Imperfect Manufacturing System Research Articles

Warranty, free service and rework policy for an imperfect manufacturing system with SAR sensitive demand under emission taxation

The aim of this study is to illustrate the impact of warranty/free service period, specific absorption rate (SAR) of the products, rework policy and emission taxation on the optimal business policy of an imperfect production inventory system in the current highly uncertain/intensified market situation. In this study, the customers’ demand is considered to be influenced by the warranty/free service period along with a permissible SAR of the items. As a result, the manufacturer invests in order to provide warranty period/free service period and fixing an appropriate SAR for the products which are shown in production cost, service cost and SAR reduction investment. Three distinct scenarios are analysed separately regarding the marketing assimilation of defective items. Each suggested scenario relying on the system is quantitatively validated using an example. Furthermore, manufacturers are bound to pay carbon emission tax due to the carbon emission during the production process. Due to high non-linearity of the objective function, a numerical example is solved using the artificial hummingbird algorithm (AHA). From the numerical experiment, it is observed that the optimal policy of the system is strongly influenced by the price and duration of the warranty, emission taxation rate and moderately affected by the SAR of the product. Finally, a sensitivity analysis is carried out, and its effect are shown graphically in order to provide guidance to the competent manager of the firm.

Optimising production, maintenance, and quality control for imperfect manufacturing systems considering timely replenishment

To optimise production planning, maintenance strategies, and quality control in imperfect manufacturing systems, most existing works set the buffer stocking time at the cycle start time. However, excess inventory holding costs will be incurred if the buffer is stocked too early. This means that while the abovementioned setting can make the optimisation model simple, it might increase costs. Taking the uncertain practical buffer stocking time of an imperfect manufacturing system into account, this study aimed to find the production cycle, maintenance frequency, quality inspection cycle, and number of inspections that will minimise the expectation unit cost of the system. To this end, we developed a new model to optimise production, maintenance, and quality control considering timely replenishment. First, excess inventory holding and shortage costs were considered and the production process was divided into five scenarios based on the buffer stocking time and inspection time for assignable causes. Second, the link between production, maintenance, and quality was addressed by capturing the dynamic and random behaviour of production systems. An x-bar control chart was integrated into the model to monitor quality. A case study and sensitivity analysis were undertaken to verify the effectiveness and superiority of the proposed optimisation strategy.

Integrated maintenance, inventory and quality engineering decisions for multi-product systems

Abstract It is essential for manufacturers to consider the interrelation among quality, inventory, and maintenance decisions to detect imperfect quality products, keep the production system in good operating condition, and manage quality and inventory costs. Hence, this paper aims to develop an integrated model of inventory planning, quality engineering, and maintenance scheduling in which the expected total cost per time unit is minimised by determining the sample size, sampling interval, control limit coefficient, along with production cycle time. In this regard, an imperfect multi-product manufacturing system is considered, in which the inventory shortage in satisfying the demand for each product type and the idle time during the production cycle are not allowed. It is assumed that the process starts in an in-control condition where most produced units are conforming. However, due to the occurrence of an assignable cause (AC), the process mean moves to an out-of-control condition in which a significant fraction of non-conforming units is produced. The efficiency of the proposed mathematical model is evaluated by a numerical example, and then the sensitivity of the proposed model to important inputs is analysed. Finally, a comparative study based on the Taguchi design approach is given to confirm the capability of the proposed model to achieve remarkable cost savings.

A Literature Review on the Sustainable EPQ Model, Focusing on Carbon Emissions and Product Recycling

Background: Many businesses want to include sustainability in their manufacturing operations. A conventional economic production quantity (EPQ) model is employed to calculate the ideal number of products to manufacture at one time. The goal of this study was to look at the current research on sustainable economic production quantity and supply chain models and suggest prospective future research directions based on existing knowledge gaps. Methods: In this perspective, we used systematic procedures to conduct a survey that included studies from two scenarios: (1a) a sustainable EPQ model that accounts for carbon emissions from inventory storage and manufacture, (1b) a sustainable EPQ model that includes product recycling, and (2) a reverse logistics model that accounts for emissions and product recycling. Results: According to the inquiry, there are reverse logistics models in the literature that consider carbon emissions and product recycling together, but they are not jointly considered for modeling a sustainable EPQ model considering the situation where the manufacturing system is imperfect, although both are vital for ensuring environmental sustainability. Conclusions: In the future, the EPQ model can be developed with these two aspects in mind to understand the effects of product recycling on carbon emissions while controlling production and inventories for an imperfect manufacturing system.

