J]. OR Spektrum,1998,20(3):147-154.
[150]Federgruen A, Zheng Y S. An effcient algorithm for computing an optimal (r, Q) policy in continuous review stochastic inventory systems[J]. Operations Research,1992,40(2):808-813.
[151]Abramowitz M, Stegun I A. Handbook of Mathematical Functions[M]. Dover, New York, N.Y.,1970.
[152]Hadley G, Whitin T M. Analysis of Inventory Systems[M]. Prentice-Hall, Englewood Cliffs N. J.,1963.
[153]Zheng Y S, Federgruen A. Finding optimal (s, S) policies is about as simple as evaluating a single policy [J]. Operations Research,1991,39(4):654-665.
[154]Heyman D P, Sobel M J. Stochastic Models in Operations Re-search, volume II[M].McGraw-Hill, New York,1984.
[155]Meyn S P, Tweedie R L. Markov Chains and Stochastic Stability[M]. Springer, London,1993.
[156]Ching W K, Yuen W O, Loh A W. An inventory model with returns and lateral transshipments [J]. Journal of the Operational Research Society,2003(54):636-641.
[157]Lippman. Applying a new device in the optimization of exponential queueing systems[J]. Operations Research,1975,23(2):687-710.
[158]Koole. Structural results for the control of queueing systems using event-based dynamic programming[J]. Queueing Systems,1998,30(3):323-339.
[159]Adan I J B F, Van der Wal J. Combining make to order and make to stock[J]. OR Spektrum,1998,20(2):73-81.
[160]Weber R R, Stidham S. Optimal control of service rates in networks of queues[J]. Advances in Applied Probability,1987,19(1):202-218.
[161]Veatch M H, Wein L M. Scheduling a make-to-stock queue:index policies and hedging points [J]. Operations Research,1996,44(2):634-647.
[162]Neuts M. Matrix Geometric Solutions in Stochastic Models[M]. Johns Hopkins University Press, Baltimore, MD,1981.
[163]Latouche G. Ramaswami V. A logarithmic reduction algorithm for quasi-birth-death proceses[J]. Journal of Applied Probability,1993,30(3):323-339.
[164]Flapper S D P, Gayon J P, Zerhouni H. Control of a production-inventory system with imperfect advance return information[R]. Working paper, University of Magdeburg, Germany,2010.
[165]Song J S, Xu S, Liu B. Order-fulfillment performance measures in an assemble-to-order system with stochastic leadtimes[J]. Operations Research,1999, 47(3):131-149.
[166]Chang K H, Lu Y S. Queueing analysis on a single-station make-to-stock/make-to-order inventory-production system[J]. Applied Mathematical Modelling,2010,34(4):978-991.
[167]Gayon J P. A make-to-stock queue with product return[C]. Proceedings of the 12th IF AC International Symposium,2006.
[168]Kimura T. Approximations for multi-server queues:system interpolations [J]. Queueing Systems,1994,17(2):347-382.
[169]Teunter R H, Vlachos D. On the necessity of a disposal option for returned items that can be remanufactured[J]. International Journal of Production Economics, 2002,75(3):257-266.
[2]孙华丽,吕帅儿,薛耀锋.逆向物流研究现状综述与展望[J].科技管理研究,2011(2)：127-129.
[3]Fleischmann M, Bloemhof-Ruwaard J M, Dekker R, Van der Laan E, Van Nunen J A E E, Van Wassenhove L N. Quantitative models for reverse logistics:A review[J]. European Journal of Operational Research,1997,85(4):103-107.
[4]Thierry M, Salomon M, Van Nunen J, Van Wassenhove L N. Strategic issues in product recovery management[J]. California Management Review,1995,37(5): 114-135.
[5]Carter C R, Ellram L M. Reverse logistics:A review of the literature and framework for future investigation[J]. Journal of Business Logistics,1998,48(1): 85-101.
[6]Carr S, Duenyas I. Optimal admission control and sequencing in a make-to-stock/ maketo-order production system[J]. Operations Research,2000,48(4):709-720.
[7]Dobos I, Richter K. The integer EOQ repair and waste disposal model-further analysis[J]. Central European Journal of Operations Research,2000,22(8):173-194.
