Multi-echelon systems: A service measure perspective.

*(English)*Zbl 0944.90501Summary: This paper reviews the most important results on divergent multi-echelon systems. In particular, we concentrate on the interactions between the elements that constitute such a multi-echelon system, in order to determine several service measures (e.g. external customer service level and inventory holding costs). We distinguish between two types of policies: installation stock and echelon stock policies. A comparison between these two types of policies revealed that the complexity of the analysis is concentrated at different aspects, which are discussed by reviewing the most important papers on both types. Special attention is given to the applicability of the models. Extensions to divergent multi-echelon systems with more than two stages are also treated.

##### MSC:

90B06 | Transportation, logistics and supply chain management |

PDF
BibTeX
XML
Cite

\textit{E. B. Diks} et al., Eur. J. Oper. Res. 95, No. 2, 241--263 (1996; Zbl 0944.90501)

Full Text:
DOI

##### References:

[1] | Axsäter, S., Modelling emergency lateral transshipments in inventory systems, Management science, 36, 1329-1338, (1990) · Zbl 0727.90021 |

[2] | Axsäter, S., Simple solution procedures for a class of two-echelon inventory problems, Operations research, 38, 64-69, (1990) · Zbl 0715.90039 |

[3] | Axsäter, S., Continuous review policies for multi-level inventory systems with stochastic demand, (), 175-197, Chapter 4 |

[4] | Axsäter, S.; Forsberg, R.; Zhang, W.F., Approximating general multi-echelon inventory systems by Poisson models, International journal of production economics, 35, 201-206, (1994) |

[5] | Axsäter, S.; Rosling, K., Notes: installation vs. echelon stock policies for multilevel inventory control, Management science, 39, 1274-1280, (1993) · Zbl 0798.90030 |

[6] | Axsäter, S.; Rosling, K., Multi-level production-inventory control: material requirements planning or reorder-point policies?, European journal of operational research, 75, 405-412, (1994) · Zbl 0804.90036 |

[7] | Badinelli, R., A model for continuous-review pull policies in serial inventory systems, Operations research, 40, 142-156, (1992) · Zbl 0764.90019 |

[8] | Baker, K.R., Safety stocks and component commonality, Journal of operations management, 6, 13-22, (1984) |

[9] | Bertrand, J.W.M.; de Kok, A.G., Performance measurements and performance control in supply chain management, () |

[10] | Chen, F.; Zheng, Y.S., Evaluating echelon stock (R, nq) policies in serial production/inventory systems with stochastic demand, Management science, 40, 1262-1275, (1994) · Zbl 0822.90043 |

[11] | Chew, E.P.; Johnson, L.A., Service levels in distribution systems with random customer order size, Naval research logistics, 42, 39-56, (1995) · Zbl 0822.90062 |

[12] | Chew, E.P.; Tang, L.C., Warehouse-retailer system with stochastic demands — non-identical retailer case, European journal of operational research, 82, 98-110, (1995) · Zbl 0904.90051 |

[13] | Cho, D.I.; Parlar, M., A survey of maintenance models for multi-unit systems, European journal of operational research, 51, 1-23, (1991) |

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

[15] | Clark, A.J.; Scarf, H., Optimal policies for a multi-echelon inventory problem, Management science, 6, 475-490, (1960) |

[16] | de Bodt, M.A.; Graves, S.C., Continuous review policies for a multi-echelon inventory problem with stochastic demand, Management science, 31, 1286-1295, (1985) · Zbl 0607.90024 |

[17] | de Kok, A.G., Basics of inventory management models, (), 520-525 |

[18] | de Kok, A.G., Hierarchical production planning for consumer goods, European journal of operational research, 45, 55-69, (1990) · Zbl 0685.90049 |

[19] | de Kok, A.G., Multi-echelon order-up-to policy systems with service-level constraints; performance and optimization, () |

[20] | de Kok, A.G., Lagodimos, A.G., and Seidel, H.E, “Stock allocation in a 2-echelon distribution network under service-constraints”, submitted to International Journal of Production Economics. |

[21] | Deuermeyer, B.L.; Schwarz, L.B., A model for the analysis of system service level in warehouse-retailer distribution systems: the identical retailer case, (), 163-193 · Zbl 0469.90031 |

[22] | Diks, E.B.; de Kok, A.G., Transshipments in a divergent two-echelon network using the consistent appropriate share rationing policy, () · Zbl 0906.90052 |

