Economic Manufacturing Quantity Model Research Articles

Economic manufacturing quantity model with quality investment

In this article, we propose the modified economic production problem by considering acceptance inspection for obtaining production quantity, mean, and quality investment. One considers unknown mean and known variability under the normal quality. The quality investment function is the declining exponential function of variability. One adopts Taguchi’s loss cost for evaluating quality.

Optimal production lot-sizing and condition-based maintenance policy considering imperfect manufacturing process and inspection errors

In this paper, we propose an integrated Economic manufacturing quantity (EMQ) model combining both the concepts of condition-based maintenance (CBM) and imperfect manufacturing process. The manufacturing process is modelled by two indicators. One possesses binary state, indicating whether the manufacturing process is in-control or not. The other one is modelled by a homogeneous Gamma process, representing the degradation of the manufacturing equipment. The system is inspected at the end of each production run, upon which, the deterioration level can be perfectly observed, while two types of errors may occur in revealing the state of the manufacturing process. Defective products can be fabricated when the manufacturing state degrades. An integrated production and CBM policy is proposed. The objective is to develop the optimal production lot-sizing and preventive maintenance threshold in order to minimize the expected cost rate in the long-time horizon. We model the problem in the framework of a semi-Markov decision process. The successive-approximations method is applied to solve the problem numerically. The applicability of the proposed model and some sensitivity analysis are presented in a numerical illustration. It can provide theoretical reference to the decision-maker in production and maintenance planning.

An economic manufacturing quantity model with rework process for deteriorating products under maintenance-quality policy

ABSTRACT This paper presents an integrated model of three interrelated topics including the statistical process monitoring, maintenance scheduling, and production cycle length for imperfect manufacturing systems. The novelty of this paper is to take five features into consideration, including: (1) The produced items deteriorate over time, hence, the inventory is depleted in two ways i.e. responding to demand and gradually deteriorating products; (2) The non-conforming products can be reworked to increase the cost-saving by eliminating the waste items; (3) A non-uniform sampling scheme is employed such that the hazard rate does not exceed its threshold value; (4) The economic-statistical design of a control chart is used to accelerate the detection of process faults as well as reduce the risk of false alarms; and (5) The time value of money is taken into account to obtain more precise financial flow estimations. Finally, four comparative studies along with a sensitivity analysis on the most important parameters are conducted. The results confirm that considering the product deterioration and time value of money improves the model adaptability in real-world applications. Besides, employing the variable sampling scheme and the rework operations reduces the production rate of non-conforming items. The results also show that the total cost in economic-statistical model is slightly higher than that of the economic one. However, the economic-statistical model performs severely better than the economic one in terms of both in-control and out-of-control average run length metrics.

Optimal lot-sizing policy for a failure prone production system with investment in process quality improvement and lead time variance reduction

<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>

Economic Manufacturing Quantity Model with Machine Failure,Overtime and Rework/Disposal of Nonconforming Items

Economic Manufacturing Quantity Model with Machine Failure,Overtime and Rework/Disposal of Nonconforming Items

Practical application of product and process parameters under the specified process capability value

In 2018, Chen and Chou proposed a jointly design model with manufacturing quantity, specification limits, process mean, and the parameters of X-bar control chart based on the specified process capability index Cpm or Cpmk value. This integrated model is a generalization of economic manufacturing quantity (EMQ) model with statistical quality control chart. In this study, the author presents the practical application of Chen and Chou’s model for the manufacturer. The manufacturer can apply these parameters in the design of a variable single rectifying inspection plan for the output product before shipping to the customer and the determination of the stock quantity for shipment to the customer in the newsvendor problem.

A two-stage multiproduct EMQ-based model with delayed differentiation and overtime option for common part’s fabrication

This study explores the two-stage multiproduct economic manufacturing quantity (EMQ)-based system with delayed product differentiation and overtime option for fabrication of common parts. The classic EMQ model determines optimal lot size under assumptions of steady production rate; however, managers of present-day’s manufacturing firms, operating in a highly competitive global business environment, must constantly seeks ways to strengthen their competitive forces, such strategies include: (i) to increase machine utilization through planning multiproduct fabrication; (ii) to evaluate different production schemes to reduce cost, e.g., a delayed differentiation strategy, when a common intermediate product exists in a multiproduct system, wherein all required common parts are manufactured in stage one and final multi-product are produced in the second stage; and (iii) to reduce the cycle time through implementing an overtime strategy. This study is motivated and intended to address the aforementioned real factors. We use mathematical modeling to depict the problem first, then employ the optimization technique to solve it. Our objectives are to not only decide the optimal replenishing policy, but also to explore the effect and joint influence of the postponement and overtime strategy on the optimal policy, machine utilization, system costs, and relevant cost components in the system. Without this in-depth investigation, various crucial information relating to decision making will still be inaccessible to managers in this field.

