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This paper discusses a production-inventory system under random machine breakdown. Holding safety stock is the common way to mitigate the effect of random machine breakdown on shortages that may occur during machine repair time. Since holding safety stock can be costly, especially for expensive products, this paper investigates an alternative strategy in which it is assumed that the production manager can purchase the same products from a supplier in order to meet the demands that may be lost due to depletion of the inventory after the machine breakdown. The supplier has known lead-time and reliability with the quality assured products. Despite holding safety stock, purchasing occurs only when the machine breakdown happens. The question is about the optimal amount of production and purchasing lot sizes to minimize the total expected costs. The optimality of the model is investigated when failure and repair time follow an exponential distribution, and a computational algorithm for finding the optimal lot sizes is presented. A comparison between the purchasing strategy and holding safety stock is performed through a sensitivity analysis regarding some effective parameters. This study shows that using the purchasing strategy when holding or production cost rises is more beneficial than holding safety stock. [ABSTRACT FROM AUTHOR]

Previous research indicates that it is feasible to incorporate carbon considerations into production and inventory management by making informed decisions based on total costs and other relevant factors. In this article, the inventory model of single-vendor single-buyer with fixed demand is considered and carbon emission costs are added to the model according to the two policies of carbon tax and emission trading, and the model is also discussed through environmental concerns. The objective of this study is to establish an equilibrium between the costs associated with single-vendor single-buyer (SV-SB) and carbon emissions, utilizing carbon tax and carbon trading policies to regulate the quantity of carbon generated. The results show using the carbon trading policy is more economical although it is much more complicated in implementation than carbon tax policy. [ABSTRACT FROM AUTHOR]

In modern times, customers are increasingly aware of the environmental risks posed by the premature expiration of smart products. To safeguard the environment, companies have embraced green technology when procuring products. As a result, it is challenging for business managers to capture the market by offering the best quality products at a reasonable price, regardless of the economic situation. This paper presents a production model incorporating reverse logistics to identify defective products. The model involves learning through production and utilizes green technologies. Additionally, a portion of the assembled products is remanufactured after being received from consumers. The remanufactured items are screened and distributed to markets. Both new and remanufactured products are sold to the market based on their quality in the first and second markets, respectively. To reduce product spoilage, manufacturers employ green technology like liquid cooling technology. The numerical results demonstrate that by investing in liquid cooling technology, the production store can reduce spoilage items by 8.50%, a positive environmental outcome regarding waste reduction, and due to the learning effect, the total cost can decrease by 1.44%. The paper includes numerical and sensitivity analyses accompanied by graphs. [ABSTRACT FROM AUTHOR]

This study proposes an economic production quantity (EPQ) model that comprehensively addresses scrap items, imperfect quality items, rework processes, and shortages. The model incorporates various types of defective items, including scrap, imperfect quality, and rework able items, and implements immediate rework processes upon the completion of regular production. Shortages are treated as lost sales, enhancing the accuracy of inventory cost estimations. Numerical experiments demonstrate the opti­mal­ity of production lot sizes and underscore the impact of production and demand rate adjustments on overall inventory costs. Sensitivity analysis further elucidates the influence of imperfect quality items on inventory costs. This EPQ model offers a comprehensive approach to efficient and effective finished product inventory management by integrating consider­ations for scrap items, imperfect quality items, and rework processes. Addi­tionally, a furniture manufacturing company case is presented to illustrate the practical application of the proposed model.

Many production systems need to be able to change the rate at which they manufacture products for various reasons, hence, the need to find the optimal lot size under these multiple levels of production. This research addresses the need for optimizing inventory in a system with a shifting production rate and other challenging product characteristics such as product deterioration with limited life span, and product demand that is dependent on the stock level, the state of freshness of the product, and the selling price. The product also needs to be discounted as it gets close to the expiry date in order to boost demand and prevent wastage beyond its life span. Our objective is to maximize profit by determining the optimal selling price and inventory cycle time by deriving the relevant equations for these decision variables. The Newton-Raphson method was used to numerically solve for the optimal values of these variables. Sensitivity analyses were performed to derive useful insights for managerial decision-making.