Emergency order replacement of substandard products under economic production quantity model, including shortages and backordering

This paper concerns inventory control under the economic production quantity model, allowing for substandard products and shortages. The imperfect manufacturing system creates a percentage of substandard products, treated as a random variable having a known probability distribution function. All products produced are screened to identify substandard products. It is commonly assumed in the literature that substandard products are subtracted from the inventory for sale as a single batch at a reduced price. However, in some situations, it may be appropriate to repair an item or to obtain a substitute from a local supplier, regardless of its higher price. Restrictions such as production programming may make it impossible to rework substandard products, but the manufacturer has the option of replacing them by purchasing products of good quality from a domestic supplier, though these will normally have a higher unit cost. Three possible cases can occur, depending on the timing of adding emergency-purchased products to the inventory. The paper presents a numerical example and a sensitivity analysis to show how the three cases are applied within the proposed inventory model. [Submitted 24 January 2020; Accepted 22 August 2020]

EPQ models for an imperfect manufacturing system considering warm-up production run, shortages during hybrid maintenance period and partial backordering

Unreliable conditions and process deterioration of machines are the major issues in several manufacturing systems. These issues not only affect the production schedules but also affect the product quality significantly. A process warm-up production and amalgamation of the preventive and corrective maintenance are important for the smooth functioning of production activities and improving the product quality. The management needs to handle the product shortages carefully and raise the backorders to upgrade the business economy. To accomplish all these objectives, we develop two production inventory models in this paper by considering a process warm-up production run, hybrid maintenance schedule, anticipated shortages during the maintenance period, and rework of imperfect items. Two different rates are used to distinguish the production of imperfect items in the warm-up and standard production periods. We use fixed and variable lengths to represent the warm-up production period in the two models respectively. The maximum customer waiting time for receiving the backorders is calculated under the consideration of finite replenishment policy and simultaneous regular demand satisfaction. Numerical examples and sensitivity analysis are provided to illustrate the models. The two models are compared based on their annual variable costs. The results suggest that a trade-off between the rework and holding costs of defective items is necessary for better inventory decisions. Determining the optimal value of the length of the warm-up production period is necessary to minimize the annual variable cost.

EPQ models with bivariate random imperfect proportions and learning-dependent production and demand rates

In this paper, three production inventory models are constructed for an imperfect manufacturing system by considering a warm-up production run, shortages during the hybrid maintenance period, and the rework of imperfect items. The proportions of imperfect items produced during the warm-up and regular production runs are random and they are represented using a bivariate random variable. The shortage quantity is partially backordered and the supply of backorder quantity is planned simultaneously with regular demand satisfaction. The learning models are designed to accommodate the different learning capabilities of workers in unit production time during warm-up and regular production periods. The production and demand rates of these models are made dependent on the learning exponents. As the resulting models are highly nonlinear in the decision variable, they are optimized using a genetic algorithm. The models are illustrated using numerical examples and sensitivity studies are performed to find the influence of the key parameters.

Production and payment policies for an imperfect manufacturing system with discount cash flows analysis in fuzzy random environments

ABSTRACT This paper considers an imperfect manufacturing system with credit policies in fuzzy random environments. The supplier simultaneously offers the retailer either a permissible delay in payments or a cash discount and retailer in turn provides its customer a permissible delay period. We used an alternate approach – discount cash flow analysis to establish an inventory problem. It is assumed that the elapsed time until the machine shifts from ‘in-control’ state to ‘out-of-control’ state is characterized as a fuzzy random variable. As a function of this parameter, the profit function is also a random fuzzy variable. Based on the credibility measure of fuzzy event, the model with fuzzy random elapsed time can be transformed into a crisp model . We establish several theoretical results to obtain the solution that provides the largest present value of all future cash flows. Finally, numerical example is given to illustrate the results and obtain some managerial insights.

Optimal production lot sizing for an imperfect manufacturing system with machine breakdown and emergency maintenance policy

Purpose The purpose of this paper is to study a production lot sizing problem with consideration of imperfect manufacturing and emergency maintenance policy, providing managerial implication for practitioners. Design/methodology/approach In this study, the authors introduce two models, where in Model I, shortages are not allowed and repair times are negligible. In Model II, shortages are allowed and are partially backlogged, and repair times are assumed to be exponentially distributed, algorithm is developed to solve the models, numerical examples were demonstrated the applications. Findings Results show that in the Model I, demand rate is the most significant parameter affecting the average expected cost, whereas the time needed to breakdown after machine shift is the most significant factor affecting the production lot size. Therefore, reduction in the time needed to breakdown after machine shift would be helpful for determining an appropriate production lot size in Model I. In Model II, repair time parameter is the most significant factor affecting the average expected cost. Reducing the value of machine shift parameter would be helpful for determining an adequate production lot size and reducing decision risk. Practical implications This paper can provide important reference value for practitioners with managerial implication of how to effectively maintain equipment, i.e. how to make product lot size considering the influence of the maintenance policy. Originality/value From the aspect of academia, this paper provides a solution to the optimal production lot sizing decision for an imperfect manufacturing system with consideration of machine breakdown and emergency maintenance, which is a supplement to imperfect EMQ model.

