In this paper, the (r,S) policy is considered for production/inventory systems where a single type items are produced on an item by item basis by a single production facility. The (r,S) policy considered in this paper is a pull type threshold policy which is very useful in situations where the time and cost required to setup the production facility are relatively high. The demand for the item is assumed to arrive according to a Poisson process. The processing time required to produce an item is assumed to follow an arbitrary distribution. When an item is demanded, one of the items in the inventory is delivered to the customer and the kanban on the item is removed. The removed kanban is immediately transmitted to the production facility. At the instant r kanbans are accumulated at the production facility, the operator turns the production facility on, which takes a random amount of time. In the production period, items are produced one by one and whenever each item is produced, a kanban is attached to it. When there are no kanbans at the production facility, the machine is shut off and a non-production period begins, which lasts until the number of kanbans accumulated at the production facility is raised back to r. In this paper, assuming a linear cost structure, an efficient search procedure is developed to find the optimal threshold value r as well as the optimal number of kanbans S, which minimizes the expected cost incurred per unit time.
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