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Control Policies for Multi-echelon Inventory Systems with Stochastic Demand

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Supply Chain Coordination under Uncertainty

Part of the book series: International Handbooks on Information Systems ((INFOSYS))

Abstract

Although supply chain management has become an important management paradigm, the optimal control of a stochastic multi-echelon supply chain inventory system is still largely an open issue. An inventory control policy for such a system has to consider at least three aspects: order coordination, information sharing, and stock or risk pooling. Each aspect can generate significant benefits. Nevertheless, an inventory control policy that can fully optimize system performance on all dimensions, even if it exists, would be very difficult to determine. In this paper, we provide a literature review of inventory control policies for multi-echelon supply chain systems with uncertain demand. We first review generic policies developed by extending the basic inventory control policies at a single location. Subsequently, we discuss the themes of coordinated replenishment and information sharing for multi-echelon inventory systems and review the relevant literature. This framework highlights the key factors that drive the performance of multi-echelon inventory systems and shed lights on directions of future research in this area.

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References

  • Arrow K, Harris T, Marschak J (1951) Optimal inventory policy. Econometrica 19:250–272

    Article  Google Scholar 

  • Atkins D, Iyogun P (1988) Periodic versus ‘can-order’ policies for coordinated multi-item inventory systems. Manage Sci 34:791–796

    Article  Google Scholar 

  • Aviv Y (2002) Gaining benefits from joint forecasting and replenishment processes: the case of auto-correlated demand. Manuf Serv Oper Manage 4(1):55–74

    Article  Google Scholar 

  • Axsäter S (1990a) Simple solution procedures for a class of two-echelon inventory problems. Oper Res 38:64–69

    Article  Google Scholar 

  • Axsäter S (1990b) Modeling emergency lateral transshipments in inventory systems. Manage Sci 36:1329–1338

    Article  Google Scholar 

  • Axsäter S (1993a) Continuous review policies for multi-level inventory systems with stochastic demand. In: Graves S, Rinnooy Kan A, Zipkin P (eds) Handbooks in operations research and management science, vol 4, Logistics of production and inventory. North-Holland, Amsterdam, pp 175–197

    Google Scholar 

  • Axsäter S (1993b) Optimization of order-up-to-S policies in two-echelon inventory systems with periodic-review. Nav Res Logist 40:245–253

    Article  Google Scholar 

  • Axsäter S (1993c) Exact and approximate evaluation of batch-ordering policies for two-level inventory systems. Oper Res 41(4):777–785

    Article  Google Scholar 

  • Axsäter S (1997) Simple evaluation of echelon stock (R, Q) policies for two-level inventory systems. IIE Trans 29:661–669

    Google Scholar 

  • Axsäter S (2000) Exact analysis of continuous review (R, Q) policies in two-echelon inventory systems with compound Poisson demand. Oper Res 48(5):686–696

    Article  Google Scholar 

  • Axsäter S (2001) A framework for decentralized multi-echelon inventory control. IIE Trans 33:91–97

    Google Scholar 

  • Axsäter S (2003a) Approximate optimization of a two-level distribution inventory system. Int J Prod Econ 81–82:545–553

    Article  Google Scholar 

  • Axsäter S (2003b) Supply chain operations: serial and distribution inventory systems. In: Graves SC, de Kok T (eds) Supply chain management: design, coordination, and operation. Handbooks in operations research and management science, vol 11, Chap. 10. Elsevier, Amsterdam, pp 525–559

    Google Scholar 

  • Axsäter S (2005) A simple decision rule for decentralized two-echelon inventory control. Int J Prod Econ 93–94:53–59

    Article  Google Scholar 

  • Axsäter S, Juntti L (1996) Comparison of echelon stock and installation stock policies for two-level inventory systems. Int J Prod Econ 45:303–310

    Article  Google Scholar 

  • Axsäter S, Marklund J (2008) Optimal position-based warehouse ordering in divergent two-echelon inventory systems. Oper Res 56(4):976–991