[8]周垂日,梁樑,许传永,查勇.逆向物流研究的新进展：文献综述[J].科研管理,2007,28(3)：123-131.
[9]Barros L, Riley M, David B. Special millennium issue of the EJOR:A global view of industrial logistics [J]. European Journal of Operation Research,2001,129(2): 231-234.
[10]宋守许.面向家电产品的逆向物流关键技术研究：[博士学位论文].合肥：合肥工业大学,2007.
[11]Mahadevan B, Pyke D F, Fleischmann M. Periodic review, push inventory policies for remanufacturing[J]. European Journal of Operational Research,2003, 151(6):536-551.
[12]Sarkis J, Darnall N, Nehman G, Priest J. The role of supply chain management within the industrial ecosystem [R]. International Symposium on Electronics and the Environment, Orlando, FL,1995,229-234.
[13]Guide Jr. Scheduling using drumfbuer-rope in a remanufacturing environment[J]. International Journal of Production Research,1996,34(4):1081-1091.
[14]Daugherty P J, Autry C W, Ellinger A.E. Reverse logistics:The relationship between resource commitment and program performance[J]. Journal of Business Logistics,2001,22(1):107-123.
[15]Krumwiede D, Dennis W, Sheu C. A model for reverse logistics entry by thirdparty providers[J]. Omega,2002,30(8):325-333.
[16]董景峰.面向逆向物流的供应链规划问题研究：[博士学位论文].哈尔滨：哈尔滨工业大学,2008.
[17]Stock J R. Development and Implementation of Reverse Logistics Program[M]. Council of Logistics Management, Oak Brook, IL,1998.
[18]Rogers D S, Tibben-Lembke R S. Going Backwards:Reverse Logistics Trends and Practices[M]. Reverse Logistics Executive Council, Pittsburgh, PA,1999.
[19]de Koster R B M, de Brito M P, Van de Vendel M A. How to organise return handling:an exploratory study with nine retailer warehouses[J]. International Journal of Retail & Distribution Management,2002,30(4):407-421.
[20]de Brito M P, Dekker R. Modelling product returns in inventory control-exploring the validity of general assumptions [J]. International Journal of Production Economics,2003,81-82(6):225-241.
[21]刘永清.逆向物流系统研究评述[J].经济学动态,2009(5)：119-123.
[22]Van der Laan E A, Salomon M. Production planning and inventory control with remanufacturing and disposal[J]. European Journal of Operational Research,1997, 102(3):264-278.
[23]刘健敏.我国废旧家电逆向物流回收机制探讨[J].物流科技,2008(8)：26-28.
[24]Guide V D R, Van Wassenhove L N. The evolution of closed-loop supply chain research[J].Operations Research,2009,57(4):10-28.
[25]郝梅玲,黄敬前,高刚.逆向物流库存控制模型与逆向供应链管理库存理论综述[J].物流科技,2005,28(3)：78-80.
[26]周海波.供应链模式下制造企业库存控制与管理的研究：[博士学位论文].上海：同济大学,2008.
[27]孟丽君.易逝品逆向物流的库存控制及车辆路径问题的优化研究：[博士学位论文].杭州：浙江大学,2009.
[28]Srivastava S K. Green supply-chain management:A state-of-the-art literature review[J]. International Journal of Management Reviews,2007,9(2):53-70.
[29]Wang J. A fuzzy project scheduling approach to minimize schedule risk for product development[J]. Fuzzy Set and System,2002,127(3):99-116.
[30]许博,吴敏.部分可观察马尔可夫决策过程研究进展[J].计算机工程与设计,2007,28(9)：147-152.
[31]刘克.实用马尔可夫决策过程[M].北京：清华大学出版社,2004,20-52.
[32]Puterman M L. Markov Decision Processes:Discrete Stochastic Dynamic Programming[M]. John Wiley and Sons:Hoboken, New Jersey,1994.
[33]Feng C, Suresh P. A Periodic Review Inventory Model with Demand Influenced by Promotion Decisions[J]. Management Science,1999,45(11):327-343.
[34]Bans T, Kamil Y. Markov chain test for time dependence and homogeneity:An analytical and empirical evaluation[J]. European Journal of Operational Research, 2002,137(5):524-543.
[35]Hansen E A, Bernstein D S, Zilberstein S. Dynamic Programming for Partially Observable Stochastic Games[J]. AAAI,2004,709-715.
