مدل مقدار تولید اقتصادی با نقطه مثبت راه اندازی مجدد تحت تقاضا تصادفی

In this paper, an extended economic production quantity (EPQ) model is investigated, where demand follows a random process. This study is motivated by an industrial case for precision machine assembly in the machinery industry. Both a positive resetup point s and a fixed lot size Q are implemented in this production control policy. To cope with random demand, a resetup point, i.e., the lowest inventory level to start the production, is adapted to minimize stock shortage during the replenishment cycle. The considered cost includes setup cost, inventory carrying cost, and shortage cost, where shortage may occur at the production stage and/or at the end of one replenishment cycle. Under some mild conditions, the expected cost per unit time can be shown to be convex with respect to decision parameters s and Q. Further computational study has demonstrated that the proposed model outperforms the classical EPQ when demand is random. In particular, a positive resetup point contributes to a significant portion of this cost savings when compared with that in the classical lot sizing policy.

Economic production quantity (EPQ) model is an extension of the well-known economic order quantity (EOQ) model where demand is assumed to be constant, e.g., see Hadley and Whitin [1]. Each replenishment cycle in EPQ consists of two stages: the duration to produce a fixed lot size where production rate is continuous and finite, and the duration to deplete remaining inventory before a new batch is launched. When the remaining inventory drops to zero, a new replenishment cycle will resume. An analytical model is developed to determine the optimal EPQ so that the sum of setup cost and inventory carrying cost is minimized. In practice, demand from customers can be dynamic or random. Donaldson [2] established an optimal replenishment schedule when demand is a linear function. Later, Deb and Chaudhuri [3] extended this work to allow for stock shortage. Hariga [4] developed a heuristic to find a lot sizing policy with linear demand when shortage is not permitted. An optimal replenishment schedule with linear or exponential time-varying demand has been studied by Hariga and Benkherouf [5], where an iterative numerical procedure is developed to find optimal schedule. The demand has been treated as deterministic with various functions of time in [2], [3], [4] and [5].

An extend EPQ model that includes a positive resetup point s and a fixed lot size Q is studied in this paper, where demand of customers follows a Poisson process. The expected production inventory cost model is analyzed. Under some mild conditions, the expected cost function can be shown to be convex with respect to the two decision parameters: resetup point and lot size. A fast search algorithm is developed to find the optimal resetup point and the production quantity. Our numerical experiment has demonstrated that the cost improvement is significant when the proposed model is used, instead of using the classical EPQ policy, when faces random demand. The implementation of resetup point in the proposed model has significant impact on the cost improvement. In addition, both the number of backorders and the probability of shortage decrease dramatically under the proposed production policy.