    Article  Google Scholar 

  • Axsäter S, Rosling K (1993) Installation vs. echelon stock policies for multilevel inventory control. Manage Sci 39(10):1274–1280

    Article  Google Scholar 

  • Axsäter S, Zhang W (1999) A joint replenishment policy for multi-echelon inventory control. Int J Prod Econ 59:243–250

    Article  Google Scholar 

  • Axsäter S, Marklund J, Silver EA (2002) Heuristic methods for centralized control of one-warehouse, N-retailer inventory systems. Manuf Serv Oper Manage 4(1):75–97

    Article  Google Scholar 

  • Azoury K (1985) Bayes solutions to dynamic inventory models under unknown demand distributions. Manage Sci 31(9):1150–1160

    Article  Google Scholar 

  • Badinelli R (1992) A model for continuous-review pull policies in serial inventory systems. Oper Res 40(1):142–156

    Article  Google Scholar 

  • Benjaafar S, Cooper W, Kim J (2005) On the benefits of pooling in production-inventory systems. Manage Sci 51(4):548–565

    Article  Google Scholar 

  • Bourland K, Powell S, Pyke D (1996) Exploiting timely demand information to reduce inventories. Eur J Oper Res 92:239–253

    Article  Google Scholar 

  • Cachon G (2001) Exact evaluation of batch-ordering inventory policies in two-echelon supply chains with periodic review. Oper Res 49(1):79–98

    Article  Google Scholar 

  • Cachon G, Fisher M (2000) Supply chain inventory management and the value of shared information. Manage Sci 46(8):1032–1048

    Article  Google Scholar 

  • Cachon G, Zipkin P (1999) Competitive and cooperative inventory policies in a two-stage supply chain. Manage Sci 45(7):936–953

    Article  Google Scholar 

  • Caldentey R, Wein L (2003) Analysis of a decentralized production-inventory system. Manuf Serv Oper Manage 5(1):1–17

    Article  Google Scholar 

  • Cetinkaya S, Lee C (2000) Stock replenishment and shipment scheduling for vendor managed inventory. Manage Sci 46(2):217–232

    Article  Google Scholar 

  • Chao X, Zhou S (2009) Optimal policy for a multiechelon inventory system with batch ordering and fixed replenishment intervals. Oper Res 57(2):377–391

    Article  Google Scholar 

  • Chao X, Zipkin P (2008) Optimal policy for a periodic-review system under a supply capacity contract. Oper Res 56(1):59–70

    Article  Google Scholar 

  • Chen F (1998) Echelon reorder points, installation reorder points, and the value of centralized demand information. Manage Sci 44(12):S221–S234

    Article  Google Scholar 

  • Chen F (1999a) 94%-effective policies for a two-stage serial inventory system with stochastic demand. Manage Sci 45(12):1679–1696

    Article  Google Scholar 

  • Chen F (1999b) Decentralized supply chains subject to information delays. Manage Sci 45(8):1076–1090

    Article  Google Scholar 

  • Chen F (2000) Optimal policies for multi-echelon inventory problems with batch ordering. Oper Res 48(3):376–389

    Article  Google Scholar 

  • Chen S (2004a) The optimality of hedging point policies for stochastic two-product flexible manufacturing systems. Oper Res 52(2):321–323

    Google Scholar 

  • Chen S (2004b) The infinite horizon periodic review problem with setup costs and capacity constraints: a partial characterization of the optimal policy. Oper Res 52(3):409–421

    Article  Google Scholar 

  • Chen F, Song J (2001) Optimal policies for multi-echelon inventory problems with Markov-modulated demand. Oper Res 49(2):226–234

    Article  Google Scholar 

  • Chen F, Zheng Y (1994a) Evaluating echelon stock (R, nQ) policies in serial production/inventory systems with stochastic demand. Manage Sci 40(10):1262–1275

    Article  Google Scholar 

  • Chen F, Zheng Y (1994b) Lower bounds for multi-echelon stochastic inventory systems. Manage Sci 40(11):1426–1443

