یک راه حل برای مدل موجودی مقاوم هنگامی که هر دو موضوع تقاضا و زمان نتیجه تصادفی هستند

We consider the reorder point, order quantity inventory model where the demand, D, and the lead time, L, are independently and identically distributed (iid) random variables. This model is analytically intractable because of order crossover. However, we show how to resolve the intractability by empirical means, for example, by regression relationships produced by simulation and factorial experiments. Using a normal approximation, we show how to obtain regression equations for the optimal cost and the optimal policy parameters (here the order quantity and the safety stock factor) in terms of the problem parameters (ordering cost per order, holding cost per unit per unit time, shortage cost per unit, the standard deviation of demand, and the standard deviation of lead time).

We examine the general stochastic inventory model, where both the demand rate, D, and the lead time, L are independently and identically distributed (iid) random variables. This model has remained analytically intractable because of the problem of order crossover, which distorts the original distribution of the lead time and consequently that of the demand during the lead time.

In the context of the order quantity, reorder point inventory model, with the shortage cost per unit, this study of the (D,L) inventory model with demand rate, D, and lead time, L, both iid random variables, had the purpose of finding out whether we could circumvent the complexity of order crossover by the use of regression equations in the problem parameters. These parameters are the ordering cost per order, the holding cost per unit per unit time, the shortage cost per unit, and the standard deviations of demand rate and of lead time. Using the normal approximation, we accomplish that purpose in that we can write the ‘optimal’ cost, the ‘optimal’ order quantity, and the ‘optimal’ safety stock factor as regression functions in the problem parameters. A practitioner may then use such equations to obtain an approximation of the ‘optimal’ cost, the ‘optimal’ order quantity, and the ‘optimal’ reorder point when faced with a situation where both demand rate and lead time are stochastic. (We put quotes around optimal to indicate that it is an optimal for an approximate cost function.) So our contribution in this paper is that we provide the practitioner a means (through regression equations) of directly calculating the inventory policy parameters.