Many production systems need to be able to change the rate at which they manufacture products for various reasons, hence, the need to find the optimal lot size under these multiple levels of production. This research addresses the need for optimizing inventory in a system with a shifting production rate and other challenging product characteristics such as product deterioration with limited life span, and product demand that is dependent on the stock level, the state of freshness of the product, and the selling price. The product also needs to be discounted as it gets close to the expiry date in order to boost demand and prevent wastage beyond its life span. Our objective is to maximize profit by determining the optimal selling price and inventory cycle time by deriving the relevant equations for these decision variables. The Newton-Raphson method was used to numerically solve for the optimal values of these variables. Sensitivity analyses were performed to derive useful insights for managerial decision-making. [ABSTRACT FROM AUTHOR]

For decades researchers have been facing the issue of adapting the economic production quantity (EPQ) to the case of multi-item production contexts characterised by a single (shared) resource with finite capacity. The economic lot scheduling problem (ELSP), which is still of interest to researchers, has addressed this issue. A recent attempt by Rossi et al. (Omega 71:106–113, 2017) addressed the problem while avoiding scheduling. Notwithstanding their relevance, these approaches present limitations in adapting the EPQ model to multi-product 'pull' production systems. The present work attempts to overcome these limitations through the development of a methodology based on the equation proposed by Mallya (1992) and restricting items production frequencies to define feasible solutions while avoiding scheduling. The feasibility and performance of the proposed model are evaluated through its application to well-known benchmarking instances (Bomberger's, Eilon's and Mallya's problems) and a large set of test problems. [ABSTRACT FROM AUTHOR]

Statistical process monitoring, maintenance policy, and production have commonly been studied separately in the literature, whereas their integration can lead to more favorable conditions for the entire production system. Among all studies on integrated models, the underlying process is assumed to generate independent data. However, there are practical examples in which this assumption is violated because of the extraction of correlation patterns. Autocorrelation causes numerous false alarms when the process is in the in-control state or makes the traditional control charts react slowly to the detection of an out-of-control state. The auto-regressive moving average (ARMA) control chart is selected as an effective tool for monitoring autocorrelated data. Therefore, an integrated model subject to some constraints is proposed to determine the optimal decision variables of the ARMA control chart, economic production quantity, and maintenance policy in the presence of autocorrelated data. Due to the complexity of the model, a particle swarm optimization (PSO) algorithm is applied to search for optimal decision variables. An industrial example and some comparisons are provided for more investigations. Moreover, sensitivity analysis is carried out to study the effects of model parameters on the solution of the economic-statistical design. [ABSTRACT FROM AUTHOR]

Fast-paced markets require complex interactions from all supply-chain agents to satisfy customer demands and needs. The manufacturing industries face some difficulties in terms of production amounts and smooth delivery rates. Technical experts found that a warm-up period before a production run helps address those challenges and improves the workability of machine tools in the manufacturing process. The use of a warm-up process causes a reduction of faulty products (an adverse production outcome) and improves operational efficiency. Also, a shortage in the supply of commodities creates difficult conditions for inventory management decisions, posing the same production problems as mentioned above. Consideration of the warm-up process has recently been included in the scope of operations research, but it is necessary to study its interaction with the presence of shortage. This study presents a system where a manufacturing environment utilizes the warm-up process in its initial phase and shortages are allowed during the production period, in addition, the study takes into account carbon emissions during manufacturing to integrate environmental concerns. We assume that the company has the capability to trade the surplus carbon capacity it hasn't produced. This study offers a comprehensive framework that incorporates former research that addresses warm-up process, carbon emissions, shortages, and defective items. To solve the proposed non-linear programming problem with inequality constraints, we employ the Karush-Kuhn-Tucker (KKT) conditions method to determine the optimal solutions. Managerial insights are derived, and sensitivity analysis highlights the effects of the system parameters on the decision variables. The sensitivity analysis results indicate that the carbon trading cost has a significant impact on the overall cost, and subsequently, the company's profit.

This paper deals with a lot-sizing problem in the economic production quantity model with imperfect production processes and failure in repair where a Brownian motion process governs the inventory level variation. We assume that the unsatisfied demand is fully backlogged. In addition, we assume that all imperfect items produced are stocked separately and then reworked. Reworking and shortage costs are included in the proposed mathematical modelling and analysis. The aim of this research is to determine the optimal production lot size and backorder level such that the long-run total expected cost of the system is minimised. For the proposed model, we prove closed-form expressions for the inventory process and for the backlog costs. Moreover, a computer code using software package for the numerical work is furnished to derive the optimal solution. Some numerical examples and sensitivity analysis are provided to illustrate the validity of the proposed model. [ABSTRACT FROM AUTHOR]

Although the joint optimisation of the three aspects - production, quality control and maintenance - helps to promote efficiency and obtain operational cost savings in the production process, these three concepts are usually studied separately in the literature. Moreover, almost all existing integration studies on this issue are centred on piece part manufacturing, and the integrated modelling in a continuous flow production environment has not been well investigated. In addition, most existing integrated models assume only one assignable cause can occur during the manufacturing process, which is not in accord with the actual production condition because of the usual complexity of production systems. In real cases, production processes are usually subject to a multiplicity of assignable causes. Based on these facts, this paper presents a joint design scheme of production, maintenance, and statistical process control for continuous flow processes with multiple assignable causes. The mathematical model is solved using a developed genetic algorithm that minimises the expected total cost (ETC) per process cycle. A comparison between the one-cause and multi-cause models from an economic aspect is conducted to verify the advantages of the suggested model. A sensitivity analysis is also carried out on some selected variables concerning the ETC and expected production quantity to gain an in-depth insight into the concern. [ABSTRACT FROM AUTHOR]

