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Some results for the dynamic ( s, S ) inventory 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.tb00148.x
Subject(s) - discounting , mathematics , economic shortage , holding cost , finite set , total cost , set (abstract data type) , limit (mathematics) , function (biology) , inventory cost , product (mathematics) , carrying cost , econometrics , economics , mathematical economics , mathematical optimization , computer science , microeconomics , supply chain , mathematical analysis , linguistics , philosophy , finance , evolutionary biology , government (linguistics) , law , political science , programming language , biology , geometry
Summary The periodic review, single item, stationary ( s, S ) inventory model is considered. There is a fixed lead time, a linear purchase cost, a fixed set‐up cost, a holding and shortage cost function, a discount factor 0 < α≤ 1 and backlogging of unfilled demand. The solution for the total expected discounted cost for the finite period (s, S ) model is found. In addition the time dependent behaviour of the inventory process is found. Further a limit theorem is given, which relates the total expected cost for the finite period ( s, S ) model with no discounting to the average expected cost per period for the infinite period ( s, S ) model. As a by‐product we obtain known results for the infinite period (s, S ) model.