Dimensional and Computational Analysis in Stationary (s,S) Inventory Problems with Gamma Distributed Demand

Abstract

In the stationary periodic review ( s , S ) inventory system with stationary demand and immediate delivery of orders, the optimal values of s and S , say s * and S *, will be a function of the input parameters defining the cost structure and the demand distribution. Assume backlogging is allowed and let the fixed order cost be K , the unit holding cost be h , and the unit penalty cost be p . Further, assume the demand per period to have a gamma distribution of order r and with parameter μ. A dimensional analysis of the basic equations dictating the optimal values s * and Q * = S * − s * shows that it is possible to express the quantities μ s * and μ Q * as a function of the three factors p / h , 2 K μ/ h , and r . This reduces the number of input parameters from five to three and enables one to compute values of μ s * and μ Q * for a range of values of the three input factors. A selected set of graphs is presented allowing one to read the optimal values for given input parameters.