The quality of products, maintenance activities, and transportation policies are primary concerns of managers in inventory and production planning problems. Environmental issues and regulations are growing increasingly and they have attracted much attention to achieve sustainable production. Previous authors have conducted a wide range of studies on these problems separately. Regarding the gap of an integrated framework, a sustainable economic production quantity model is formulated by considering preventive maintenance and multiple shipments policy where a portion of produced items is defective. Two particular cases are studied. In Case I, the production period's demand has been satisfied by the items produced in the previous cycle. In Case II, simultaneous production and consumption during the production period are considered and mathematically formulated. An analytical method is presented for solving the models, and a numerical example is discussed for both cases. The comparison of two cases proves that Case II is more beneficial and the overall cost of the inventory system is reduced. Sensitivity analysis of the models is performed, and some insights are derived by changing some of the parameters. [ABSTRACT FROM AUTHOR]

Currently, the primary objective of every manufacturing organization is in customers' satisfaction and system cost reduction while keeping in mind both production quantity (economic issues) and environmental issues (sustainability). This study investigates the effects of machine warm-up period on an imperfect production process with rework. In this case, the maintenance process is intended to maximize the efficiency and effectiveness of the production machine. In this manufacturing system, it assumed that after the setup time, the machine starts at the lower rate than the regular production process, commonly called as warm-up period. The warm-up period will increase the useful life of the machine. On the other hand, the machine's defects that occur during this warm-up period are identified and repaired before the regular production starts. Also, this warm-up period reduces waste as it improves machine performance; resulting in the decrease of scrapped items that makes the process friendly for the environment. The purpose of this proposed model is to determine the optimum value of production quantity to minimize the total costs by considering the warm-up period and set-up time. Finally, numerical experiments have been conducted to validate the efficacy of the model as well as to obtain some managerial insights. [ABSTRACT FROM AUTHOR]

The paper aims to provide a technical framework for the enactment of procedures for the production management of large-scale industry. During production, the inspection process aids in the identification of high-quality and scrapped items. Furthermore, the deterioration of perishable products and machine breakdowns during production run time complicate the production. To handle such things, this paper incorporates the proportion of defective items and the proportion of scrap items with a uniform distribution to attain an optimal solution. The uncertainties in the data related to the proportion of scrap items, and the repair time are treated as pentagonal fuzzy numbers. An optimization model to minimize the total cost is stated with fuzzy parameter features. A graded mean differentiation method is used to defuzzify the fuzzy output. The major outcome acquired from this model is the optimal total cost, order quantity, and expected total profit of the production process. Additionally, a value-added process for degradable items has been used to develop an economic production quantity model. Finally, a sensitivity analysis has been conducted to show how the optimal values vary when the various cost parameters are varied. [ABSTRACT FROM AUTHOR]

In this paper, we study a reformulation of the Economic Production Quantity (EPQ) problem. We study a more general version of the problem first and derive the conditions for an optimal solution, as well as the optimal solution itself, all without using derivatives. Then, we apply the approach to the reformulated EPQ problem. This version of the EPQ problem has been tackled by a number of researchers, wherein they have derived the conditions for the optimal solution and proposed algebraic derivations. However, their derivations for the conditions, as well as the optimal solution, have been shown to be questionable. Other than being questionable, the existing approaches are so complicated that they defeat the purpose of simplifying the optimization by using a derivative-free approach. We propose a correct and more succinct, much less complicated approach to derive the conditions and the optimal solution without using derivatives.

The classical economic production quantity (EPQ) model was developed to manage inventory costs in companies last decade ago. This model is extended in various directions in recent years. The classic EPQ has some unrealistic assumptions. The model assumes that all products are perfect, while the production of defective items is inevitable in the real-world environment. Another assumption relates to the continuous demand satisfaction, which ignores the commonly used multiple shipments policy in practice. Finally, the classic model does not consider the probabilistic breakdown of the machine and the required maintenance activities. The present work aims to develop a new imperfect EPQ model under probabilistic machine failure, corrective maintenance, and multiple shipments policy. Two cases are investigated: 1- Considering the production of a fixed percentage of imperfect items 2- Considering no production of defective items. Due to the complexity of the problem, a numerical bisection method is utilized to solve the problem and finding the best possible production time. This method's performance is evaluated by comparing it to the obtained solutions by MATLAB optimization toolbox for genetic and simulated annealing algorithms. Sensitivity analysis is performed, and finally, some directions for future research are suggested.

