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

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 μs* and μQ* as a function of the three factors p/h, 2Kμ/h, and r. This reduces the number of input parameters from five to three and enables one to compute values of μs* and μQ* 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.