Economic Manufacturing Quantity 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.

Joint optimization of production lot-sizing and condition-based maintenance in an imperfect production process with dependent indicators

ABSTRACT This paper addresses the integrated optimization of the economic manufacturing quantity and the condition-based maintenance policy of a deteriorating manufacturing system. The considered facility produces a single type of product and is inspected at the end of each production run. Upon inspection, two dependent indicators are revealed: one implies whether the production process is in control or not and the other one represents the deterioration level of the facility. The dependence between the two indicators is that whenever the facility deterioration exceeds a pre-determined level, the system becomes more vulnerable such that the production process may switch to the out-of-control state. In the out-of-control state, a proportion of defective items is fabricated. Considering the inter-dependencies between production process and machine degradation, this paper develops an integrated production and maintenance model to minimize the overall cost. The expected cost rate in the long run is taken as the objective function to assess the proposed model, where the joint optimization of the lot-sizing and the maintenance policy is developed. The problem is formulated in the context of a semi-Markov decision process and solved with the successive approximation method. A numerical example is given to illustrate the applicability of the proposed model.

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 lot-size problem for a cleaner manufacturing system with warm-up period

There are instances that production machines require a warm-up period to reach their anticipated productivity. This study extends an economic manufacturing quantity (EMQ) problem by considering warm-up issue in the model. Warming up the machine decreases production loss, emission, and machine depreciation. Therefore, this study helps industry to enhance the profitability and also to reduce the environmental impact by decreasing waste generation and improving machine efficiency. In this study, we divide our system into three subsystems based on the relationships between production and consumption. Then we provide a mathematical model for each subsystem (three in total). The first two models are single-item EMQ inventory problems and the third one is a multi-item single-machine EMQ problem. In the third model, a machine/facility manufactures some items under a limited manufacturing volume. The purpose of these proposed models is to find the optimum cycle length to minimize the total system cost that consists of manufacturing, inventory and setup costs. Finally, we propose exact solution procedures after proving the convexity of these mathematical models.

Optimal production policy for economic production lot-sizing model with preventive maintenance

ABSTRACT In this study, we determine the optimal manufacturing quantity for an economic production lot-sizing model with a defective rate and preventive maintenance for a manufacturing machine. We investigate the properties of economic manufacturing quantity to minimize expected costs during the production run when a random defective rate for that product is considered using an in-control condition and an out-of-control condition. If a manufacturing machine produces a proportion of defective items which is larger than the lot tolerance percent defective, then a machine shifts from an in-control condition to an out-of-control condition, and it should have a maintenance service to decrease the possibility that it will produce imperfect-quality products. A research model is developed to determine optimal manufacturing quantity and optimal production time when a defective rate and maintenance service are considered. Numerical examples are given for the applicability of the methodology derived in the paper.

Application of Learning Curves in Operations Management Decisions

In the time of industry 4.0 and big data, methods which are based on the collection and the processing of a large amount of data in order to support managerial decisions have outstanding significance. The learning curve theory pertains to these methods. The purpose of this paper is to explore some application possibilities of the classical learning curve in manufacturing and service operations. The learning effect assumes that as the quantity of units manufactured increases, the time needed to produce an individual unit decreases. The function describing this phenomenon is the learning curve. Various learning curves have been developed and applied in the area of production economics and much research studies the significance of the learning effect in management decisions. This study summarizes the main learning curve models and demonstrates how learning can be considered in three classical areas of operations management. First, the calculation of economic manufacturing quantity in the presence of learning is studied. Next, the effect of learning in break-even analysis and assembly line balancing is explored. The results show that with the consideration of the learning effect, calculations become more complex and require greater efforts, but the application of the learning curve concept can provide valuable insight both at operational and strategic levels.

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.

