Economic manufacturing quantity model with investment and tolerance

This study proposes a modified economic manufacturing quantity (EMQ) model with deteriorating production process. Assume that the quality characteristic of the product is normally distributed. Consider the unstable production process with positive shift and an age-dependent positive drift while process variance increases. The target value of product characteristic is considered to be equal to its specification center and Taguchi’s symmetric quadratic quality loss function is applied to evaluate the product quality. The specification limits, process mean, and EMQ are jointly determined by minimizing the total expected cost of product per unit time under the specified process capability index Cpm value. A solution procedure is devised to find the optimal solution for modified EMQ model and the sensitivity analysis of key parameters is conducted to investigate the effect on the optimal solution. Numerical results show that the expected total cost of product per unit time is significantly influenced by the process capability index, the quality loss coefficient, the production rate, the demand rate, and process standard deviation.

Traditional economic manufacturing quantity (EMQ) model addressed that the perfect production for product. However, there possibly exists the defective product in the manufacturing process. Hence, it is necessary to include the quality cost in the EMQ model. In this paper, we propose a modified EMQ model with quality loss and inventory cost. By solving the modified EMQ model, we can obtain the optimum production run length and process mean by considering the minimum expected total cost. Taguchi’s symmetric quadratic quality loss function will be adopted for evaluating the product quality.

This paper studies the effects of service-level constraint and failure-in-repair on an economic manufacturing quantity (EMQ) model with random defective rate. It starts with the proof that the long-run average cost of an EMQ model with backlogging permitted is less than or equal to that of the same model without backlogging. The relationship between the ‘imputed backorder cost’ and maximal permitted shortage level is dependent for decision making on whether or not the required service level is achievable. An equation that calculates the intangible backorder cost is proposed for dealing with situations when the required service level is not attainable. Finally, by utilizing this intangible backorder cost in the proposed mathematical analysis, an optimal lot-size policy that minimizes expected overall costs as well as satisfies the service-level constraint can be derived. A numerical example with a discussion that demonstrates the effects of service-level constraint and failure-in-repair on the EMQ model is provided.

In this study, the author proposes a jointly setting model for determining the process mean and economic manufacturing quantity (EMQ) under the machine breakdown and deteriorating production process. The system addresses the corrective maintenance, preventive maintenance, and allowable shortage. The quality loss of conforming product is considered and Taguchi’s asymmetric quadratic quality loss function is used for evaluating the product quality. The optimal process mean and economic manufacturing quantity are jointly determined by minimizing the total expected cost of product per unit time including the set-up cost, holding cost, corrective maintenance cost, preventive maintenance cost, shortage cost. A solution procedure is devised to obtain the optimal solution and the sensitivity analysis of key parameters is conducted to investigate the effect on the optimal solution.

This paper studies the optimal production run time in an economic manufacturing quantity (EMQ) model with imperfect rework and Poisson machine breakdowns under abort/resume (A/R) control policy. In most realistic manufacturing processes, generation of defective items and random machine breakdowns are inevitable. In this study, a random defective rate is assumed and all defective items produced are reworked when regular production ends. The rework process is assumed to be imperfect. A proportion of reworked items fail during the reworking and become scrap. The system is subject to random breakdowns. The A/R inventory control policy is adopted when breakdowns occur, under such a policy, and the production of the interrupted lot will be immediately resumed when the machine is fixed and restored. Mathematical modelling is used and the integrated long-run average production-inventory cost per unit time is derived. Theorems on conditional convexity and on bounds of optimal production run times are proposed and proved. A recursive searching algorithm is developed for locating the optimal run time within the bounds, which minimizes the expected production-inventory costs. A numerical example with sensitivity analysis is provided to give insight into the operational planning and control of such a realistic production system.

An economic manufacturing quantity model with probabilistic deterioration in a production system

An imperfect production process for time varying demand with inflation and time value of money – An EMQ model

Traditional economic manufacturing quantity (EMQ) model assumes that the perfect production for product. However, there possibly exists the defective product in the production process. In 1996, Chen and Chung presented the quality selection problem to the imperfect production system for obtaining the optimum production run length and target level. In 1998, Wu and Tang proposed the optimum manufacturing target based on Taguchi’s quadratic quality loss function. In this paper, we further integrate Chen and Chung’s and Wu and Tang’s models in the modified EMQ model for obtaining the optimum production run length and manufacturing target. The normal, uniform, and triangular quality characteristics are considered in the modified EMQ model. The asymmetric quadratic and linear quality loss functions are adopted for measuring the product quality. The numerical example and sensitivity analysis of parameters are provided for illustration.