    Article  Google Scholar 

  • Chen F, Zheng Y (1997) One-warehouse multi-retailer systems with centralized stock information. Oper Res 45(2):275–287

    Article  Google Scholar 

  • Chen F, Zheng Y (1998) Near-optimal echelon-stock (R, nQ) policies in multistage serial system. Oper Res 46(4):592–602

    Article  Google Scholar 

  • Chen F, Drezner Z, Ryan J, Simchi-Levi D (2000) Quantifying the bullwhip effect in a simple supply chain: the impact of forecasting lead time and information. Manage Sci 46(3):436–443

    Article  Google Scholar 

  • Cheung K, Hausman W (2000) An exact performance evaluation for the supplier in a two-echelon inventory system. Oper Res 48(4):646–653

    Article  Google Scholar 

  • Cheung K, Lee H (2002) The inventory benefit of shipment coordination and stock rebalancing in a supply chain. Manage Sci 48(2):300–306

    Article  Google Scholar 

  • Clark A (1958) A dynamic, single-item, multi-echelon inventory model. Report. Rand Corporation, Santa Monica, CA

    Google Scholar 

  • Clark A (1972) An informal survey of multi-echelon inventory theory. Nav Res Logistics Q 19:621–650

    Article  Google Scholar 

  • Clark A, Scarf H (1960) Optimal policies for a multi-echelon inventory problem. Manage Sci 6(4):475–490

    Article  Google Scholar 

  • Clark A, Scarf H (1962) Approximate solutions to a simple multi-echelon inventory problem. In: Arrow KJ, Karlin S, Scarf H (eds) Studies in applied probability and management science. Stanford University Press, Stanford, CA

    Google Scholar 

  • De Bodt M, Graves S (1985) Continuous review policies for a multi-echelon inventory problem with stochastic demand. Manage Sci 31(10):1286–1299

    Article  Google Scholar 

  • Deuermeyer B, Schwarz L (1981) A model for the analysis of system service level in warehouse/retailer distribution systems: the identical retailer case. In: Schwarz LB (ed) Studies in the management sciences, vol 16, Multi-level production/inventory control systems. North-Holland, Amsterdam, pp 163–193

    Google Scholar 

  • Dvoretzky A, Kiefer J, Wolfowitz J (1952) The inventory problem. Econometrica 20:187–222

    Article  Google Scholar 

  • Eppen G, Schrage L (1981) Centralized ordering policies in a multiwarehouse system with leadtimes and random demand. In: Schwarz LB (ed) Studies in the management sciences, vol 16, Multi-level production/inventory control systems. North-Holland, Amsterdam, pp 88–110

    Google Scholar 

  • Eynan A, Fouque T (2003) Capturing the risk-pooling effect through demand reshape. Manage Sci 49(6):704–717

    Article  Google Scholar 

  • Eynan A, Kropp D (1998) Periodic review and joint replenishment in stochastic demand environment. IIE Trans 30:1025–1033

    Google Scholar 

  • Federgruen A (1993) Centralized planning models for multi-echelon inventory systems under uncertainty. In: Graves S, Rinnooy Kan A, Zipkin P (eds) Handbooks in operations research and management science, vol 4, Logistics of production and inventory. North-Holland, Amsterdam, pp 133–173

    Google Scholar 

  • Federgruen A, Zipkin P (1984a) Computational issues in an infinite-horizon, multi-echelon inventory model. Oper Res 32(4):818–836

    Article  Google Scholar 

  • Federgruen A, Zipkin P (1984b) Approximations of dynamic, multilocation production and inventory systems. Manage Sci 30(1):69–84

    Article  Google Scholar 

  • Federgruen A, Zipkin P (1984c) Allocation policies and cost approximation for multilocation inventory systems. Nav Res Logistics Q 31:97–131

    Article  Google Scholar 

  • Federgruen A, Groenevelt H, Tijms H (1984) Coordinated replenishments in a multi-item inventory system with compound Poisson demands and constant lead times. Manage Sci 30:344–357

    Article  Google Scholar 

  • Feng K, Rao U (2007) Echelon-stock (R, nT) control in two-stage serial stochastic inventory systems. Oper Res Lett 35:95–104