[36]Becker R, Zilberstein S, Lesser V, Goldman C. Solving transition independent decentralized markov decision processes [J], Journal of Artificial Intelligence Research,2004,22(3):423-455.
[37]Thomas D, Shieu-Hong L. Decomposition Techniques for Planning in Stochastic Domains[J]. IJCAI 1995,18(5):1121-1129.
[38]廖金福主编.库存管理入门[M].广东经济出版社,2004.
[39]Fogarty D, Blackstone J, Hoffmann T. Production and Inventory Management[M]. South-Western,1991.
[40]Davis R A, Markland R E, Vickery S K. Operations Management 2nd[M]. OhiO: South-Western College Publishing,1998.
[41]Simchi-Levi D, Kaminsky P, Simchi-Levi E. Designing and managing the supple chain:concepts, strategies, and case studies[M]. Singapore:McGraw-Hill,2000.
[42]隋明刚.闭环供应链库存优化研究：[博士学位论文].上海：同济大学,2008.
[43]周海波.供应链模式下制造企业库存控制与管理的研究：[博士学位论文].上海：同济大学,2008.
[44]梁金萍.现代物流学(第3版)[M].东北财经大学出版社,2011.
[45]Silver E A, Peterson R. Decision Systems for Inventory Management and Production Planning[M]. New York, John Wiley,1985.
[46]Srivastava S K. Green supply-chain management:A state-of-the-art literature review[J]. International Journal of Management Reviews,2007,22(9):53-80.
[47]Silver E A. Operations research in inventory management:A review and critique[J]. Operations Research,1981,29(4):628-645.
[48]Raafat F. Survey of literature on continuously deteriorating inventory models[J]. Journal of the Operational Research Society,1991,42(1):27-37.
[49]de Koster M B M, Van de Vendel M. Effcient return handling in the retail:A comparison[R]. Working paper, Erasmus University Rotterdam, The Netherlands, 1999.
[50]Sunil C, Peter M. Supply Chain Management:Strategy, Planning and Operations Third Edition (3nd ed.)[M]. NY:Pearson Custom Publishing,2007.
[51]Lee H L. Effective Inventory and Service Management through Product and Process Redesign[J]. Operations Research,1996,44(1):151-159.
[52]Scarf H. The optimality of (S, s) policies in the dynamic inventory problem. Mathematical Method in the Social Science[M]. Stanford University Press,1960.
[53]Zohurl Kabir A B M, Al-Olayan A S. A stocking policy for spare part provisioning under age based preventive replacemen[J]. European Journal of Operational Research,1996,90(4):171-181.
[54]Das C. Explicit formulas for the order size and reorder point in certain inventory problems[J]. Naval Research Logistics,1976,22(9):25-30.
[55]Matheus P, Gelders L. The (R, Q) inventory policy subject to a compound Poisson demand pattern[J]. International Journal of Production Economics,2000, 68(4):307-317.
[56]Verrijdt J H C M, de Kok A G. Distribution planning for a divergent depotless two-echelon network under service constraints [J]. European Journal of Operational Research,1996,89(5):341-354.
[57]Ramasesh R V, Ord J K, Hayya C, Pan A. Slove versus dual sourcing in stochastic lead-time (s, Q) inventory models[J]. management science,1991,37(4): 428-443.
[58]Schrady D A. A deterministic inventory model for repairable items[J]. Naval Research Logistics Quarterly,1967,14(3):391-398.
[59]Stock J R. The 7 Deadly Sins of Reverse Logistics[J]. Material Handling Management,2001,56(3):5-12.
[60]Fleischmann M, Bloemhof-Ruwaard M, Dekker R, Van der Lann E. Quantitative models for reverse logistics:Areview[J]. European Journal of Operational Research,1997,103(2):1-17.
[61]谢家平,黄雪琪,赵忠.逆向物流系统中的库存成本分析[J].江西财经大学学报,2008(1)：9-14.
[62]Tibben-Lembke R S. (1999). The impact of reverse logistics on the total cost of ownership[J]. Journal of Marketing:Theory and Practice.1999,32(7):51-60.
[63]Petrovic D, Roy R, Petrovic R. Modelling and simulation of a supply chain in an uncertain environment[J]. European Journal of Operational Research,1998,109(2): 299-309.