[23] | Diks, E.B.; de Kok, A.G., Optimal control of a divergent N-echelon inventory system, () · Zbl 0948.90004 |

[24] | Ehrhardt, R., The power approximation for computing (s, S) inventory policies, Management science, 25, 777-786, (1979) · Zbl 0435.90047 |

[25] | Ehrhardt, R.; Schultz, C.R.; Wagner, H.M., (s, S) policies for a wholesale inventory system, () · Zbl 0469.90023 |

[26] | Eppen, G.; Schrage, L., Centralized ordering policies in a multi-warehouse system with lead times and random demand, Management science, 16, 51-67, (1981) · Zbl 0471.90044 |

[27] | Federgruen, A., Centralized planning models for multiechelon inventory systems under uncertainty, (), 133-173, Chapter 3 |

[28] | Federgruen, A.; Axsäter, S., Logistics of production and inventory, (), 757 |

[29] | Feeney, G.J.; Sherbrooke, C.C., The (S − 1, S) inventory policy under compound Poisson demand, Management science, 12, 391-411, (1966) · Zbl 0131.18803 |

[30] | Graves, S.C., A multi-echelon inventory model for a repairable item with one-for-one replenishment, Management science, 31, 1247-1256, (1985) · Zbl 0601.90035 |

[31] | Hadley, G.; Whitin, T.M., Analysis of inventory systems, (1963), Prentice-Hall Englewood Cliffs, NJ · Zbl 0133.42901 |

[32] | van der Heijden, M.C., Analysing divergent logistic networks with local (R, S) inventory control, International journal of production economics, 27, 187-219, (1992) |

[33] | Iglehart, D., Dynamic programming and stationary analysis of inventory problems, (), Chapter 1 · Zbl 0126.16004 |

[34] | Iglehart, D., Optimality of (s,S) policies in the infinite horizon dynamic inventory problem, Management science, 9, 259-267, (1963) |

[35] | Jackson, P.L., Stock allocation in a two-echelon distribution system or ‘what to do until your ship comes in’, Management science, 34, 880-895, (1988) |

[36] | Jönsson, H.; Silver, E.A., Stock allocation among a central warehouse and identical regional warehouses in a particular push inventory control system, International journal of production research, 25, 191-205, (1987) · Zbl 0612.90032 |

[37] | Kaplan, R.S., A dynamic inventory model with stochastic lead times, Management science, 16, 491-507, (1970) · Zbl 0193.19603 |

[38] | Lagodimos, A.G., Multi-echelon service models for inventory systems under different rationing policies, International journal of production research, 30, 939-958, (1992) · Zbl 0729.90977 |

[39] | Lagodimos, A.G., Models for evaluating the performance of serial and assembly MRP systems, European journal of operational research, 68, 49-68, (1993) · Zbl 0800.90507 |

[40] | Lagodimos, A.G.; de Kok, A.G.; Verrijdt, J.H.C.M., The robustness of multi-echelon service models under autocorrelated demands, Journal of the operational research society, 46, 92-103, (1995) · Zbl 0828.90043 |

[41] | Lee, H.L., A multi-echelon inventory model for repairable items with emergency lateral transshipments, Management science, 33, 1302-1316, (1987) |

[42] | Lee, H.L.; Moinzadeh, K., Operating characteristics of a two-echelon inventory system for repairable and consumable items under batch ordering and shipment policy, Naval research logistics quarterly, 34, 365-380, (1987) · Zbl 0653.90012 |

[43] | Little, J., A proof of the queuing formula L = λW, Operations research, 383-387, (1961) · Zbl 0108.14803 |

[44] | Mabini, M.C.; Gelders, L.F., Repairable item inventory systems: a literature review, Belgian journal of operations research, 30, 57-69, (1990) |

[45] | Muckstadt, J.A., A model for multi-item, multi-echelon, multi-indenture inventory system, Management science, 20, 472-481, (1973) · Zbl 0303.90013 |

[46] | Nahmias, S., Managing repairable items inventory systems: A review, (), 253-277 |

[47] | Palm, C., Analysis of the Erlang traffic formula for busy-signal arrangements, Ericsson technics, 5, 39-58, (1938) |

[48] | Rosenbaum, B.A., Inventory placement in a two-echelon inventory system: an application, (), 195-207 |

[49] | Rosenbaum, B.A., Service level relationships in a multi-echelon inventory system, Management science, 27, 926-945, (1981) · Zbl 0461.90024 |

