Mixed convexity and optimization results for an (S − 1, S) inventory model under a time limit on backorders

Das (Oper Res 25(5):835–850, <CitationRef CitationID="CR4">1977</CitationRef>) considered the optimization of a cost function associated with an (S − 1, S) inventory model assuming the parameters to be the initial number of items in the stock and the service rate. A similar optimization problem associated with an M/E <Subscript> k </Subscript>/1 queueing system with parameters being the number of servers and the service rate was considered by Kumin (Manag Sci 20:126–129, <CitationRef CitationID="CR11">1973</CitationRef>). Both carried out case-dependent computations and indicated the difficulty of finding general convexity and optimization results for functions with both integer and real variables. In this paper, generalized mixed convexity and computational optimization results for the cost function associated with the (S − 1, S) inventory system suggested by Das are provided. The generalized convexity results determine the convexity region of the cost function, and therefore the region of possible minimal values of the cost function in the domain. In addition, algorithms to determine the generalized convexity and computational optimization results for the cost function are given. Copyright Springer-Verlag 2012