[64]戴菁.逆向物流网络设计与库存控制模型述评[J].商业经济与管理,2004,11(157)：22-24
[65]Fleischmann M, Kuik R. On optimal inventory control with independent stochastic item returns[J]. European Journal of Operational Research,2003,1511 25-37.
[66]Mahadevan B, Pyke D F, Fleischmann M. Periodic review, push inventory policies for remanufacturing[J]. European Journal of Operational Research,2003, 151(6):536-551.
[67]赵晓敏,帅萍,林英晖.产品再生系统的供应链管理研究进展[J].管理工程学报,2009(1)：128-138.
[68]程晋石,裴九芳.考虑修复成本的逆向物流多级库存优化研究[J].成组技术与生产现代化,2009,26(1)：19-22.
[69]岳辉,钟学燕,叶怀珍.逆向物流库存问题的研究现状及展望[J].商场现代化,2005(11)：209-211.
[70]Guide J. Production planning and control for remanufacturing:Industry practice and research needs[J]. Journal of Operations Management,2000,18(3):467-483.
[71]Stock J R. The 7 Deadly Sins of Reverse Logistics[J]. Material Handling Management,2001,56(3):5-12.
[72]Rubio S, Chamorro A, Miranda F J. Characteristics of the research on reverse logistics (1995-2005)[J]. International Journal of Production Research,2008, 46(4):1099-1120.
[73]Richter K. An EOQ repair and waste disposal model[C]. Igls/Innsbruck, Austria:In Proceedings of the Eighth International Working Seminar on Production Economics,1994,83-91.
[74]Teunter R H. Economic ordering quantities for remanufacturable item inventory systems [R]. Working Paper 31/98, University of Magdeburg, Germany,1998.
[75]刘备林,陈娜.闭环供应链双源库存控制策略模型研究[J].哈尔滨商业大学 学报自然科学版,2006,22(1)：140-143.
[76]王斌.单周期产品逆向物流库存控制问题研究[J].徐州建筑职业技术学院学报,2007,7(4)：41-45.
[77]Mabini M C, Pintelon L M, Gelders L F. EOQ type formulations for controlling repairable inventories[J]. International Journal of Production Economics,1992, 28(3):21-33.
[78]Penev K D, de Ron A J. Determination of a disassembly strategy [J]. International Journal of Production Research,1996,34(2):495-506.
[79]Richter K. The EOQ repair and waste disposal model with variable setup numbers[J]. European Journal of Operational Research,1996,95 (2):313-324.
[80]Richter K. The EOQ repair and waste disposal model with variable set-up numbers[J]. European Journal of Operational Research,1996a,96(3):313-324.
[81]Richter K. The extended EOQ repair and waste disposal model[J]. International Journal of Production Economics,1996b,45(4):443-447.
[82]Richter K. Pure and mixed strategies for the EOQ repair and waste disposal problem[J]. OR Spektrum,1997,19(5):123-129.
[83]Teunter R. Economic ordering quantities for recoverable item inventory systems[J]. Naval Research Logistics,2001,48(5):484-95.
[84]Fleischmann M, Kuik R. On optimal inventory control with independent stochastic item returns[J]. European Journal of Operational Research,2003,151(3): 25-37.
[85]Dobos I, Richter K. A production/recycling model with quality consideration[J]. International Journal of Production Economics,2006,104(2):571-579.
[86]卢荣花,宁宣熙,谢忠赞.逆向物流确定型库存控制策略研究[J].价值工程,2007(5)：101-105.
[87]陈阳,龙芳.含逆向物流的电子产品生产企业库存控制研究[J].商场现代化,2008(2)：137-138.
[88]陶琴,倪明.逆向物流累积批量处理库存控制模型[J].当代经济,2009(2)：152-153.
[89]方春河,周晶洁.允许退货的多品种多级库存系统库存控制研究[J].物流技术,2009,28(6)：70-71.
[90]张姣.供应链环境下含逆向物流的库存控制问题研究[J].商场现代化,2011(5)：45-46.
[91]Wagner H M, Whitin T M. Dynamic version of the economic lot size model[J]. Management Science,1958,5(2):212-219.
[92]Simpson V P. Optimum solution structure for a repairable inventory problem[J]. Operations Research,1978,26(2):270-281.
