A deterministic inventory model of deteriorating items with two rates of production, shortages, and variable production cycle (Q420225)

Summary: A Continuous production control inventory model is developed for a deteriorating item having shortages and variable production cycle. It is assumed that the production rate is changed to another at a time when the inventory level reaches a prefixed level \(Q_1\) and continued until the inventory level reaches the level \(S(> Q_1)\). The demand rate is assumed to be constant, and the production cycle \(T\) is taken as variable. The production is started again at a time when the shortage level reaches a prefixed quantity \(Q_2\). For this model, the total cost per unit time as a function of \(Q_1, Q_2, S\), and \(T\) is derived. The optimal decision rules for \(Q_1, Q_2, S\), and \(T\) are computed. The sensitivity of the optimal solution towards changes in the values of different system parameters is also studied. Results are illustrated by numerical examples.