A supplement to an EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales return

Hsu and Hsu (2013a) established a closed-form solution for an EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns, where the customers who return the defective items will receive full price refunds; i.e., the returned items are not replaced with good items. In this note, we extend Hsu and Hsu's (2013a) work to consider the case that returned items are replaced with good items. A closed-form solution is developed for the optimal order size and the maximum shortage level. Numerical examples are provided to show the differences in the optimal solutions when returned items are replaced, and when they are not

An inventory system with time-dependent demand and partial backordering under return on inventory investment maximization

Producción CientíficaIn this article, we study an inventory system for items that have a power demand pattern and where shortages are allowed. We suppose that only a fixed proportion of demand during the stock-out period is backordered. The decision variables are the inventory cycle and the ratio between the initial stock and the total quantity demanded throughout the inventory cycle. The objective is to maximize the Return on Inventory Investment (ROII) defined as the ratio of the profit per unit time over the average inventory cost. After analyzing the objective function, the optimal global solutions for all the possible cases of the inventory problem are determined. These optimal policies that maximize the ROII are, in general, different from those that minimize the total inventory cost per unit time. Finally, a numerical sensitivity analysis of the optimal inventory policy with respect to the system input parameters and some useful managerial insights derived from the results are presented.Ministerio de Ciencia, Innovación y Universidades - Fondo Europeo de Desarrollo Regional (project MTM2017-84150-P

EPQ Model with Imperfect Quality Raw Material

MSC 2010: 26A33, 33E12, 33C60, 44A20The classical economic production model (EPQ) has been extended in many directions to incorporate factors encountered in real-life situations. In this paper, an EPQ model that accounts for the cost of raw material needed for production is examined. It is assumed that the raw material acquired from the supplier contains a percentage of imperfect quality items. At the beginning of the inventory cycle, the raw material is received instantaneously, and a 100% screening process for detecting the imperfect quality items is conducted. Two different scenarios are considered. In the first, the imperfect quality items of the raw material are sold at a discounted price at the end of the screening period. In the second scenario, the imperfect quality items are kept in stock until the end of the inventory cycle and returned to the supplier when the next order is received

Incorporating machine reliability issue and backlogging into the EMQ model - Part I: Random breakdown occurring in backorder filling time

This study is concerned with determination of the optimal replenishment policy for economic manufacturing quantity (EMQ) model with backlogging and machine reliability issue. Classic EMQ model does not consider nonconforming items generated during a production cycle, nor does it deal with the machine breakdown situation. It is noted that in manufacturing system when back-ordering is permitted, a random machine failure can take place in either backorder filling time or in on-hand inventory piling period. The first phase of this study examines the aforementioned practical issues by incorporating rework process of defective items, scrap and random machine failure taking place specifically in backorder satisfying time into the EMQ model. The objective is to determine the optimal replenishment lot-size that minimizes the overall production-inventory costs. Mathematical modelling and analysis is used and the renewal reward theorem is employed to cope with the variable cycle length. Theorem on conditional convexity of total cost function is proposed and proved. The optimal lot size for such a real-life imperfect manufacturing system is derived. A numerical example is given to demonstrate its practical usage

Inventory ordering policies for mixed sale of products under inspection policy, multiple prepayment, partial trade credit, payments linked to order quantity and full backordering

The situation where serviceable products are sold together with a proportion of deteriorating products to consumers is rarely discussed in the literature. This article proposes an inventory model with disparate inventory ordering policies under a situation where a portion of serviceable products and a portion of deteriorating products are sold together to consumers (i.e. mixed sales). The ordering policies consider a hybrid payment strategy with multiple prepayment and partial trade credit schemes linked to order quantity under situations where no inventory shortage is allowed and inventory shortage is allowed with full backorder. The hybrid payment policy offered by a supplier is introduced into the classical economic ordering quantity model to investigate the optimal inventory cycle and the fraction of demand that is filled from the deteriorating products under inspection policy. Further, a new solution method is proposed that identifies optimal annual total profit with mixed sales assuming no inventory shortage and inventory shortage with full backorder. The impact of an inspection policy is investigated on the optimality of the solution under hybrid payment strategies for the deteriorating products. The validation of the proposed model and its solution method is demonstrated through several numerical examples. The results indicate that the inventory model along with the solution method provide a powerful tool to the retail managers under real-world situations. Results demonstrate that it is essential for the managers to consider inclusion of an inspection policy in the mixed sales of products, as the inspection policy significantly increases the net annual profit