Background: Determining the optimum shipment quantity in a traditional production system is a competitive business dimension, and developing a reliable shipment policy is decisive for long-term objectives. Currently, significant research in this domain has mainly focused on the optimum shipment lot sizing in a perfect production system without considering the imperfections in the production processes and logistics. It has been well established that the real production inventory system acts as an imperfection in the overall production management loop. Methods: This research deals with designing a new shipment policy considering the imperfections in the production processes and undertaking some influential factors, such as the transportation cost, the actual production inventory, defective items, and backorders. Results: In the developed mathematical framework, the lot-sizing problems, imperfections in the production processes, retailers, and distributors are considered with equal-sized shipment policy to attain pragmatic and real-time results. Conclusions: The developed framework considers an all-unit-discount transportation cost structure. The numerical computations, as well as sensitivity analysis, are performed to point out the specifications and validation of the proposed model. [ABSTRACT FROM AUTHOR]

• New EPQ model with two stages of quality control: early-stage screening after the most critical operation and final screening. • The impact of the screening time on both screening costs and the defect detection rate are considered. • Managerial insights are dealing with highly relevant trade-offs. • Rich set of examples presented to show the nature of the problem. • Results highlight the importance of careful estimation of the defect rate. Most manufacturing systems contain a critical operation in their production where defects are more likely to occur. Letting the defective items pass through further stages of the process can result in a significant loss of time, materials, and money. Therefore, this study considers a manufacturing process with an early stage of quality control. Unlike most academic literature, the presented model considers the impact of the screening time on both screening costs and defect detection rate via different linear and nonlinear functions to derive a better understanding of those dependencies. We develop and analyze a mathematical model to determine the optimal lot size jointly with the optimal screening time during production. We run multiple numerical examples to illustrate the impact of various parameters of the model. Sensitivity analysis shows the robustness of the proposed model with respect to small changes in its parameters. Managerial insights are dealing with highly relevant trade-offs. Firstly, devoting more time to the initial screening increases the inspection cost but allows a greater proportion of defects to be detected. Secondly, discarding defective items at an early production stage decreases production costs at subsequent stages. In addition, the maximum gain is obtained when the relationships between the screening time and the cost, as well as the efficiency of the detection method, are well-understood. Our results also highlight the importance of careful estimation of the defect rate. A higher proportion of defective items increases the required screening time, lot size, and total cost. [ABSTRACT FROM AUTHOR]

A model of a two-level single-producer multi-buyer supply chain (TSPMBSC) is focused on in this article with a single product made by the producer (or vendor) given to the buyers. The operational form of vendor managed inventory (VMI) is utilized by vendors and buyers. We assume the economic production quantity (EPQ) model used by the producer for inventory control with a limited production rate. Sales quantity and sales price are the parameters of each buyer as well as a certain production rate. Two objectives are considered for the model; the first objective is the maximization of channel profit while the second objective is the maximization of the production periods variances whereby the required storage space is minimized. Because of NP-hardness, the weighted sum multi-objective genetic algorithm (WSMOGA), the multi-objective particle swarm optimization algorithm (MOPSO) and the Non-dominated sorting genetic algorithm II (NSGAII) are the three distinct heuristics embedded for tackling the problem. The instances of the considered problems with small, medium and large sizes are used to compare these heuristics. Considering the metrics of comparison, The MOPSO-based heuristic outperformed the other heuristics. [ABSTRACT FROM AUTHOR]

This study presents an integrated model of three dependent concepts including production planning, maintenance scheduling, and statistical process monitoring (SPM) in order to improve both economic and statistical features of the production systems. To bring the proposed model closer to real applications, the possibility of occurring several types of assignable causes during the production cycle is taken into account. Besides, a noncentral chi-square chart is used for simultaneous monitoring of the process mean and variability parameters. Moreover, it is assumed that both time-to-failure and time-to-shift are Weibull distributed random variables. In other words, the system may suddenly fail and goes to an out-of-control condition with two different increasing rates including the failure rate function and the shift occurrence rate function. Hence, to improve the system reliability, a nonuniform sampling scheme is developed in which a same integrated shift occurrence rate is obtained for all intervals. The goal of the model is to minimize the expected total cost per time unit, subject to some statistical constraints. Ultimately, three comparative studies are given to demonstrate the efficiency of the proposed model. The first one indicates that a nonuniform sampling scheme reduces the expected total cost and the length of out-of-control period. The second one confirms that considering the system failure not only increases the length of in-control period but also improves the economic feature of the production system. The third one shows that using chi-square chart decreases the quality loss cost which in turn decreases the expected total cost. [ABSTRACT FROM AUTHOR]