Economic manufacturing quantity model with machine breakdown and deteriorating production process

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.

An Application of Time-Dependent Holding Costs and System Reliability in a Multi-Item Sustainable Economic Energy Efficient Reliable Manufacturing System

Sustainable efficient energy is the key factor of any sustainable manufacturing system. This study addresses a multi-item sustainable economic energy efficient reliable manufacturing quantity (MSEEERMQ) model. The manufacturing system produces defective products during long-runs, where those products may be reworked under the optimum effect of energy and carbon footprint with some costs. As all products are not sold immediately, the holding cost increases based on time. The management decides the system design variable to reduce energy consumption cost and increase system reliability under some time-dependent holding costs, and the optimum energy such that the maximum profit of the production model is obtained with a system reliability as a decision variable. The inflation and time-value of money are considered to calculate the cost of the production model under efficient energy. Using control theory, an Euler–Lagrange method is employed to obtain the sustainable critical path, which gives the optimal solution of the model. There are two lemmas to prove the global optimal solution of the model through the control theory. There is an illustrative example to test the model. Under different conditions there are other two examples with graphical representation and sensitivity analysis. Numerical studies reveal that maximum profit is obtained at the optimal value of the decision variable.

Process mean and production quantity settings by considering modified economic manufacturing quantity model

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.

Economic design of product and process parameters under the specified process capability value

In this paper, the author presents a jointly design model with manufacturing quantity, specification limits, process mean and the parameters of X-bar control chart based on the specified process capability index value. The quality loss of a product is set to be related to the limits of the control chart. Assume that the quality characteristic of a product is normally distributed with known standard deviation and adjustable mean. The production process may have a shift in the process mean, while the process standard deviation remains constant. The optimal combination of parameters is determined by minimizing the expected total cost of product under the specified value. This integrated model is a generalization of the economic manufacturing quantity (EMQ) model with statistical quality control chart. Finally, the numerical example and sensitivity analysis of parameters will be provided for illustration.

The joint determination of specification limits, process mean, and economic manufacturing quantity

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.

Setup cost reduction EMQ inventory system with probabilistic defective and rework in multiple shipments management

This paper considers an economic manufacturing quantity (EMQ) model for defective products with imperfect production processes and rework, in which the setup cost is logarithmic function of capital investment. In this study, fixed quantity multiple installments of the finished batch are delivered to customers at a fixed interval of time. We also consider three types of continuous probabilistic defective function to find the associated cost. The way our basic business operations like decision making, marketing strategies, financial management, etc. are done are being reformed with the use of computers and mathematics. In view of that the mathematical modeling and computational algorithm are employed in this study for optimizing the replenishment lot-size and setup cost simultaneously with the objective of minimizing total cost of the EMQ system. The long-run average cost function is derived, its convexity is proved via differential calculus. A computer code using the software Matlab is developed to derive the optimal solution and present numerical examples to illustrate the model.

Mathematical modeling of a multi-product EMQ model with an enhanced end items issuing policy and failures in rework.

This study uses mathematical modeling to examine a multi-product economic manufacturing quantity (EMQ) model with an enhanced end items issuing policy and rework failures. We assume that a multi-product EMQ model randomly generates nonconforming items. All of the defective are reworked, but a certain portion fails and becomes scraps. When rework process ends and the entire lot of each product is quality assured, a cost reduction n + 1 end items issuing policy is used to transport finished items of each product. As a result, a closed-form optimal production cycle time is obtained. A numerical example demonstrates the practical usage of our result and confirms a significant savings in stock holding and overall production costs as compared to that of a prior work (Chiu et al. in J Sci Ind Res India, 72:435–440 2013) in the literature.