Optimal decision of an economic production quantity model for imperfect manufacturing under hybrid maintenance policy with shortages and partial backlogging

Considering the characteristics of the stochastic shift of the machine state and the uncertainty of the product quality of production, in this paper, we develop an optimisation decision of economic production quantity model for an imperfect manufacturing system under hybrid maintenance policy with shortages and partial backlogging. We assume that the production process is imperfect stemming from the machine reliability and the probability of out-of-control, a hybrid maintenance policy combined of emergency maintenance and preventive maintenance is executed during each production run. Three decision models based on the scenarios of machine breakdown and repair time are developed. The optimal production quantity and maintenance inspection number during each production run are solved with minimising the expected average cost of the system. Numerical examples are used to demonstrate the effectiveness and feasibility of the model. Sensitivity analysis is conducted to analyse the impacts of key parameters on the optimal decision. Some implications related to the effective and economical execution of maintenance policy for practitioners are derived.

Determining an optimal replenishment run time and lot size for an imperfect manufacturing system and rework under markdown policy

This study proposes a continuous production inventory model for deteriorating items with preservation technology, rework and price-dependent demand under markdown policy. In this study, we have adopted the markdown policy to reduce inventory cost and clearance at the end of the season or to sell old or slow-moving inventory at the end of its life. Rework is another main factor to reduce production cost and environmental problem. The preservation technology is also considered during product deterioration period to control the deterioration rate of products. The shortages are not allowed. We have also considered that in one cycle, the production system can produce items in several determined replenishment cycles under markdown policy. The aim of this research is to derive the optimal production-run time, the optimal replenishment cycle length, the optimal length of time horizon and the optimal production quantity so as to minimize the total average cost. An example and sensitivity analysis is shown to illustrate the model.

Optimization of an Imperfect Manufacturing System for Deteriorating Items with Rework and Shortage Under Inflation

In this research, an imperfect manufacturing inventory model for deteriorating items has been developed wherein a manufacturer produces items in m determined imperfect replenishment cycles. In each replenishment cycle, production facility can produce items in four different imperfect replenishment cycles and one rework-run, (m : 4 − 1) policy. Demand rate is considered as inflation rate and selling price dependent. Many researchers focused on economic production quantity (EPQ) model under the three assumptions that the items produced in replenishment cycles are all perfect, all the deteriorated items can be detached from the stock, and all the items are produced in a single replenishment cycle. In this work, these three assumptions are relaxed to create positive impact on corporate image and reduce the holding cost of the inventory model. Shortages are allowed and fully backordered. The aim of the research is to determine the optimal replenishment-run time, the economic replenishment lot size, and the optimal backordered quantity so as to minimize the total cost of the inventory model. Finally, a numerical example along with graphical representation and sensitivity analysis is discussed to validate the results of the model.

An Imperfect Multi-Item Single Machine production system with Shortage, Rework, and Scrapped Considering Inspection, Dissimilar Deficiency Levels, and Non-Zero Setup Times

In this paper, we consider a deficient production system with permissible shortages. The production system consists of a unique machine that manufactures a number of products that a part of them are imperfect in form of rework or scrap. These defective products are identified by 100% inspection during production, then, they are whether reworked or disposed of after normal production process. Like real-world production systems, there are diverse kinds of errors creating dissimilar breakdown severity and rework. Moreover, reworks have non-zero setup times that makes the problem closer to real-world instances where machines require some preparations before starting a new production cycle. Thus, we introduce an economic production quantity (EPQ) problem for an imperfect manufacturing system with non-zero setup times for rework items. The rework items are classified into several categories based on their type of failure and rework rate. The aim of this study is to obtain optimum production time and shortage in each period that minimizes inventory system costs including setup costs in reworks, holding costs, production costs, inspection costs, disposal costs, and shortage. Finally, a numerical example is proposed to assess efficiency and validation of the proposed algorithm.

Imperfect production process model with product rework, multi-delivery, and quality loss

Krishnamoorthi and Panayappan developed an imperfect manufacturing system with multi-delivery policy and rework for determining the optimal number of deliveries and production run. However, their model did not consider the quality cost of conforming products. In this article, the authors presents a modified Krishnamoorthi and Panayappan’s model for obtaining the optimal process mean (process quality level), production run, and the number of deliveries based on the minimization of the expected total cost of product per unit time. Taguchi’s asymmetric quadratic quality loss function is considered for measuring the product quality.