In this paper, we study a reformulation of the Economic Production Quantity (EPQ) problem. We study a more general version of the problem first and derive the conditions for an optimal solution, as well as the optimal solution itself, all without using derivatives. Then, we apply the approach to the reformulated EPQ problem. This version of the EPQ problem has been tackled by a number of researchers, wherein they have derived the conditions for the optimal solution and proposed algebraic derivations. However, their derivations for the conditions, as well as the optimal solution, have been shown to be questionable. Other than being questionable, the existing approaches are so complicated that they defeat the purpose of simplifying the optimization by using a derivative-free approach. We propose a correct and more succinct, much less complicated approach to derive the conditions and the optimal solution without using derivatives. [ABSTRACT FROM AUTHOR]

The classical economic production quantity (EPQ) model was developed to manage inventory costs in companies last decade ago. This model is extended in various directions in recent years. The classic EPQ has some unrealistic assumptions. The model assumes that all products are perfect, while the production of defective items is inevitable in the real-world environment. Another assumption relates to the continuous demand satisfaction, which ignores the commonly used multiple shipments policy in practice. Finally, the classic model does not consider the probabilistic breakdown of the machine and the required maintenance activities. The present work aims to develop a new imperfect EPQ model under probabilistic machine failure, corrective maintenance, and multiple shipments policy. Two cases are investigated: 1- Considering the production of a fixed percentage of imperfect items 2- Considering no production of defective items. Due to the complexity of the problem, a numerical bisection method is utilized to solve the problem and finding the best possible production time. This method's performance is evaluated by comparing it to the obtained solutions by MATLAB optimization toolbox for genetic and simulated annealing algorithms. Sensitivity analysis is performed, and finally, some directions for future research are suggested. [ABSTRACT FROM AUTHOR]

This paper proposes an integrated preventive maintenance and economic production quantity model. A condition-based maintenance policy is described by a random coefficient regression model, based on which the monitored condition is divided into two parts: the actual condition and random error. Products are produced in batches and the system is monitored at the end of each batch. If the observed system condition either reaches or exceeds the critical level, the system should be renewed by preventive maintenance. However, if the actual system condition reaches the failure level during the production process, the system fails and should be renewed immediately. Based on these two renewal situations, we construct a model of expected cost per unit time using the renewal reward theory. The critical level and production lot size are decision variables, which can be obtained by minimizing the cost model. We also develop a simulation process to obtain the optimal results in another way and validate our proposed cost model. Finally, a real case study is given to demonstrate the model and the simulation process.

The study explores a dynamic economic production quantity model whose demand function in consideration of market-trend issue to decide the optimal number of production cycles, the corresponding optimal production time points, and the best time to withdraw from the production line. The objective function of the total relevant costs considered in the model is formulated as a nonlinear programming problem, and a complete search procedure is developed to find the optimal solution of inventory cost. The characteristics of daily necessaries, technology products and fashion products are also analyzed to develop different strategies for the decision makers. The proposed model and algorithm not only provided the optimal solution of the production period and cycle time but also gave the suggestion of the best time to withdraw from the market. Moreover, in order to provide the managers with useful information of the impacts of inventory cost, Monte Carlo technique is used to simulate the stochastic demand. In considering of the stochastic demand, the situation of shortage will definitely happen without or insufficient safe stock. Finally, a numerical example and the corresponding sensitivity analyses are carried out to illustrate the features of our model by utilizing the search procedure developed in this study.

In most of the production-based model, the effect of deterioration at initial stage of the production is not assumed even if assumed than considered to be constant, in few productions-based model deteriorations is assumed time-dependent but during initial level of production its effect was not considered. For a product whose life is high this phenomenon is justifying but for those products whose life is very less this is not faring to not assume the effect of deterioration. In the present study, author have considered the effect of deterioration at the initial level of the model and for the rest cycle of the model as well. After a fixed time, a price discount is also offered for partially deteriorated items where a discount rate is offer at the original one, Shortages are not allowed, production is assumed as demand dependent, and demand is assumed as stock dependent where holding cost of the inventory is assumed as a function of time. A numerical example is also discussed. [ABSTRACT FROM AUTHOR]

