مدل مقدار تولید اقتصادی برای اقلام با کیفیت ناقص

The assumptions necessary to justify the use of economic production quantity (EPQ/EOQ) models are rarely met. To provide mathematical models that more closely conform to actual inventories and respond to the factors that contribute to inventory costs, the models must be extended or altered. This paper hypothesizes a production/inventory situation where items, received or produced, are not of perfect quality. Items of imperfect quality; not necessarily defective; could be used in another production/inventory situation, that is, less restrictive process and acceptance control. The electronics industry gives good examples of such situations. This paper extends the traditional EPQ/EOQ model by accounting for imperfect quality items when using the EPQ/EOQ formulae. This paper also considers the issue that poor-quality items are sold as a single batch by the end of the 100% screening process. A mathematical model is developed and numerical examples are provided to illustrate the solution procedure.

Ever since the EPQ/EOQ (economic production/order quantity) inventory control model was introduced in the earliest decades of this century, it appears that it is still widely accepted by many industries today [1]. Regardless of such an acceptance, the analysis for finding an economic order quantity has several weaknesses. The obvious one is the number of unrealistic assumptions. This has led many researchers to study the EOQ extensively under real-life situations. The result was a vast literature on inventory and production models generalizing the economic order quantity (EOQ) model in numerous directions. Examples of such directions are surveyed below. Yanasse [2] examined the anticipated price increase in a standard EOQ. Mehra et al. [3] analyzed the effect of inflation on order quantity decisions by means of a model that takes into account inflationary trends and time discounting over an infinite time horizon. Tersine and Barman [4] studied the problem of scheduling replenishment orders under the classical EOQ model when both quantity and freight rate discounts are encountered. Pantumsinchai and Knowles [5] presented solutions to the standard container size discount schedule for the economic order quantity (EOQ) case. Min and Chen [6] presented a profit maximizing EOQ model is extended to the case of symmetric oligopoly consisting of several producers who compete with each other for the same potential buyers. Brill and Chaouch [7] presented a model that incorporates variations in the demand rate at random time points into the inventory planning decision.

This paper presents a modified inventory model which accounts for imperfect quality items when using the EPQ/EOQ formulae. It shows that the economic lot size quantity tends to increase as the average percentage of imperfect quality items increase. This contradicts with the finding of Rosenblatt and Lee [14] of reducing the lot size quantity as the average percentage of imperfect quality items increase. The reasonable explanation is that Rosenblat and Lee [14] assume that defective items are reworked instantaneously and kept in stock. This increases the holding cost per unit per unit time that results in lower lot sizes, whereas in this paper, items of imperfect quality are withdrawn from stock resulting in lower holding cost per unit per unit time and larger lot sizes.