A continuous review inventory model, with deteriorating items, time-varying demand, linear replenishment cost, partially time-varying backlogging
A finite time horizon inventory model for deteriorating items with time-varying demand has undergone extensive mathematical developments in the past 30 years. However, it is often assumed that the shortages are either completely backlogged or completely lost. The highlight of this paper is that the backlogging rate, during the shortage period, is variable and is dependent on the length of the waiting time for the next replenishment. Indeed, the assumption makes the model more complete and applicable in practice. The authors show in a rigorous way that the optimal solution case not only exists but also is unique under specific circumstance, \(0\leq\alpha\leq C_2/(C+C_2H-C_4)\). However, their theory is limited only to the exponential class of backlogging rate. In practice, one can observe periodically the proportion of demand which would like to accept backlogging and the corresponding waiting time for the next replenishment. Then the statistical techniques, such as the nonlinear regression method, can be used to estimate the backlogging rate. Therefore, the backlogging rate can be relaxed to be more general. Furthermore, their solution procedure was too complex and tedious in computing. One can find the approximate solution of the inventory system by the \textit{B. C. Giri}, \textit{K. S. Chakrabarty} and \textit{K. S. Chaudhuri} [Comput. Oper. Res. 27, 495-505 (2000; Zbl 0955.90005)] algorithm.
scientific article; zbMATH DE number 1795034
scientific article