• We investigate cost-effective production decisions with raw and recycled materials. • Recycled materials are inexpensive but have setup time uncertainty. We embrace the maximum allowed setup time when setting up recycled materials. • We analyze the decisions with exogenous and endogenous maximum allowed setup time. • We explore the extent to which adopting recycled materials is beneficial. In this study, we investigate the production decision making of a manufacturer, considering the sequential use of raw and recycled materials in a single production process, in which the production setup notably influences the product conformance. Compared with raw materials, recycled materials are less expensive but may not have a sufficiently stable quality, which may lead to a variable setup time. We consider the maximum allowed setup time for recycled materials to mitigate the risk of a prolonged setup time. By minimizing the expected cost per unit time, we determine the manufacturer's lot size for the raw materials in settings in which the maximum allowed setup time is exogenous and endogenous and the lot size of the recycled materials is exogenous. The results of the numerical analyses demonstrate that the maximum setup time and lot size of the recycled materials can serve as cost reduction drivers for the manufacturer. Furthermore, production with raw and recycled materials involves a lower cost than production with raw materials owing to the lower purchase cost and average setup time incurred when using recycled materials. [ABSTRACT FROM AUTHOR]

The smart production system is implemented for more effective labor, less waste, and a reduction of energy consumption. Biofuels are significant substitutes for conventional fuels and decreases air pollution and carbon monoxide, can be made through a smart production system with automated machines. Biodiesel can be produced using an assortment of sources that can be both edible and inedible, but animal fat is a sensible alternative among inedible sources because of its affordable price and ease of availability. The model studies the smart biodiesel production system with energy utilization and less carbon emissions to produce pure biodiesel. The multi-objective mathematical model minimizes the total biodiesel supply chain cost followed by minimizing the total biodiesel supply chain environmental impact and enhancing its social impact. The smart production system with a variable production rate produces the biodiesel with less impurities, but still impurities in the biodiesel, that can be detected by a two-stage autonomated inspection system. The impure biodiesel is remanufactured in the biorefineries at the end of every natural production cycle. For the best utilization of energy, various energy costs, such as lighting and air handling costs are calculated. The improved augmented ϵ -constraint approach with lexicographic optimization is utilized to solve the model. The four mathematical examples are studied, and the repercussions of mathematical experiments reveal that the animal fat purchasing cost is 44.32% of the total cost, and the percentage of impurities in biodiesel can be decreased through minimum energy consumption. The managerial insights of the model, graphical representation, and sensitivity analysis of key parameters are provided in this research. The conclusions can be useful to investors in a sustainable smart production system and biofuel policymakers. [ABSTRACT FROM AUTHOR]

Talep miktarının satış fiyatına karşı duyarlı olması ve kusurlu üretim varsayımlarının optimal politika üzerindeki etkisi birçok üretim probleminde ele alınmıştır. Bu modellerde, tarama işleminin üretim süresi sonunda tamamlandığı varsayılmıştır. Bu çalışmada, tek kalem ürünün tek bir makinede partiler halinde üretildiği bir üretim sistemi için talep miktarının satış fiyatının doğrusal bir fonksiyonu olduğu varsayımı ile bir ekonomik üretim miktarı modeli geliştirilmektedir. Üretim sürecinin kusurlu olduğu, tarama işleminin üretimden sonra da devam ettiği ve belirlenen kusurlu ürünlerin tarama süresi sonunda tek parti halinde indirimli fiyattan satıldığı varsayılmaktadır. Bu çalışmadaki temel amaç, toplam kârı maksimum yapacak üretim miktarı ve satış fiyatının belirlenmesidir. Optimal çözümler önerilen bir algoritma ile elde edilmektedir. Geliştirilen modelin geçerliliğini göstermek amacıyla duyarlılık analizlerine sahip sayısal bir örnek verilmektedir.

Rework products and warehouse capacity are common problems experienced by companies in the production process. Several Economic Production Quantity (EPQ) models were developed to minimize the costs of purchasing raw materials. This study aims to develop an Economic Production Quantity (EPQ) model with rework processes and warehouse constraints, assuming that the product is not perfect and can rework. The proposed model considers several cost components, including setup, holding, production, rework, and warehouse. The two proposed models are EPQ models with reworks and warehouse costs, and EPQ models with reworks and warehouse constraints. Based on several tests conducted, it obtains that the increase in the value of the maximum inventory amount did not have an impact on the production costs and the cost of the rework process. Based on several numerical experiments, the total cost of the rework process and production costs do not change to the maximum inventory value.

