Summary
This paper considers a stochastic inventory system with Poisson demand and exponentialy distributed delivery time. Unsatisfied demand is lost. Optimality of ans, S policy andD=S−s≥s are assumed. The steady state probabilities of the system are calculated, average costs are obtained and the minimized. Two limiting cases may be solved in closed form: rate of demand much larger or much smaller than rate of delivery. In the last case the Wilson lot size formula is regained.
Stochastic inventory systems have been studied extensively in the literature (see, for example, Arrow, Karlin and Scarf 1958 [1]. Hadley and Within 1963 [3], Veinott and Wagner 1966 [9], Beckmann 1961 [2], Kaplan 1970 [4], Simon 1971 [5], Sivazlian 1974 [6]).
Zusammenfassung
Ein stochastisches Lagerhaltungssystem mit Poisson-Nachfrage und exponentieller Lieferzeit wird betrachtet. Nichtbefriedigte Nachfrage geht verloren. Die Optimalität einers, S Politik wird vorausgesetzt und die Annahme gemacht, daß die Bestellmenge größer ist als der Wiederbestellpunkt. Die Zustandswahrscheinlichkeiten des Systems werden berechnet und die Durchschnittskosten bestimmt und minimiert. Zwei Grenzfälle werden näher untersucht: die durchschnittlichen Intervalle zwischen den Nachfragen sind entweder sehr groß oder sehr klein im Vergleich zur mittleren Lieferzeit. Im letzten Fall erhält man wieder die Wilsonsche Losgrößenformel.
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References
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This work has been supported by a grant from the Deutscher Akademischer Austausch Dienst (DAAD). We should like to thank Dr. Joachim Fischer for several corrections, for drawing Fig. 1 and for computing Table 1
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Beckmann, M.J., Srinivasan, S.K. An (s, S) inventory system with poisson demands and exponential lead time. OR Spektrum 9, 213–217 (1987). https://doi.org/10.1007/BF01719831
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DOI: https://doi.org/10.1007/BF01719831