Simultaneous settings of order quantity, wholesale price, production run length, process mean, and warranty period

In this article, the authors propose a modified version of S.L. Chen and Liu's model with a two-stage production system. Assume that the retailer's order quantity is concerned with the manufacturer's selling price and the warranty period of product. The used cost of the customer is measured under the Taguchi's quadratic quality loss function and concluded in the retailer's profit function. The quality of the lot for the manufacturer is determined by adopting a two-stage single sampling rectifying inspection plan. The modified economic manufacturing quantity (EMQ) model is addressed in formulating the manufacturer's expected profit. The retailer's order quantity, manufacturer's wholesale price, production run length, process mean, and warranty period of product will be jointly determined by maximizing the total expected profit of the supply chain system including the manufacturer and the retailer. Finally, the quality investment policy is introduced to illustrate the profit improvement for the supply chain system.

The Modified Economic Manufacturing Quantity Model Based on Inspection Error, Quality Loss, and Shortage

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.

Modified Imperfect Economic Manufacturing Quantity Model with Limited Investment Capital

Traditional economic manufacturing quantity model assumes that the perfect product for production. Recently, Teng proposes an imperfect production process with limited investment capital for determining the optimal investment cost and production run time. Teng assumes that the percentage of process defectives with uniform distribution is a decreasing function of the investment cost. However, Teng's model does not include the customer's used cost for the conforming product. In this study, the authors adopt another investment cost function, i.e., the exponential reduction of process mean and standard deviation as the function of quality investment cost, for formulating the modified Teng's model. Taguchi's quadratic quality loss will be used for measuring the product quality. Finally, the numerical example and sensitivity analysis of parameters are provided for illustration.

An EMQ inventory model for defective products involving rework and sales team’s initiatives-dependent demand

This paper investigates the issue of an economic manufacturing quantity model for defective products involving imperfect production processes and rework. We consider that the demand is sensitive to promotional efforts/sales teams’ initiatives as well as the setup cost can be reduced through further investment. It also assumes that fixed quantity multiple installments of the finished batch are delivered to customers at a fixed interval of time. The long-run average cost function is derived and its convexity is proved via differential calculus. An effective iterative solution procedure is developed to achieve optimal replenishment lot-size, setup cost and the initiatives of sales teams so that the total cost of system is minimized. Numerical and sensitivity analyses are performed to evaluate the outcome of the proposed solution procedure presented in this research.

Issuing for perishable inventory management with a minimum inventory volume constraint

We study a perishable inventory system that requires to maintain a minimum inventory volume at all times, where the minimum amount in the constraint is significant with respect to regular market demand and the traditional Economic Manufacturing Quantity (EMQ) models do not suffice. The problem is motivated by applications in homeland security, which are related to the management of pharmaceuticals in the Strategic National Stockpile (SNS) for emergency preparedness. We use a modified EMQ model to represent the system and consider the issuing policy given a fixed ordering quantity, as well as the joint ordering and issuing policy problem. We aim to maximize the profit of the system under a linearly-decreasing price structure assumption. We first present the optimal issuing policy with a given ordering quantity for this modified EMQ model. Then we demonstrate that maximizing the revenue of the ordering policy with FIFO (first-in, first-out) and LIFO (last-in, first-out) issuing policies can be formulated as a non-convex non-smooth unconstrained optimization problem. The properties of both problems (e.g. optimizing issuing policy with a fixed ordering quantity and optimizing ordering policy with a fixed issuing policy) is analyzed and an efficient exact algorithm is presented to solve the joint ordering and issuing problem. We show that the LIFO issuing policy is optimal with a linearly-decreasing price structure that deteriorates with the age of the item.

An EMQ model with price and time dependent demand under the effect of reliability and inflation

The paper deals with an economic manufacturing quantity (EMQ) model for the selling price and the time dependent demand pattern in an imperfect production process. Due to long-run, machine breakdown may occur, as a result, the system may shift to out-of-control state from in-control state and production systems begin to produce imperfect quality items. The production of imperfect items increases with time. All imperfect quality items are reworked at a fixed cost to restore these to its original quality. To reduce the production of the imperfect quality items, we consider reliability as a decision variable along with the development cost and the production cost as a function of reliability. The profit function is maximized by Euler–Lagrange formula. The numerical example, sensitively analysis, and graphical illustrations are given to illustrate the model.