In this paper, we present a modified economic manufacturing quantity (EMQ) model under the imperfect product quality. Taguchi's quadratic quality loss function is adopted for measuring the product quality. The modified EMQ model denotes the total loss to the society which includes the producer's loss and the customer's loss. The total inventory cost of the modified EMQ model includes the set-up cost, the holding cost, and the product cost. The perfect and imperfect reworks of product are considered in the modified EMQ model, respectively. By solving the modified EMQ model, we can obtain both the optimum combination of EMQ and process mean in order to have the minimum total loss of society.

Computational aspects of an extended EMQ model with variable production rate

This article studies the optimal replenishment policy for an economic manufacturing quantity (EMQ) model with failure in rework, backlogging and random breakdown. A recent article [P.A. Hayek and M.K. Salameh, Prod. Plann. Control 2001;12:584–590] investigated the optimal lot size problem on an imperfect quality EMQ model. However, in most real-life manufacturing systems random breakdown is another inevitable reliability factor. To cope with the stochastic machine failures, the production planners need to calculate the mean time between failures and establish a robust plan accordingly, so that the overall production-inventory costs for such an unreliable system can be minimized. This study incorporates random machine breakdown and failure in rework factors into the imperfect EMQ model examined by the aforementioned paper. Mathematical modelling and cost analysis are employed and the renewal reward theorem is used to deal with variable cycle length. Convexity of the long-run average cost function is proved and optimal replenishment policy for such an imperfect EMQ model is derived. Numerical example demonstrates its practical usages.

In this paper, the author presented a modified Chen and Chung's model considering that the process mean may not be equal to the target value when the process is in the in-control state. Taguchi's asymmetric quadratic quality loss function will be applied in evaluating the product quality. Subsequently, the modified economic manufacturing quantity (EMQ) model based on modified the Chen and Chung's model is formulated for obtaining the expected total cost per year. The numerical result shows that for an in-control process, the modified EMQ model when the process mean is not equal to the target value has smaller expected total cost per year than that of the modified EMQ model when the process mean is equal to the target value.

This paper derives the optimal replenishment policy for imperfect quality economic manufacturing quantity (EMQ) model with rework and backlogging. The classic EMQ model assumes that all items produ...

In this paper we further extend Chen and Wang's study concerning a CSP‐1 plan applied to the economic manufacturing quantity (EMQ) model with imperfect quality. Adopting the backorder assumption for shortages, the modified total inventory cost includes the setup cost, the holding cost, the backordering cost, the inspection cost, and the internal and external failure cost. By solving the modified EMQ model, we not only obtain the required level of product quality but also determine the minimum of the total inventory cost.

To increase their competitive advantage in turbulent marketplaces, contemporary manufacturers must show determination in seeking ways to: fulfill buyer orders with quality merchandise; meet deadlines; handle unexpected production disruptions; and lower the total relevant expense. To tackle the abovementioned challenges, this study explores an economic manufacturing quantity (EMQ) model with machine failure, overtime, and rework/disposal of nonconforming items; the goal is to find the best fabrication uptime that minimizes total relevant expenses. Specifically, we consider a production unit with overtime capacity as an operational feature that is linked to higher unit and setup costs. Further, its EMQ-based process is subject to random nonconforming items and failure rates. Extra screening separates the reworkable nonconforming items from scrap, and the rework is executed at the end of each cycle of regular fabrication. The failures follow a Poisson distribution, and a machine repair task starts as soon as a failure occurs; the fabrication of the lot that was interrupted resumes after the repair has been carried out. A decision model is built to capture the characteristics of the problem. Mathematical and optimization processes help in determining the optimal fabrication uptime. A numerical example not only illustrates the applicability of the research outcomes, but also reveals a diverse set of information about the individual or joint influences of deviations in mean-time-to-failure, overtime factors, and rework/disposal ratios linked to nonconforming rates related to the optimal replenishment uptime, total operating expenses, and various cost contributors; this facilitates better decision making.