    Article  Google Scholar 

  • Feng Q, Sethi S, Yan H, Zhang H (2006) Are base-stock policies optimal in inventory problems with multi delivery modes? Oper Res 54(4):801–807

    Article  Google Scholar 

  • Forsberg R (1995) Optimization of order-up-to-S policies for two-level inventory systems with compound Poisson demand. Eur J Oper Res 81:143–153

    Article  Google Scholar 

  • Forsberg R (1997) Exact evaluation of (R, Q)-policies for two level inventory systems with Poisson demand. Eur J Oper Res 96:130–138

    Article  Google Scholar 

  • Fox E, Metters R, Semple J (2006) Optimal inventory policy with two suppliers. Oper Res 56(4):696–707

    Google Scholar 

  • Gallego G, Ozer O (2001) Integrating replenishment decisions with advance demand information. Manage Sci 47(10):1344–1360

    Article  Google Scholar 

  • Gallego G, Ozer O (2003) Optimal replenishment policies for multi-echelon inventory systems under advance demand information. Manuf Serv Oper Manage 5:157–175

    Article  Google Scholar 

  • Gallego G, Ozer O (2005) A new algorithm and a new heuristic for serial supply systems. Oper Res Lett 33:349–362

    Article  Google Scholar 

  • Gallego G, Toktay L (2004) All-or-nothing ordering under capacity constrain. Oper Res 52(6):1001–1002

    Article  Google Scholar 

  • Gallego G, Ozer O, Zipkin P (2007) Bounds, heuristics, and approximations for distribution systems. Oper Res 55(3):503–517

    Article  Google Scholar 

  • Ganeshan R, Jack E, Magazine M, Stephens P (1998) A taxonomic review of supply chain management research. In: Tayur S, Magazine M, Ganeshan R (eds) Quantitative models for supply chain management, vol 17, International series in operations research and management science. Kluwer, Norwell, MA, pp 839–879

    Google Scholar 

  • Gavieneni S (2002) Information flows in capacitated supply chains with fixed ordering cost. Manage Sci 48(5):644–651

    Article  Google Scholar 

  • Gavieneni S, Kapuscinski R, Tayur S (1999) Value of information in capacitated supply chains. Manage Sci 45(1):16–24

    Article  Google Scholar 

  • Glasserman P, Tayur S (1994) The stability of a capacitated, multi-echelon production-inventory system under a base-stock policy. Oper Res 42(5):913–925

    Article  Google Scholar 

  • Glasserman P, Tayur S (1995) Sensitivity analysis for base-stock levels in multi-echelon production-inventory systems. Manage Sci 41(2):263–281

    Article  Google Scholar 

  • Graves S (1985) A multi-echelon inventory model for repairable item with one-for-one replenishment. Manage Sci 31(10):1247–1256

    Article  Google Scholar 

  • Graves S (1996) A multi-echelon inventory model with fixed replenishment intervals. Manage Sci 42(1):1–18

    Article  Google Scholar 

  • Graves S (1999) A single-item inventory model for a nonstationary demand process. Manuf Serv Oper Manage 1(1):50–61

    Article  Google Scholar 

  • Gunasekaran A, Ngai E (2004) Information systems in supply chain integration and management. Eur J Oper Res 159:269–295

    Article  Google Scholar 

  • Gurbuz M, Moinzadeh K, Zhou Y (2007) Coordinated replenishment strategies in inventory/distribution systems. Manage Sci 53(2):293–308

    Article  Google Scholar 

  • Hariharan R, Zipkin P (1995) Customer-order information, leadtimes, and inventories. Manage Sci 41(10):1599–1607

    Article  Google Scholar 

  • Iglehart D (1964) The dynamic inventory problem with unknown demand distributions. Manage Sci 10(3):429–440

    Article  Google Scholar 

  • Iyer A, Ye J (2000) Assessing the value of information sharing in a promotional retail environment. Manuf Serv Oper Manage 2(2):128–143

