Joint settings of economic manufacturing quantity (EMQ), process variance, quality investment, and parameters of acceptance sampling

Economic manufacturing quantity, optimum process mean, and economic specification limits setting under the rectifying inspection plan

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.

The problem of determining the optimal economic manufacturing quantity and the optimal process parameters is an important problem in production and quality control. This problem has been addressed by Chen and Lai using profit maximization as a criterion to obtain the optimal manufacturing quantity and the mean of the process. In this paper Chen and Lai has been extended to determine the optimal manufacturing quantity, the mean and the variance of the process and the specification limits using rectifying inspection. The simulated annealing approach has been applied to obtain the optimal solution. The utility of the model is demonstrated via a realistic example. The model developed can be utilized to determine the optimal economic manufacturing quantity and process target simultaneously and is expected to provide more insights in managing this important problem.

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 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.

This paper deals with economic manufacturing quantity (EMQ) models with stochastic machine breakdown and repairs. Under two minimal repair policies to maintain a production machine, the expected cost functions per unit time in the steady state, incurred in the manufacturing operation, are formulated and the optimal policies which minimize them are calculated. As a special case, we consider the case where the machine breakdown time follows the homogeneous Poisson process and calculate the optimal EMQ policies numerically. Also, an approximation method is used to represent the expected cost.

AbsractIn 1996, Pulak and Al-Sultan presented the problem of determining the optimum process mean for a product with the one-sided specification limit under the rectifying inspection plan. However, they didn't consider the quality loss within the specification limit. The inspection is perfect and the non-conforming items of the accepted lot aren't eliminated or replaced by the conforming ones in their model. 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 consider the quality loss of product in the modified EMQ model. In this study, the author integrates the modified Pulak and Al-Sultan's model with inspection error and quality loss into the Cardenas-Barron's production lot model with shortage for determining the economic manufacturing quantity, shortage and optimum process mean.

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 article, the author proposes a modified economic manufacturing quantity (EMQ) model with deteriorating production process. Assume that the two independent quality characteristics of the product are normally distributed with known process standard deviation for a period of time. Consider the unstable production process with positive shift and an age-dependent positive drift while process variance increases. The bivariate quality loss function is applied to evaluate the product quality. The process mean and economic manufacturing quantity are jointly determined by minimizing the total expected cost of product per unit time. 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.

<p style='text-indent:20px;'>To survive in today's competitive market, it is not enough to produce low-cost products but also quality-related issues and lead time needs to be considered in the decision-making process. This paper extends the previous research by developing a stochastic economic manufacturing quantity (EMQ) model for a production system which is subject to process shifts from an <i>in-control</i> state to an <i>out-of-control</i> state at any random time. Moreover, we consider the option of investment to increase the process quality and decrease the lead-time variability. Closed-form solutions of the proposed models are obtained by applying the classical optimization technique. Some lemmas and theorems are developed to determine the optimal solution of the decision variables. Numerical results are obtained for each of these models and compared with those of the basic <i>EMQ</i> model without any investment. From the numerical analysis, it has been observed that our proposed model can significantly reduce the cost of the system compared to the basic model.</p>

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.

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 consider the production process state in the modified EMQ model. Chen and Chung presented the quality selection problem to the imperfect production system for obtaining the optimum production run length and target level. Ladany and Shore proposed the problem of determining optimal warranty period of product in relation to the manufacturer’s lower specification limit. In this paper, we further integrate Chen and Chung’s and Ladany and Shore’s models in modified EMQ model for obtaining the optimum production run length and warranty period of product for the imperfect production system.

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, 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.