[50] | Schneider, H., Methods for determining the reorder point of an (s, S) ordering policy when a service-level is specified, Operational research quarterly, 29, 1181-1193, (1978) · Zbl 0394.90035 |

[51] | Schneider, H., Effect of service-levels on order-points or order-levels in inventory models, International journal of production research, 19, 615-631, (1981) |

[52] | Schneider, H.; Rinks, D.B.; Kelle, P., Power approximations for a two-echelon inventory system using service levels, Production and operations management, 4, 381-400, (1951) |

[53] | Schultz, C., Computing demand properties at the wholesale warehouse level, Naval research logistics quarterly, 30, 37-48, (1983) · Zbl 0525.90035 |

[54] | Seidel, H.P.; de Kok, A.G., Analysis of stock allocation in a 2-echelon distribution system, () |

[55] | Sherbrooke, C.C., METRIC: A multi-echelon technique for recoverable item control, Operations research, 16, 122-141, (1968) |

[56] | Sherbrooke, C.C., An evaluator for the number of operationally ready aircraft in a multi-echelon availability model, Operations research, 19, 618-635, (1971) · Zbl 0213.45501 |

[57] | Sherbrooke, C.C., Waiting time in an (S − 1, S) inventory system — constant service time case, Operations research, 23, 819-820, (1975) · Zbl 0306.90027 |

[58] | Sherbrooke, C.C., VARI-METRIC: improved approximations for multi-indenture, multi-echelon availability models, Operations research, 34, 311-319, (1986) |

[59] | Sherbrooke, C.C., Optimal inventory modeling of systems, () · Zbl 0213.45501 |

[60] | Silver, E.A.; Peterson, R., Decision systems for inventory management and production planning, (1985), Wiley New York |

[61] | Simon, R.M., Stationary properties of a two-echelon inventory model for low-demands items, Operations research, 19, 761-773, (1971) · Zbl 0239.90012 |

[62] | Slay, M., VARI-METRIC — an approach to modellng multi-echelon resupply when the demand process is Poisson with a gamma prior, (1980), Logistics Management Institute Washington, DC, Working paper |

[63] | Svoronos, A.P., A general framework for multi-echelon inventory and production control problems, () |

[64] | Svoronos, A.; Zipkin, P., Estimating the performance of multi-level inventory systems, Operations research, 36, 57-72, (1988) · Zbl 0644.90021 |

[65] | Tijms, H.C., Stochastic models: an algorithmic approach, (1994), Wiley Chichester · Zbl 0838.60075 |

[66] | van Donselaar, K., Integral stock norms in divergent systems with lot-sizes, European journal of operational research, 45, 70-84, (1990) · Zbl 0697.90024 |

[67] | van Donselaar, K.; Wijngaard, J., Commonality and safety stocks, Engineering costs and production economics, 12, 197-204, (1987) |

[68] | van der Heijden, M.C., Supply rationing in multi-echelon divergent systems, (1996), School of Management Studies, University of Twente The Netherlands, Technical report · Zbl 0916.90091 |

[69] | van der Heijden, M.C.; de Kok, A.G., Customer waiting times in an (R, S) inventory system with compound Poisson demand, Zeitschrift für operations research, 36, 315-332, (1992) · Zbl 0764.90027 |

[70] | van Houtum, G.J.; Inderfurth, K.; Zijm, W.H.M., Materials coordination in stochastic multi-echelon systems, European journal of operational research, 95, 1-23, (1996) · Zbl 0955.90502 |

[71] | van Houtom, G.J.; Zijm, W.H.M., Computational procedures for stochastic multi-echelon production systems, International journal of production economics, 23, 223-237, (1991) |

[72] | Verrijdt, J.H.C.M.; de Kok, A.G., Distribution planning for a divergent N-echelon network without intermediate stocks under service restrictions, International journal of production economics, 38, 225-243, (1995) |

[73] | Verrijdt, J.H.C.M.; de Kok, A.G., Distribution planning for a divergent depotless two-echelon network under service restrictions, European journal of operational research, 89, 341-354, (1996) · Zbl 0913.90096 |

[74] | Wolff, R.W., Poisson arrivals see time averages, Operations research, 30, 223-231, (1982) · Zbl 0489.60096 |

[75] | Zipkin, P., On the imbalance of inventories in multi-echelon systems, Mathematics of operations research, 9, 402-423, (1984) · Zbl 0555.90033 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.