    Article  Google Scholar 

  • Jackson P (1988) Stock allocation in a two-echelon distribution system or “what to do until your ship comes in”. Manage Sci 34(7):880–895

    Article  Google Scholar 

  • Jacobs F, Chase R, Aquilano N (2009) Operations and supply management, 12th edn. McGraw-Hill, New York

    Google Scholar 

  • Johansen S, Thorstenson A (1998) An inventory model with Poisson demands and emergency orders. Int J Prod Econ 56–57:275–289

    Article  Google Scholar 

  • Kapuscinski R, Tayur S (1998) A capacitated production-inventory model with period demand. Oper Res 46(6):899–911

    Article  Google Scholar 

  • Khouja M, Goyal S (2008) A review of the joint replenishment problem literature: 1989–2005. Eur J Oper Res 186:1–16

    Article  Google Scholar 

  • Kukreja A, Schmidt C, Miller D (2001) Stocking decisions for low-usage items in a multilocation inventory system. Manage Sci 47(10):1371–1383

    Article  Google Scholar 

  • Kumar A, Schwarz L, Ward J (1995) Risk-pooling along a fixed delivery route. Manage Sci 41:344–362

    Article  Google Scholar 

  • Lee H (1987) A multi-echelon inventory model for repairable items with emergency lateral transshipments. Manage Sci 33:1302–1316

    Article  Google Scholar 

  • Lee H, Moinzadeh K (1987a) Two-parameter approximations for multi-echelon repairable inventory models with batch ordering policy. IIE Trans 19:140–149

    Article  Google Scholar 

  • Lee H, Moinzadeh K (1987b) Operating characteristics of a two-echelon inventory system for repairable and consumable items under batch ordering and shipment policy. Nav Res Logistics Q 34:365–380

    Article  Google Scholar 

  • Lee H, Whang S (1999) Decentralized multi-echelon supply chains: incentives and information. Manage Sci 45(5):633–640

    Article  Google Scholar 

  • Lee H, Padmanabhan V, Whang S (1997) Information distortion in a supply chain: the bullwhip effect. Manage Sci 43(4):546–558

    Article  Google Scholar 

  • Lee H, So K, Tang C (2000) The value of information sharing in a two-level supply chain. Manage Sci 46(5):626–643

    Article  Google Scholar 

  • Li X, Wang Q (2007) Coordination mechanisms of supply chain systems. Eur J Oper Res 179:1–16

    Article  Google Scholar 

  • Lovejoy W (1990) Myopic policies for some inventory models with uncertain demand distributions. Manage Sci 36(6):724–738

    Article  Google Scholar 

  • Marklund J (2006) Controlling inventories in divergent supply chains with advance order information. Oper Res 54(5):988–1010

    Article  Google Scholar 

  • McGavin E, Schwarz L, Ward J (1993) Two-interval inventory-allocation policies in a one-warehouse N-identical retailer distribution system. Manage Sci 39(9):1092–1107

    Article  Google Scholar 

  • McGavin E, Ward J, Schwarz L (1997) Balancing retailer inventories. Oper Res 45(6):820–830

    Article  Google Scholar 

  • Milner J, Kouvelis P (2002) On the complementary value of accurate demand information and production and supplier flexibility. Manuf Serv Oper Manage 4(2):99–113

    Article  Google Scholar 

  • Moinzadeh K (2002) A multi-echelon inventory system with information exchange. Manage Sci 48(3):414–426

    Article  Google Scholar 

  • Moinzadeh K, Lee H (1986) Batch size and stocking levels in multi-echelon repairable systems. Manage Sci 32:1567–1581

    Article  Google Scholar 

  • Moinzadeh K, Nahmias S (1988) A continuous review model for an inventory system with two supply modes. Manage Sci 34:761–773

    Article  Google Scholar 

  • Moinzadeh K, Schmidt C (1991) An (S-1, S) inventory system with emergency orders. Oper Res 39:308–321

    Article  Google Scholar 

  • Muckstadt J (1973) A model for a multi-item, multi-echelon, multi-indenture inventory system. Manage Sci 20:472–481