Production control policy and economic sampling plan design problems have been studied separately in previous research. This paper considers a joint production control policy and economic single sampling plan design for an unreliable batch manufacturing system. The production is controlled by a modified hedging point policy which consists of building and maintaining a safety stock of finished product to avoid shortages during corrective maintenance. The main objective of this paper is to determine simultaneously the economic production quantity, the optimal safety stock level and the economic sampling plan design which minimise the expected overall cost. A stochastic mathematical model is developed and solved using a simulation optimisation approach based on the response surface methodology. Simulation is used to imitate the complex dynamic and stochastic behaviour of processes as in the real-life industrial systems. The obtained results show clearly strong interactions between production quantity, inventory state and sampling plan design which confirm the necessity of jointly considering production and quality control parameters in an integrated model. Moreover, it is shown a significant impact of production system reliability on the economic sampling plan design and therefore on the quality of finished product delivered to consumers. Numerical example and sensitivity analyses are presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

The economic order quantity and economic production quantity models are the most commonly used inventory models in production environments for the calculation of optimum lot size. However, these models are based on the unrealistic assumption that every process produces good quality products every time. Moreover, the impact of inspection is neglected in all extended inventory control models involving work in process inventory. By taking both imperfect production and lot size inspection into consideration, this paper presents a more realistic approach for the modelling of optimum lot size and total cost with a focus on the work in process inventory. A mathematical model is derived for optimum lot size based on the minimisation of the average cost. Our approach incorporates the effect of rework, rejects and inspection on work in process inventory. The significant effect of imperfect production and inspection on optimum lot size is evaluated via numerical examples. In comparison to existing models, the proposed model is a more generalised and flexible form of inventory model for independent demands. [ABSTRACT FROM AUTHOR]

Background: Determining the optimum shipment quantity in a traditional production system is a competitive business dimension, and developing a reliable shipment policy is decisive for long-term objectives. Currently, significant research in this domain has mainly focused on the optimum shipment lot sizing in a perfect production system without considering the imperfections in the production processes and logistics. It has been well established that the real production inventory system acts as an imperfection in the overall production management loop. Methods: This research deals with designing a new shipment policy considering the imperfections in the production processes and undertaking some influential factors, such as the transportation cost, the actual production inventory, defective items, and backorders. Results: In the developed mathematical framework, the lot-sizing problems, imperfections in the production processes, retailers, and distributors are considered with equal-sized shipment policy to attain pragmatic and real-time results. Conclusions: The developed framework considers an all-unit-discount transportation cost structure. The numerical computations, as well as sensitivity analysis, are performed to point out the specifications and validation of the proposed model.

A joint economic production quantity (EPQ) and delivery quantity model for a production system is investigated in this paper. More specifically, an EPQ policy is implemented in the production system, while a smaller shipping quantity is periodically dispatched to the customer. The production system is also responsible for the shipment cost, i.e. a delivery price-based procurement from the customer. The considered cost includes setup cost to launch the batch production, inventory carrying cost, and transportation cost, where the transportation cost is a function of the delivery quantity. A per unit time cost model is developed and analysed to determine the optimal production and delivery quantities. Under some mild conditions, it can be shown that the joint cost function is convex with respect to the production quantity; and the number of delivery is an integer in each replenishment cycle. Computational study has demonstrated the significant impact of the joint decision model on the operating cost. In particular, the reduction in total cost can be more than 15% when inventory carrying costs, and/or transportation costs, are high. [ABSTRACT FROM PUBLISHER]

This study develops an economic production quantity (EPQ) model and solution procedure for imperfect items with shortage and screening constraint. The Renewal Reward Theorem (RRT) is applied to formulate the exact expected total profit per unit time. We have shown the robustness of our model using time interval as decision variable rather than the traditional order size and backorder quantity. A solution procedure is provided to derive the optimal policy. Special cases of the EOQ/EPQ models can be obtained by taking the parameter limiting values. Numerical examples and sensitivity analysis are presented to verify our results. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of production planning of unreliable batch processing manufacturing systems. The finished goods are produced in lots, and are then transported to a storage area in order to continuously meet a constant demand rate. The main objective of this work is to jointly determine the optimal lot sizing and optimal production control policy that minimise the total expected cost of inventory/backlog and transportation, over an infinite time horizon. The decision variables are the lot sizing and the production rate. The problem is formulated with a stochastic dynamic programming model and the impulse control theory is applied to establish the Hamilton–Jacobi–Bellman (HJB) equations. Based on a numerical resolution of the HJB equations, it is shown that the optimal control policy is governed by a base stock policy for production rate control and economic lot size for batch processing. A thorough analysis and practical issues are addressed with a simulation-based approach. Thus, a combined discrete–continuous simulation model is developed to determine the optimal parameters of the proposed policy when the failure and repair times follow general distributions. The results are illustrated with numerical examples and confirmed through sensitivity analysis. [ABSTRACT FROM PUBLISHER]

