بهینه سازی سیاست تکمیل دوباره در یک مدل موجودی مبتنی بر EPQ-همراه با عدم انطباق و شکست

The optimal replenishment policy for an economic production quantity (EPQ)-based inventory model with nonconforming items and breakdown is presented. A real-life production system inevitably generates nonconforming items and has equipment breakdowns owing to process deterioration or other uncontrollable factors. This study addressed these issues in an EPQ-based system to optimize a replenishment policy that minimizes the long-run average cost for the proposed system. Whenever a breakdown occurs, the machine is assumed to immediately be under repair, and an abort/resume inventory control policy is adopted. Under this control policy production of the interrupted lot resumes immediately after the machine is fixed and restored. A mathematical model and a recursive algorithm were used to derive the optimal replenishment policy. A numerical example was used to demonstrate the practical application and better cost efficiency of the proposed policy compared to a breakdown that occurs under a no-resumption policy.

This paper is concerned with determining the optimal replenishment policy for an economic production quantity (EPQ) based inventory model with nonconforming items and random machine breakdown. Harris (1913) first introduced the economic order quantity (EOQ) model to assist corporations in minimizing total inventory costs. He employed the mathematical techniques to balance the setup and stock holding costs in order to derive the optimal order size that minimizes the long-run average cost. For the manufacturing firms, when items are produced in-house instead of being acquired from outside suppliers, the EPQ model is often adopted to cope with the non-instantaneous stock replenishment rate in order to obtain minimum production-inventory cost per unit time (Taft, 1918). Disregarding the simplicity of the original EOQ and EPQ models, the concept of cost minimization and the technique of mathematical modeling remain broadly used (Nahmias, 2009 and Silver et al., 1998). Quite a few more complicated and practical production-inventory models have since been extensively studied and developed (Alghalith, 2013, Bylka, 2003, Chen et al., 2012, Chiu et al., 2013, de Kok, 1985, Hadley and Whitin, 1963, Kohli and Park, 1994, Latha Shankar et al., 2013, Mishra et al., 2011, Sana, 2012 and Schneider, 1979). The classic EPQ model implicitly assumes that all items made are of perfect quality. However, in real-life manufacturing systems, due to process deterioration or various other factors, production of imperfect quality items is inevitable. Studies that extended the EOQ and EPQ models by undertaking issues of the defectiveness and its corresponding quality cost have been broadly conducted (Chen et al., 2013, Chiu et al., 2010, Chiu et al., 2011a, Hariga and Ben-Daya, 1998, Mahata, 2012, Pal et al., 2012, Rahim and Ben-Daya, 2001, Rosenblatt and Lee, 1986 and Sarkar and Sarkar, 2013). Samples of articles are surveyed as follows. Hariga and Ben-Daya (1998) studied the economic production quantity problem in the presence of imperfect processes. The time to shift from the in-control state to the out-of-control state was assumed to be flexible, and they provided distribution-based and distribution-free bounds on the optimal cost respectively. For the exponential case, they compared the optimal solutions to approximate solutions proposed in the literature. Rahim and Ben-Daya (2001) examined the simultaneous effects of both deteriorating product items and deteriorating production processes on the economic production quantity, inspection schedules, and the economic design of control charts. Deterioration times for both product and process were assumed to follow arbitrary distributions, and the product quality characteristic was assumed to be normally distributed. Applications of their models were demonstrated through illustrative examples. Chiu et al. (2011a) studied an economic manufacturing quantity (EMQ) with rework and multiple shipments. They incorporated quality assurance and multiple deliveries into classic EMQ model and derived the optimal inventory replenishment policy that minimizes the expected total production-inventory costs. Two special cases to their proposed model were discussed and examined. Unexpected breakdown of the production equipment is another critical reliability factor which can be disruptive when occurring — especially in a highly automated production environment. Groenevelt et al. (1992) studied two control policies that deal with random machine breakdown. The first one assumes that after a breakdown the production of the interrupted lot is not resumed (called the no resumption-NR policy). The second policy considers that the production of the interrupted lot will be immediately resumed (called the abort-resume-AR policy) after the breakdown is fixed and if the current on-hand inventory is below a certain threshold level. The repair time is assumed to be negligible in their study. The effect of machine breakdown and corrective maintenance on the economic lot size decisions is investigated. Studies have since been carried out to address the issue of machine failures during production (see for instance, Abboud, 2001, Arreola-Risa and DeCroix, 1998, Berg et al., 1994, Chakraborty et al., 2009, Chiu et al., 2011b, Chiu et al., 2012, Das et al., 2011, Giri and Dohi, 2005, Makis and Fung, 1998 and Moinzadeh and Aggarwal, 1997). Moinzadeh and Aggarwal (1997) studied a production-inventory system that is subject to random disruptions. They assumed that the time between breakdowns is exponential, restoration times are constant, and excess demand is backordered. An (s, S) policy was proposed and the policy parameters that minimize the expected total cost per unit time were investigated. A procedure for finding the optimal values of the policy was also developed. Arreola-Risa and DeCroix (1998) explored an (s, S) stochastic-demand inventory management system under random supply disruptions and partial backorders. Their analysis yields the optimal values of the policy parameters and provides insight into the optimal inventory strategy when there are changes in the severity of supply disruptions or in the behavior of unfilled demands. Giri and Dohi (2005) developed an exact formulation of stochastic EMQ model for an unreliable production system. Their model is formulated based on the net present value (NPV) approach, and by taking limitation on the discount rate the traditional long-run average cost model is obtained. They also provided the criteria for the existence and uniqueness of the optimal production time and computational results showing that the optimal decision based on the NPV approach is superior to that based on the long-run average cost approach. Chakraborty et al. (2009) investigated the lot size problem with process deterioration and machine breakdown under inspection schedule. Chiu et al. (2011b) studied the manufacturing run time problem with random defective rate and stochastic machine breakdown under a no resumption (NR) inventory control policy. Modeling and numerical analyses were used in order to establish the solution procedure. As a result, the optimal run time that minimizes the long-run average production-inventory cost is derived. For the reason that little attention was paid to the investigation of the joint effects of random nonconforming rate and machine breakdown (under the AR inventory control policy) on the optimal replenishment policy of the EPQ-based system, this paper intends to bridge the gap.

For practitioners in the production management field, who are interested in applying the aforementioned research results, two conditions must be satisfied. First, we must have (P–d–λ) > 0 to prevent stock-out situation from occurring. The second condition: 0 < t1 < z(t1) must also be satisfied (see Theorem 1 in Section 4) in order to assure that the long-run expected cost function E[TCU(t1)] is a convex function, and the optimal production run time that minimizes the cost function exists. Stochastic machine breakdowns and random defective rate are two common and inevitable reliability factors that trouble production managers and practitioners most. This paper studies the joint effect of the scrap and random breakdown (under AR inventory control policy) on the economic production run time decision for such a realistic EPQ model. We employ a recursive algorithm along with mathematical modeling and analyses to solve the proposed problem. As a result, a complete solution procedure has been established and a numerical example is provided to demonstrate how the recursive algorithm works. For future study, to examine the effect of stochastic demand on the production run time for the same model will be an interesting topic.