    Article  Google Scholar 

  • Muckstadt J (1979) A three-person, multi-item model for recoverable items. Nav Res Logistics Q 26:199–221

    Article  Google Scholar 

  • Ozer O (2003) Replenishment strategies for distribution systems under advance demand information. Manage Sci 49(3):255–272

    Article  Google Scholar 

  • Ozer O, Wei W (2004) Inventory control with limited capacity and advance demand information. Oper Res 52(6):988–1001

    Article  Google Scholar 

  • Porteus E (1990) Stochastic inventory theory. In: Heyman D, Sobel M (eds) Stochastic models, handbooks in operations research and management science, vol 12. Elsevier (North-Holland), Amsterdam

    Google Scholar 

  • Raghunathan S (2001) Information sharing in a supply chain: a note on its value when demand is nonstationary. Manage Sci 47(4):605–610

    Article  Google Scholar 

  • Raghunathan S (2003) Impact of demand correlation on the value of and incentives for information sharing in a supply chain. Eur J Oper Res 146:634–649

    Article  Google Scholar 

  • Rao U (2003) Properties of the periodic-review (R, T) inventory control policy for stationary, stochastic demand. Manuf Serv Oper Manage 5(1):37–53

    Article  Google Scholar 

  • Rosling K (1989) Optimal inventory policies for assembly systems under random demands. Oper Res 37(4):565–579

    Article  Google Scholar 

  • Roundy R (1985) 98%-effective integer-ratio lot-sizing for one-warehouse multi-retailer systems. Manage Sci 31(11):1416–1429

    Article  Google Scholar 

  • Roundy R (1986) A 98%-effective lot sizing rule for a multi-product, multi-stage production/distribution system. Math Oper Res 11(4):699–727

    Article  Google Scholar 

  • Sahin F, Robinson E (2002) Flow coordination and information sharing in supply chains: review, implications, and directions for future research. Decis Sci 33(4):505–535

    Article  Google Scholar 

  • Schmidt C, Nahmias S (1985) Optimal policy for a two-stage assembly system under random demand. Oper Res 33:1130–1145

    Article  Google Scholar 

  • Schwarz L (1989) A model for assessing the value of warehouse risk-pooling: risk-pooling over outside-supplier leadtimes. Manage Sci 35(7):828–842

    Article  Google Scholar 

  • Shang K, Song J (2003) Newsvendor bounds and heuristic for optimal policies in serial supply chains. Manage Sci 49(5):618–638

    Article  Google Scholar 

  • Shang K, Song J (2007) Serial supply chains with economies of scale: bounds and approximations. Oper Res 55(5):843–853

    Article  Google Scholar 

  • Shang K, Zhou S (2010) Optimal and heuristic echelon (r, nQ, T) policies in serial inventory systems with fixed costs. Oper Res 58(2):414–429

    Article  Google Scholar 

  • Shanker K (1981) Exact analysis of a two-echelon inventory system for recoverable items under batch inspection policy. Nav Res Logistics Q 28:579–601

    Article  Google Scholar 

  • Sheopuri A, Janakiraman G, Seshdri S (2010) New policies for the stochastic inventory control problem with two supply sources. Oper Res 58(3):734–747

    Article  Google Scholar 

  • Sherbrooke C (1968) METRIC: a multi-echelon technique for recoverable item control. Oper Res 16:122–141

    Article  Google Scholar 

  • Sherbrooke C (1986) VARI-METRIC: improved approximation for multi-indenture, multi-echelon availability models. Oper Res 34:311–319

    Article  Google Scholar 

  • Silver E, Peterson R (1998) Decision systems for inventory management and production. Wiley, New York

    Google Scholar 

  • Simon R (1971) Stationary properties of a two-echelon inventory model for low demand items. Oper Res 19:761–777

    Article  Google Scholar 

  • Song J, Yao D (2002) Performance analysis and optimization of assemble-to-order systems with random lead times. Oper Res 50(5):889–903