[93]Beltran J L, Krass D. Dynamic lot sizing with returning items and disposals[R]. Working paper, University of Toronto, Faculty of Management, Toronto. Canada, 1997.
[94]Richter K, Sombrutzki M. Remanufacturing planning by reverse Wagner/Whitin models [J]. European Journal of Operational Research,2000,121(1):304-315.
[95]Richter K, Weber J. The reverse Wagner/Whitin modell with variable manufacturing and remanufacturing cost[J]. Int. J. of Production Economics,2001, 71(3):447-456.
[96]Richter K, Dobos I. Production-inventory control in an EOQ-type reverse logistics system[J]. Supply Chain Management and Reverse Logistics, Springer Verlag,2004,67(14):139-160.
[97]赵道致,詹燕,霍艳芳.累积批量处理的逆向物流最优库存控制研究[J].系统工程理论与实践,2007(4)：67-71.
[98]朱慧敏,王丽萍,戴海容.基于概率分布约束的逆向物流多周期库存模型[J].浙江工业大学学报,2008,36(5)：504-508.
[99]彭维,胡媛.含逆向物流的销售商库存控制研究[J].价值工程,2008(10)：75-78.
[100]Nahmias S, Rivera H. A deterministic model for a repairable item inventory system with a finite repair rate[J]. International Journal of Production Research, 1979,17(2):215-221.
[101]Silver E A, Pyke D F, Peterson R. Inventory Management and Production Planning and Scheduling.3rd edition [M]. John Wiley & Sons, New York,1998.
[102]Bayindir Z P, Erkip N. A model to evaluate inventory costs in a remanufacturing environment. International Journal of Production Economics,2003,81-82(2): 567-607.
[103]Minner S, Kleber R. Optimal Control of Production and Remanufacturing in a Simple Recovery Model with Linear Cost Functions[J]. OR Spektrum,2001,23(2): 3-24.
[104]Muckstadt J A, Isaac M H. An analysis of single item inventory systems with returns[J]. Naval Research Logistics Quarterly,1981,28(4):237-254.
[105]Van der Laan E, Dekker R, Salomon M. Product remanufacturing and disposal:A numerical comparison of alternative control strategies[J]. International Journal Of Production Economics,1996,45(1-3):489-498.
[106]黄祖庆,达庆利.一个允许退货的库存控制策略模型[J].东南大学学报(自然科学版),2003,33(6)：792-795.
[107]黄祖庆,达庆利.基于逆向物流定期和定量处理的最优库存控制策略研究[J].东南大学学报(自然科学版),2005,35(2)：302-307.
[108]杨杰,周磊山,孟羽中,刘佳.包含逆向物流的供应链库存控制问题研究[J].北京交通大学学报(社会科学版),2006(5)2：15-18.
[109]李常洪,石磊.一次逆向物流循环的库存控制模型探讨[J].物流技术,2009,28(10)：65-68.
[110]操露,韩瑞珠.基于多产品的动态回收系统库存优化研究[J].武汉理工大学学报·信息与管理工程版,2010,32(2)：311-344.
[111]Fleischmann M, Bloemhof-Ruwaard J M, Dekker R, Van der Laan E A, Van Nunen J A E E, Van Wassenhove L N. Quantitative models for reverse logistics:A review[J]. European Journal of Operational Research,1997a,103(3):1-17.
[112]Simpson V P. An ordering model for recoverable stock items [J]. AIIE Transactions,1970,2(4):315-320.
[113]Whisler W D. A stochastic inventory model for rented equipment[J]. Management Science,1967,13(9):640-647.
[114]Thompson G L, Sethi S P. Turnpike Horizons for Production Planning[J]. Management Science,1980,26(4):229-241.
[115]Cohen M A, Nahmias S, Pierskalla W P. A dynamic inventory system with recycling[J]. Naval Research Logistics Quarterly,1980,27(2):289-296.
[116]Kelle P, Silver E A. Purchasing policy of new containers considering the random returns of previously issued containers[J]. HE Transactions,1989,21(4): 349-354.
[117]Beltran J L, Krass D, Beyer D, Sridhar R. Stochastic inventory models with returns and delivery commitments[R]. Working paper, University of Toronto, Faculty of Management, Toronto, Canada,1997.
