Some remarks on an optimal order quantity and reorder point when supply and demand are uncertain

In the reports in the literature on inventory control, the effects of the random capacity on an order quantity and reorder point inventory control model have been integrated with lead time demand following general distribution. An iterative solution procedure has been proposed for obtaining the optimal solution. However, the resulting solution may not exist or it may not guarantee to give a minimum to the objective cost function, the expected cost per unit time. The aim of this study was to introduce a complete solution of the order quantity/reorder point problem, optimality, properties and bounds on the optimal order quantity and reorder point. The two most appealing distributions of lead time demand, normal and uniform distributions, in conjunction with an exponentially distributed capacity, are used to illustrate our findings in determining the optimal order quantity and reorder point.