    Article  Google Scholar 

  • Sosic G (2006) Transshipment of inventories among retailers: myopic vs. farsighted stability. Manage Sci 52(10):1493–1508

    Article  Google Scholar 

  • Svoronos A, Zipkin P (1988) Estimating the performance of multi-level inventory systems. Oper Res 36(1):57–72

    Article  Google Scholar 

  • Svoronos A, Zipkin P (1991) Evaluation of one-for-one replenishment policies for multiechelon inventory systems. Manage Sci 37:68–83

    Article  Google Scholar 

  • Tagaras G, Vlachos D (2001) A periodic review inventory system with emergency replenishments. Manage Sci 47(3):415–429

    Article  Google Scholar 

  • Tan K (2001) A framework of supply chain management literature. Eur J Purch Supply Manage 7:39–48

    Article  Google Scholar 

  • Tsay A, Nahmias S, Agrawa N (1998) Modeling supply chain contracts: a review. In: Tayur S, Magazine M, Ganeshan R (eds) Quantitative models for supply chain management, vol 17, International series in operations research and management science. Kluwer, Norwell, MA, pp 299–336

    Google Scholar 

  • van Houtum G, Scheller-Wolf A, Ji X (2007) Optimal control of serial inventory systems with fixed replenishment intervals. Oper Res 55(4):674–687

    Article  Google Scholar 

  • Veinott A, Wagner H (1965) Computing optimal (s, S) inventory problems. Manage Sci 11:525–552

    Article  Google Scholar 

  • Véricourt F, Karaesmen F, Dallery Y (2002) Optimal stock allocation for a capacitated supply system. Manage Sci 48(11):1486–1501

    Article  Google Scholar 

  • Viswanathan S (1997) Note. Periodic review (s, S) policies for joint replenishment inventory systems. Manage Sci 43:1447–1454

    Article  Google Scholar 

  • Wang Q (2010) Integer-ratio policies for distribution systems with multiple retailers and stochastic demand. Working paper, Nanyang Business School, Nanyang Technological University, Singapore

    Google Scholar 

  • Wang Q, Axsäter S (2010) Fixed-interval order-up-to policies for distribution systems with multiple retailers and stochastic demand. Working paper, Nanyang Business School, Nanyang Technological University, Singapore

    Google Scholar 

  • Wang T, Toktay B (2008) Inventory management with advance demand information and flexible delivery. Manage Sci 54(4):716–732

    Article  Google Scholar 

  • Wee K, Dada M (2005) Optimal policies for transshipping inventory in a retailer network. Manage Sci 51(10):1519–1533

    Article  Google Scholar 

  • Yano C, Carson C (1988) Safety stocks for assembly systems with fixed production schedules. J Manuf Oper Manage 1:182–201

    Google Scholar 

  • Zheng Y (1992) On properties of stochastic inventory systems. Manage Sci 38(1):87–103

    Article  Google Scholar 

  • Zheng Y, Federgruen A (1991) Finding optimal (s, S) policies is about as simple as evaluating a single policy. Oper Res 39(4):654–665

    Article  Google Scholar 

  • Zheng Y, Zipkin P (1990) A queuing model to analyze the value of centralized inventory information. Oper Res 38(2):296–307

    Article  Google Scholar 

  • Zipkin P (1986a) Stochastic leadtimes in continuous-time inventory models. Nav Res Logistics Q 33:763–774

    Article  Google Scholar 

  • Zipkin P (1986b) Inventory service level measures: convexity and approximation. Manage Sci 32(8):975–981

    Article  Google Scholar 

  • Zipkin P (1995) Performance analysis of a multi-item production-inventory system under alternative policies. Manage Sci 41(4):690–703

    Article  Google Scholar 

  • Zipkin P (2000) Foundations of inventory management. McGraw-Hill, New York

    Google Scholar 

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Wang, Q. (2011). Control Policies for Multi-echelon Inventory Systems with Stochastic Demand. In: Choi, TM., Cheng, T. (eds) Supply Chain Coordination under Uncertainty. International Handbooks on Information Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19257-9_4

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