An economic production quantity model with random defective rate,rework process and backorders for a single stage production system

This paper revisits the economic production quantity (EPQ) model with rework process at a single-stage manufacturing system with planned backorders. It is well known that any imperfect production system of real life has random defective rates. In this direction, this paper extends an inventory model to allow random defective rates. Basically, three different inventory models are developed for three different distribution density functions such as uniform, triangular, and beta. The analytical derivation provides closed-form solution for each inventory model. We have made comparison tables of optimal results among the distribution functions. Some numerical examples and sensitivity analysis are given to illustrate the inventory models.     

An alternative analysis and solution procedure for the EPQ model with rework process at a single-stage manufacturing system with planned backorders

This paper revisits the work by Cárdenas-Barrón (Cárdenas-Barrón, L. E., (2009). Economic production quantity with rework process at a single-stage manufacturing system with planned backorders. Computers and Industrial Engineering, 57(3), 1105–1113). The optimal solution condition is analyzed using the production time and the time to eliminate backorders as decision variables instead of the classical decisions variables of lot and backorder quantities. This new approach leads to an alternative inventory policy for imperfect quality items when the optimal production time is less than the optimal time. This is a new method that has not been explored before; it improves and complements the work by Cárdenas-Barrón (2009) and provides interesting managerial insights. An easy to apply solution procedure is provided to obtain the optimal policy. Finally, numerical examples are solved to illustrate our results.     

Optimal manufacturing batch size with rework process at a single-stage production system

Determining an optimal batch quantity in a production system that produces defective items has been the primary focus recently among the researchers. While most of the work has been reported to explore the traditional optimal inventory level in ideal cases, little appears to have been done with rework option. In this paper, models have been developed to determine the optimum batch quantity in a single-stage system in which rework is done under two different operational policies to minimize the total system cost. The first policy deals with rework being completed within the same cycle. The second policy deals with the rework being done after N cycles causing less than the desired quantity of good products in each cycle. The models have been validated with illustrating numerical examples and the sensitivity of optimal batch size and total system cost with respect to the defective proportion have also been performed.     

Economic production quantity model for items with continuous quality characteristic,rework and reject

The economic production quantity (EPQ) model is a well-known and commonly used inventory control technique. However, the model is built on an unrealistic assumption that all the produced items need to be of perfect quality. Having relaxed this assumption, some researchers have studied the effects of the imperfect products on the inventory control techniques. This article, thus, attempts to develop an EPQ model with continuous quality characteristic and rework. To this end, this study assumes that a produced item follows a general distribution pattern, with its quality being perfect, imperfect or defective. The analysis of the model developed indicates that there is an optimal lot size, which generates minimum total cost. Moreover, the results show that the optimal lot size of the model equals that of the classical EPQ model in case imperfect quality percentage is zero or even close to zero.     

考虑缺货的模糊随机缺陷生产系统

针对不可靠的生产过程,研究了生产故障时间为模糊随机变量且允许缺货的缺陷生产系统.建立含缺货费和模糊随机重修费的经济生产批量模型.基于可信性理论,建立其期望费用模型,揭示了费用函数的性质,并证明了使费用最小的最优生产时间的存在性和唯一性,从而确定了最优生产时间的上下界.基于此,设计了最优生产时间的二分法求解过程.最后通过算例验证了所提出模型的有效性,并分析了缺货费用、重修费用和缺陷产品比例对最优生产策略的影响.     

Alternative approach for solving replenishment lot size problem with discontinuous issuing policy and rework

Conventional approach for solving the replenishment lot size problem is by using differential calculus on the long-run average production cost function with the need to prove optimality first. Recent studies proposed an algebraic approach to the solution of classic economic order quantity (EOQ) and the economic production quantity (EPQ) models without reference to the use of derivatives. This paper extends it to the solution of a specific EPQ model as was examined by Chiu et al. [Chiu, S. W, Chen, K. -K, Lin, H. -D. Numerical method for determination of the optimal lot size for amanufacturing system with discontinuous issuing policy and rework. International Journal forNumerical Methods in Biomedical Engineering. doi: 10.1002/cnm.1369. (in Press; Published online March-10-2010).]. As a result, optimal replenishment lot size and a simplified optimal production-inventory cost formula for such a particular EPQ model can be derived without derivatives. This alternative approach may enable practitioners who with little knowledge of calculus to understand the realistic production systems with ease.     

Economic production quantity models for deteriorating/imperfect products and service with rework

In this paper, two economic production quantity (EPQ) models are proposed for deteriorating/imperfect items with rework process. The production process is imperfect, and imperfect quality items are reworked to become serviceable. At the same time, the remaining good quality items may deteriorate. The inspection of deteriorated items is also imperfect, so that deteriorated items may be sold to customers, which will create negative impact on corporate image. In the first model, a single production-rework plant system is considered. The optimal production times and the economic production quantities are obtained analytically. In the second model, a system that consists of n production plants and one rework plant is considered. A solution procedure is developed in order to obtain the optimal operating cost. Numerical examples are provided to compare the performance of the two systems.     

Incorporating human learning into a fuzzy EOQ inventory model with backorders

Even though publications on fuzzy inventory problems are constantly increasing, modelling the decision maker’s characteristics and their effect on his/her decisions and consequently on the planning outcome has not attracted much attention in the literature. In order to fill this research gap and model reality more accurately, this paper develops a new fuzzy EOQ inventory model with backorders that considers human learning over the planning horizon. The paper is an extension of an existing EOQ inventory model with backorders in which both demand and lead times are fuzzified. Here, the assumption of constant fuzziness is relaxed by incorporating the concept of learning in fuzziness into the model considering that the degree of fuzziness reduces over the planning horizon. The proposed fuzzy EOQ inventory model with backorders and learning in fuzziness has a good performance in efficiency. Finally, it is worth mentioning that learning in fuzziness decreases the total inventory cost.     

Batching work and rework processes with limited deterioration of reworkables

We study a deterministic problem of planning the production of new and recovering defective items of the same product manufactured on the same facility. Items of the product are produced in batches. The processing of a batch includes two stages. In the first work stage, all items of a batch are manufactured and good quality items go to the inventory to satisfy given demands. In the second rework stage, some of the defective items of the same batch are reworked. Each reworked item has the required good quality. While waiting for rework, defective items deteriorate. There is a given deterioration time limit. A defective item, that is decided not to be reworked or cannot be reworked because its waiting time will exceed the deterioration time limit, is disposed of immediately after its work operation completes. Deterioration results in an increase in time and cost for performing rework processes. It is assumed that the percentage of defective items is the same in each batch, and that they are evenly distributed in each batch. A setup time as well as a setup cost is required to start batch processing and to switch from production to rework. The objective is to find batch sizes and positions of items to be reworked such that a given number of good-quality items is produced and total setup, rework, inventory holding, shortage and disposal cost is minimized. A polynomial dynamic programming algorithm is presented to solve this problem.