Order level inventory system with power demand pattern for items with variable rate of deterioration.

*(English)*Zbl 0666.90026This paper deals with a standard inventory situation, linear holding and shortage cost, instantaneous delivery of goods, a fixed production cycle of length T and backlogging, except that a variable fraction of inventory, o(t), deteriorates at time t.

In this model \(\theta (t)=kt\), \(0<k\ll 1\), \(0<t<T\), while cumulative demand until time t is given by \(d(t)=d(t/T)^{1/n}\), \(0<t<T\), where d is either a constant or a random variable. For both deterministic and random demand, the authors calculate various optimal quantities, such as \(Q^*\), the amount of inventory to be purchased as the start of each interval, and \(S^*\), the level to which inventory should be raised at the start of the interval. It should be noted that because k is assumed to be very small, second and higher powers of k are neglected thus simplifying the calculations.

In this model \(\theta (t)=kt\), \(0<k\ll 1\), \(0<t<T\), while cumulative demand until time t is given by \(d(t)=d(t/T)^{1/n}\), \(0<t<T\), where d is either a constant or a random variable. For both deterministic and random demand, the authors calculate various optimal quantities, such as \(Q^*\), the amount of inventory to be purchased as the start of each interval, and \(S^*\), the level to which inventory should be raised at the start of the interval. It should be noted that because k is assumed to be very small, second and higher powers of k are neglected thus simplifying the calculations.

Reviewer: E.Boylan

##### MSC:

90B05 | Inventory, storage, reservoirs |