Inventory control in multi-echelon divergent systems with random lead times

Abstract. This paper deals with integral inventory control in multi-echelon divergent systems with stochastic lead times. The policy considered is an echelon stock, periodic review, order-up-to (R, S) policy. A computational method is derived to obtain the order-up-to level and the allocation fractions required to achieve given target fill rates. Extensive numerical experimentation shows that the accuracy of our approximate method is satisfactory. Further we show that variation in the lead times may have a significant effect on the stock levels required to achieve given target fill rates, hence this variation may not be ignored. Also, it appears that the correlation structure in the lead times may have a significant impact as well.Zusammenfassung. Die Arbeit behandelt das Problem des Bestandsmanagements in mehrstufigen, divergierenden Lagerhaltungssystemen mit stochastischen Wiederbeschaffungszeiten. Die Steuerung erfolgt mittels einer systemweiten Bestellgrenzenregel bei periodischer Kontrolle. Es wird ein Verfahren zur Bestimmung von Bestellgrenzen und Allokationsparametern zur Einhaltung vorgegebener ( $\beta$-) Servicegrade konstruiert. Ausführliche numerische Untersuchungen zeigen die zufriedenstellende Genauigkeit der heuristischen Vorgehensweise. Weiterhin wird gezeigt, daß die Variabilität der Wiederbeschaffungszeiten einen erheblichen Einfluß auf die erforderlichen Bestände haben kann und nicht vernachlässigt werden darf. Außerdem zeigt sich, daß die Korrelationsstruktur in den Wiederbeschaffungszeiten ebenfalls von erheblicher Bedeutung sein kann.

[1]  Eb Erik Diks,et al.  Modeling stochastic lead times in multi-echelon systems , 1996 .

[2]  S. Nahmias,et al.  Mathematical Models of Retailer Inventory Systems: A Review , 1993 .

[3]  Begnaud Francis Hildebrand,et al.  Introduction to numerical analysis: 2nd edition , 1987 .

[4]  Eb Erik Diks,et al.  Multi-echelon systems: A service measure perspective , 1996 .

[5]  A. Federgruen.  Chapter 3 Centralized planning models for multi-echelon inventory systems under uncertainty , 1993, Logistics of Production and Inventory.

[6]  de Ag Ton Kok,et al.  Stock allocation in a two-echelon distribution network under service constraints , 1994 .

[7]  Graham K. Rand,et al.  Decision Systems for Inventory Management and Production Planning , 1979 .

[8]  de Ag Ton Kok.  Hierarchical production planning for consumer goods , 1990 .

[9]  Sven Axsäter,et al.  Chapter 4 Continuous review policies for multi-level inventory systems with stochastic demand , 1993, Logistics of Production and Inventory.

[10]  de Ag Ton Kok,et al.  Allocation policies in general multi-echelon distribution systems with (R, S) order-up-to-policies , 1996 .

[11]  J. Wolfowitz,et al.  Introduction to the Theory of Statistics. , 1951 .

[12]  Kok de Ag,et al.  Distribution planning for a divergent 2-echelon network without intermediate stocks under service restrictions , 1993 .

[13]  W. Zijm,et al.  European Journal of Operational Research Materials Coordination in Stochastic Multi-echelon Systems , 2022 .

[14]  J. Wijngaard,et al.  Commonality and safety stocks , 1987 .

[15]  Paul Zipkin,et al.  Evaluation of base‐stock policies in multiechelon inventory systems with compound‐poisson demands , 1991 .

[16]  W. D. Ray,et al.  Stochastic Models: An Algorithmic Approach , 1995 .

[17]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[18]  D. Gross,et al.  The Effect of Reducing Leadtime on Inventory Levels-Simulation Analysis , 1969 .