In this paper, an economic production quantity (EPQ) inventory model with scrap and rework is developed. The inventory model is for multiple products and all products are manufactured in a single machine. Clearly, the existence of one machine results in limited production capacity and shortages. Therefore, shortages are permitted and partially backordered. We show that the model of the problem is a constrained non-linear program and use GAMS modelling language to solve it. Our objectiveis to minimize the joint total cost of the system and the supply cost of warehouse space, subject to capacity, service level, budget and warehouse space constraints. Subsequently, a nonlinear programming solver BARON is used to solve the model. At the end, numerical examples are provided to demonstrate the applicability of the model in real-world manufacturing problems.To verify the solution obtained and to evaluate the performance of MCDM (Multi Criteria Decision Making) methods , TUKEY test is employed to compare the means of the primary objective values, the mean values of the second objective , and the mean needed CPU time of solving the problem using various methods of MCDM. Also, To compare the methods we used TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). The results show that torabi-hasini method is the most efficient method to solve the model and the solution qualities of the methods differ significantly. Finally, some conclusions and future researches are included.

In the fashion industry, a flexible backup agreement contract allows the retailer to order a partial amount from the backup quantity to allay the risk of uncertain market demand. However, under such a contract, the manufacturer faces the risk of bearing a huge leftover if the quantity realized by the retailer in backup is small. Accordingly, the present study considers a modified backup agreement in which the manufacturer is permitted to urgently purchase substitute products to satisfy the backup order from a third-party supplier, but at a unit purchase cost greater than the original unit manufacturing cost. The corresponding expected total profit function for the manufacturer is established and shown to be concave. The profit function is used to explore various useful properties for determining the optimal production lot size. In addition, an illustrated numerical example is provided to analyze the impact of the backup contract terms on the optimal production lot size and manufacturer's profit. [ABSTRACT FROM AUTHOR]

One of the classical models for inventory control is economic production quantity (EPQ), which is widely used in industry. In this paper, an EPQ model with partial shortage is developed by considering the real world conditions, and costs related to the backorder demand are taken as fixed and time-dependent. In the proposed model, determination of the inventory cycle length, the length of positive inventory cycle and backordered demand rate are considered in shortage period. The aim of the presented research is to minimize the total inventory costs and the space required for storage products so that the stochastic and classic constraints including holding costs, lost sales, backorder, budget, total number of productions and average shortage times should be satisfied while optimizing the multi-objective problem. Presented model is a bi-objective nonlinear programming model. Then, to solve the proposed model, three multi-objective decision-making methods including Lp-metric, goal programming and goal attainment are used. Besides, numerical examples are executed in small, medium and large scales by use of GAMS software, and the performance of the methods is compared in terms of objective functions and required CPU time. Finally, sensitivity analysis is done to determine the effect of change in the main parameters of the model on the objective function value. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper aims to develop a robust multi-item EPQ formulation considering rework process and imperfect items. The mathematical model consists of two objective functions targeting minimization of total inventory costs and the total required warehouse space, respectively. Since, in real-world applications, parameters of the mathematical formulation are due to uncertainty, in this paper, Basic Chance Constraint Programming and Robust Fuzzy Chance Constraint Programming models are developed to handle uncertainties in both objective function and constraints. By solving examples, the superiority of the RFCCP over the BCCP model is showed and its ability to provide risk-averse solutions is ensured. Due to the nonlinearity of the RFCCP model and to provide the decision maker with the Pareto front, two algorithms, namely, Multi-Objective Grey Wolf Optimizer and Multi-Objective Water Cycle Algorithm, are used to optimize the decision variables. The performance of the algorithms is evaluated within different large-size test problems, using diversity, Spacing, number of non-dominated solutions and CPU-time. In the end, to investigate significant differences and to determine the best algorithm ANOVA test is implemented. In the end, we also offer new research directions, e.g. in terms of further ways of uncertainty modelling and risk management. [ABSTRACT FROM AUTHOR]

The notion of quality control is introduced into the classic economic production quantity (EPQ) model. Based on previous research, this paper contributes to an integrated EPQ model combining the concepts of statistical process control and maintenance. An imperfect production process involving three different conditions is considered. A control chart is adopted to monitor the whole process with Taguchi's loss function estimating the quality cost of each condition. A corresponding maintenance policy is planned for the machine depending on what condition it runs in. Thus the proposed EPQ model takes quality-related costs and maintenance-related costs into account other than storage costs and ordering costs already considered in the classic model. The objective of this model is to minimise the total expected production cost per production cycle while simultaneously determining the optimal parameters of control chart design, the interval between sampling, the sample size and the maintenance decision policy. The pattern search method is used to solve the problem using the MATLAB toolbox. In addition, a case study, sensitivity analysis and comparison analysis are presented to demonstrate the application of the model. [ABSTRACT FROM PUBLISHER]