Determining the optimal cycle length for a multiproduct EMQ problem considering rework and overtime options

To satisfy the increasing trend of diverse customer product needs and to cope with internal capacity constraints, the management of current manufacturing firms must plan multiproduct batch fabrication and be able to reduce its completion time and/or smooth overall production schedules. Furthermore, because of various unforeseen problems in real fabrication processes, defective items may be randomly produced. These items need to be identified and separated from perfect stocks to maintain the required quality level. Inspired by these facts, we explore a multiproduct economic manufacturing quantity (EMQ) problem considering rework and overtime options. An exact model is built to study the characteristics of the problem that have not yet been explicitly examined in the literature. This newly developed model employs a mathematical technique together with differential calculus to not only obtain the total cost function of the system, but also to prove its convexity and determine the optimal cycle time that minimizes the total system cost. A numerical illustration is provided to demonstrate its applicability. Subsequently, the impact of overtime and rework on the optimal solution, relevant cost variables, and the completion time of batch fabrication, machine utilization, can be obtained. This information on the cost-effectiveness of problem characteristics is valuable in facilitating managerial decisions.

PENGEMBANGAN MODEL PERSEDIAAN ECONOMIC MANUFACTURING QUANTITY (EMQ) DENGAN PRODUK GANDA DAN STOCHASTIC

In the current era of globalization, there is freedom of the flow of products that make the competition between companies become more stringent. In order to survive, PT. XYZ must perform its activities effectively and efficiently on all its parts. One of these lines is the warehouse or inventory line. The existing inventory system and run by PT XYZ is a production environment that produces more than one final product and the demand for its products is uncertain. Based on the condition of PT XYZ, the writer approached the existing inventory system at PT XYZ with inventory model of Economic Manufacturing Quantity, multi item, and probabilistic.

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.

Producer-retailer integrated EMQ system with machine breakdown, rework failures, and a discontinuous inventory issuing policy.

This study develops two extended economic manufacturing quantity (EMQ)-based models with a discontinuous product issuing policy, random machine breakdown, and rework failures. Various real conditions in production processes, end-product delivery, and intra-supply chains such as a producer–retailer integrated scheme are examined. The first model incorporates a discontinuous multi-delivery policy into a prior work (Chiu et al. in Proc Inst Mech Eng B J Eng 223:183–194, 2009) in lieu of their continuous policy. Such an enhanced model can address situations in supply chain environments, where finished products are transported to outside retail stores (or customers). The second model further combines retailer’s stock holding costs into the first model. This extended EMQ model is applicable in situations in present-day manufacturing firms where finished products are distributed to company’s own retail stores (or regional sales offices) and stocked there for sale. Two aforementioned extended EMQ models are investigated, respectively. Mathematical modeling along with iterative algorithms are employed to derive the optimal production run times that minimize the expected total system costs, including the costs incurred in production units, transportation, and retail stores, for these integrated EMQ systems. Numerical examples are provided to demonstrate the practical application of the research results.

Joint optimization of lot-sizing and maintenance policy for a partially observable two-unit system

In this paper, we present a new model to find the jointly optimal economic manufacturing quantity (EMQ) and preventive maintenance (PM) policy for a complex production facility. Unlike the previous joint models which dealt with EMQ and maintenance policy considering a single unit production facility and traditional maintenance approaches, we consider a production facility which consists of two modules with economic dependence. The more expensive module (unit 1) is subject to condition monitoring (CM), and only the age information of the second module (unit 2) is available, which follows a general distribution. The deterioration process of unit 1 is modeled as a continuous time hidden-Markov process. CM data is available at the end of each production run, and it provides only partial information about the hidden state of unit 1. The failure state of unit 1 is observable at any time. The objective is to develop a jointly optimal lot sizing and maintenance policy for a two-unit production facility using multivariate Bayesian control approach by minimizing the long-run expected average cost per unit time. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. Also, a formula for the mean residual life (MRL) of the production facility is derived, which is an important statistic for practical applications. A practical example of the wind turbine CM and maintenance is provided and a comparison with other policies shows an outstanding performance of the new model and the control policy proposed in this paper.