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The optimality of ( s,S ) inventory policies in the infinite period model *
Author(s) -
Tijms H. C.
Publication year - 1971
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1971.tb00131.x
Subject(s) - economic shortage , holding cost , mathematics , total cost , product (mathematics) , function (biology) , constant (computer programming) , average cost , upper and lower bounds , inventory cost , set (abstract data type) , mathematical optimization , economics , discounting , mathematical economics , computer science , microeconomics , business , mathematical analysis , linguistics , marketing , evolutionary biology , government (linguistics) , programming language , finance , philosophy , supply chain , geometry , biology
Summary The infinite period stationary inventory model is considered. There is a constant lead time, a nonnegative set‐up cost, a linear purchase cost, a holding and shortage cost function, a fixed discount factor β, 0 < β < 1, and total backlogging of unfilled demand. Both the total discounted cost (β < 1) and the average cost (β= 1) criteria are considered. Under the assumption that the negatives of the one period holding and shortage costs are unimodal, a unified proof of the existence of an optimal ( s.S ) policy is given. As a by‐product of the proof upper and lower bounds on the optimal values of s and S are found. New results simplify the algorithm of V einott and W agner for finding an optimal ( s , S) policy for the case β < 1. Further it is shown that the conditions imposed on the one period holding and shortage costs can be weakened slightly.