[118]Buchanan D J, Abad P L. Optimal policy for a periodic review returnable inventory system[J]. HE Transactions,1998,30(2):1049-1055.
[119]Inderfurth K. Simple optimal replenishment and disposal policies for a product recovery system with leadtimes[J]. OR Spektrum,1997,19(2):111-122.
[120]Veinott A F. On the optimality of (s; S) inventory policies:New conditions and a new proof[J]. SIAM Journal of Applied Mathematics,1966,14(5):1067-1083.
[121]Van der Laan E A, Salomon M. Production planning and inventory control with remanufacturing and disposal[J]. European Journal of Operational Research,1997, 102(4):264-278.
[122]Van der Laan E, Salomon M, Dekker R. An investigation of lead-time effects in manufacturing/remanufacturing systems under simple PUSH and PULL control strategies[J]. European Journal of Operational Research,1999 a,115(1):195-214.
[123]Kiesmuller GP. A new approach for controlling a hybrid stochastic manufacturing/remanufacturing system with inventories and different leadtimes[J]. European Journal of Operational Research,2003,147(1):62-71.
[124]Kiesmuller GP, Minner S. Simple expressions for finding recovery system inventory control parameter values[J]. Journal of the Operational Research Society, 2003,54(3):83-88.
[125]Guide V D R, Van Wassenhove L N. The evolution of closed-loop supply chain research[J]. Operations Research,2009,57(3):10-18.
[126]乔新妮,毛海军,李旭宏,何杰.基于提前期非零时的再制造逆向物流库存控制策略研究[J].中国制造业信息化,2007,36(3)：17-21.
[127]董景峰,周燕,许恒勤.面向内外部逆向物流的库存控制模型[J].计算机集成制造系统,2010,16(1)：64-69.
[128]Wassenhove L N. Quantitative models for reverse logistics:A review[J]. European Journal of Operational Research,1997,103(2):1-7.
[129]Gupta S M, Ilgin M A. Environmentally conscious manufacturing and product recovery (ECMPRO):A review of the state of the art[J]. Journal of Environmental Management,2010,91(2):563-591.
[130]Inderfurth K, Van der Laan E. Leadtime effects and policy improvement for stochastic inventory control with remanufacturing[J]. International Journal of Production Economics,2001,71(1-3):381-390.
[131]Inderfurth K. Optimal policies in hybrid manufacturing/remanufacturing systems with product substitution[J]. International Journal of Production Economics, 2004,90(3):325-434.
[132]江玮蟠.基于定期处理的多品种逆向物流库存控制研究.数学的实践与认识,2010,40(6)：46-53.
[133]江玮璠,李文.基于蒙特卡罗的逆向物流库存控制研究.南昌工程学院学报,2010,29(3)：51-54.
[134]Heyman D P. Optimal disposal policies for a single-item inventory system with returns[J]. Naval Research Logistics Quarterly,1977,24(2):385-405.
[135]Sennott L I. Average cost optimal stationary policies in infinite state markov decision processes with unbounded costs[J]. Operations Research,1989,37(4): 626-633.
[136]Koh S G, Hwang H, Sohn K, Ko C. An optimal ordering and recovery policy for reusable items[J]. Computers & Industrial Engineering,2002,43(2)59-73.
[137]Nenes G, Panagiotidou S, Dekker R. Inventory control policies for inspection and remanufacturing of returns:A case study [J]. International Journal of Production Economics,2010,125(2):300-312.
[138]Chang K H, Lu Y S. Queueing analysis on a single-station make-to-stock/make-to-order inventory-production system[J]. Applied Mathematical Modelling,2010,34(3):978-991.
[139]Van der Laan E A, Dekker R, Salomon M. Product remanufacturing and disposal:A numerical comparison of alternative control strategies [J]. International Journal of Production Economics,1996b,45(1):489-498.
[140]Van der Laan E, Salomon M. Production planning and inventory control with remanufacturing and disposal[J]. European Journal of Operational Research,1997, 102(2):264-278.
[141]Van der Laan E A, Salomon M, Dekker R. Leadtime effects in push and pull controlled manufacturing/remanufacturing systems[J].European Journal of Operational Research,1999a,115(1):195-214.
