Abstract
The classic economic production quantity (EPQ) model has been widely used to determine the optimal production quantity. However, the analysis for finding an EPQ model has many weaknesses which lead many researchers and practitioners to make extensions in several aspects on the original EPQ model. The basic assumption of EPQ model is that 100% of manufactured products are non-defective that is not valid for many production processes generally. The purpose of this paper is to develop an EPQ model with grey demand rate and cost values with maximum backorder level allowed with the good quality items in units under an imperfect production process. The imperfect items are considered to be low quality items which are sold to a particular purchaser at a lower price and, the others are reworked and scrapped. A mathematical model is developed and then an industrial example is presented on the wooden chipboard production process for illustration of the proposed model.
Highlights
The questions of when and how much to order must be answered for an inventory control system
The economic production quantity (EPQ) model is still widely accepted by many industries today, due to many unrealistic assumptions regarding to the model input parameters, especially setup cost, holding cost and demand rates, some practitioners and researchers were discussed to modify the EPQ model to match real-life situations and published hundreds of papers and books under various conditions and assumptions such as production rates, shortages, backorders, imperfect items, inspection/with errors, learning effects, delay in payments and trade credit policies [2,3,4,5,6,7,8]
( ) [, ] : grey demand rate in units per unit time (β) 1 [K, K ] : grey setup cost for each production run (K) 2 [C, C ] : grey production cost per item ($/item, inspection cost per item is included; C) 3 [CR, CR ] : grey repair cost for each imperfect quality item reworked ($/item, CR) 4 [CS, CS ] : grey disposal cost for each scrap item produced ($/ scrap item, CS) 5 [h, h ] : grey holding cost per item per unit time ($/item/unit item, h) 6 [h1, h1] : grey holding cost for each imperfect quality items being reworked per unit time ($/item/unit item, h1)
Summary
The questions of when and how much to order must be answered for an inventory control system. Rosenblatt and Lee [9] derived an EPQ model with imperfect production process since the system reached out-of control point by producing 100% good items with an exponential distribution. Their model is extended with the assumption of general randomness during the good item production process by Kim and Hong [10]. Hayek and Salameh [11] model derived with random defective rate, reworking and backlogging for optimal lot size model by Chiu [12]. We expanded Eroglu et al [35] model with greyness of demand rate and cost values and supported with a numerical example of wooden particleboard industry
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