The EOQ model with items of imperfect quality and replenishment from different suppliers

The classical economic order quantity model is extended to the case where the items may be acquired from various suppliers. It is assumed that any lot size received from a supplier contains perfect and imperfect quality items. The percentage of perfect quality items in a lot size is a random variable having a known probability distribution. The imperfect quality items are detected through a 100% screening process conducted at the start of the inventory cycle. When the screening process is concluded, the imperfect quality items are sold in one batch at a discounted price. A mathematical model is developed to determine the total profit function. The optimal order quantity and proportions of the order acquired from the suppliers are obtained by maximising the total profit function. Iterative numerical algorithms that determine the optimal solution are proposed. Numerical examples are presented to illustrate the calculations in the case when the percentages of imperfect quality items follow the uniform distribution.