[142]Fleischmann M, Kuik R, Dekker R. Controlling inventories with stochastic item returns:A basic model[J]. European Journal of Operational Research,2002,138(6): 63-75.
[143]Fleischmann M, Kuik R. On Optimal inventory control with independent stochastic item returns[J]. European Journal of Operational Research,2003,151 (4): 25-37.
[144]Teunter R, Bayindir Z P, Van den Heuvel W. Dynamic lot sizing with product returns and remanufacturing[J]. International Journal of Production Research,2006, 44(4):377-400.
[145]谢家平,黄雪琪,赵忠.逆向物流系统中的库存成本分析[J].江西财经大学学报,2008(1)：9-14.
[146]欧阳惠卿,朱向阳.一种面向逆向物流的库存控制策略[J].上海交通大学学 报,2010,44(3)：369-372.
[147]陈玲丽.缺货的模糊需求回收物流库存控制模型及算法[J].系统管理学报,2010,19(1)：104-107.
[148]李常洪,马佳,石磊.二次循环下逆向物流库存控制模型探讨[J].物流科技,2011(3)：38-41.
[149]Yuan X M, Cheung K L. Modeling returns of merchandise in an inventory system[J]. OR Spektrum,1998,20(3):147-154.
[150]Federgruen A, Zheng Y S. An effcient algorithm for computing an optimal (r, Q) policy in continuous review stochastic inventory systems[J]. Operations Research,1992,40(2):808-813.
[151]Abramowitz M, Stegun I A. Handbook of Mathematical Functions[M]. Dover, New York, N.Y.,1970.
[152]Hadley G, Whitin T M. Analysis of Inventory Systems[M]. Prentice-Hall, Englewood Cliffs N. J.,1963.
[153]Zheng Y S, Federgruen A. Finding optimal (s, S) policies is about as simple as evaluating a single policy [J]. Operations Research,1991,39(4):654-665.
[154]Heyman D P, Sobel M J. Stochastic Models in Operations Re-search, volume II[M].McGraw-Hill, New York,1984.
[155]Meyn S P, Tweedie R L. Markov Chains and Stochastic Stability[M]. Springer, London,1993.
[156]Ching W K, Yuen W O, Loh A W. An inventory model with returns and lateral transshipments [J]. Journal of the Operational Research Society,2003(54):636-641.
[157]Lippman. Applying a new device in the optimization of exponential queueing systems[J]. Operations Research,1975,23(2):687-710.
[158]Koole. Structural results for the control of queueing systems using event-based dynamic programming[J]. Queueing Systems,1998,30(3):323-339.
[159]Adan I J B F, Van der Wal J. Combining make to order and make to stock[J]. OR Spektrum,1998,20(2):73-81.
[160]Weber R R, Stidham S. Optimal control of service rates in networks of queues[J]. Advances in Applied Probability,1987,19(1):202-218.
[161]Veatch M H, Wein L M. Scheduling a make-to-stock queue:index policies and hedging points [J]. Operations Research,1996,44(2):634-647.
[162]Neuts M. Matrix Geometric Solutions in Stochastic Models[M]. Johns Hopkins University Press, Baltimore, MD,1981.
[163]Latouche G. Ramaswami V. A logarithmic reduction algorithm for quasi-birth-death proceses[J]. Journal of Applied Probability,1993,30(3):323-339.
[164]Flapper S D P, Gayon J P, Zerhouni H. Control of a production-inventory system with imperfect advance return information[R]. Working paper, University of Magdeburg, Germany,2010.
[165]Song J S, Xu S, Liu B. Order-fulfillment performance measures in an assemble-to-order system with stochastic leadtimes[J]. Operations Research,1999, 47(3):131-149.
[166]Chang K H, Lu Y S. Queueing analysis on a single-station make-to-stock/make-to-order inventory-production system[J]. Applied Mathematical Modelling,2010,34(4):978-991.
[167]Gayon J P. A make-to-stock queue with product return[C]. Proceedings of the 12th IF AC International Symposium,2006.
[168]Kimura T. Approximations for multi-server queues:system interpolations [J]. Queueing Systems,1994,17(2):347-382.
[169]Teunter R H, Vlachos D. On the necessity of a disposal option for returned items that can be remanufactured[J]. International Journal of Production Economics, 2002,75(3):257-266.