Optimum ordering policy for an imperfect single-stage manufacturing system with safety stock and planned backorder

Manufacturing industries prefer to produce extra units as safety stock especially when demand for these units varies. The phenomena of producing additional units is also observed when processes are imperfect and production managers are sure that product can be consumed in market. In addition, customer is also willing to wait for demands to be backordered in the case of shortages. However, inventory carrying and backordering costs may play vital role if products are produced in relatively large amount. Therefore, a mathematical model is needed that can define the ordered quantity taking safety stock and planned backordering into consideration with imperfect production setup. This paper is an attempt towards development of such mathematical model that considers safety stock, lot size, and planned backorders for a single-stage imperfect production setup. Mathematical model is developed based on minimization of total average cost function. Three decision variables including order quantity, safety stock, and planned backorders have been optimized simultaneously using classical optimization approach. Numerical examples are used to illustrate the proposed model for calculation of decision variables. Impact of changes in processes imperfection, holding costs, and backordering costs over variables have been numerically computed to highlight model significance in daily industrial life. Results prove that safety stock and planned backorder reduce the total cost significantly.

Integrated maintenance–quality policy taking into account the economical impact of reworking activities

ABSTRACTIn this paper, we study integrated strategies joining maintenance and quality. We consider an imperfect manufacturing system composed of a single machine subject to an increasing random failure rate and producing conforming (first and second choice) and non conforming items. In order to decrease the failure rate and its impact on teh quality of output products, a preventive maintenance (PM) policy, block type, with minimal reapair is applied. Indeed, two different strategies are developed: The first strategy consists on selling top quality products at the best price, selling products with substandard quality at a lower price and rejecting non-conforming items. For the second strategy, we propose reworking activities for products with substandard quality and non-conforming items in order to be sold at the best price. We aim to establish the optimal number of batches produced N* before each PM action maximizing the total profit per time unit. These two strategies are studied for both an infinite and finite horizon. A comparative study between these two strategies for an infinite horizon is developed in order to identify the most economical strategy. Numerical and sensitivity studies are developed, inspired from an industrial case, in order to illustrate the proposed models.

Some Observations to: Lot Sizing with Non-zero Setup Times for Rework

Haji et al. (J Syst Sci Syst Eng 17(2):230–240, 2008) proposed a single machine multiproduct economic batch quantity for an imperfect manufacturing system that includes perfect and re-workable items. They assumed the setup time in rework process is non-zero. They presented two inventory models; one for a single product and one for the case that several products manufactured on a unique machine. However, in these inventory models, there exists the possibility that shortages occur. Therefore, this technical paper identifies some inconsistencies in the research paper of Haji et al. (2008). With a numerical example, it is shown that Haji et al. (2008)’s solution is not held for all instances. Furthermore, this technical paper provides some observations and corrections to the shortcomings in order to improve two solution procedures for single product and multi-product cases.

Study of Imperfect Manufacturing System with Preservation Technology Investment Under Inflationary Environment for Quadratic Demand: A Reverse Logistic Approach

This paper focuses on imperfect manufacturing system with remanufacturing, manufacturing and product returned cycle for a single item which deteriorates with respect to time. The product has maximum fixed lifetime. To decrease deterioration of the product, manufacturer spends capitals on preservation technology to preserve the item. In this paper, the effect of inflation is also considered. Here, time-dependent quadratic demand is debated which is suitable for the products whose demand increases initially and afterward it starts to decrease. The objective is to minimize the total cost of manufacturer with respect to cycle time and investment for preservation technology. The model is supported with numerical example. Sensitivity analysis is done to derive insights for decision makers. Graphical result, in three dimensions, is exhibited with supervisory decision.

Joint inventory-production inventory model with defective items, uncertain demand and allowable shortage

Due to uncertain demand observed in the industries, it is important to investigate on the effect of this crucial issue on integrated vendor-buyer inventory model. Hence, in a specific imperfect manufacturing system, this paper, presents an integrated vendor-buyer inventory model wherein buyer's lead time demand is follows a normal distribution. As a consequence of demand uncertainty, a full backorder system for allowable shortage is considered. A solution procedure is proposed to find optimal joint strategy of both vendor and buyer and numerical example is presented to illustrate the results of the proposed model. This study, also, shows a respective probabilistic inventory model to be minimised is jointly convex in the decision variables. The proposed algorithm is coded by MATLAB 2012b.

Joint inventory-production inventory model with defective items, uncertain demand and allowable shortage

Due to uncertain demand observed in the industries, it is important to investigate on the effect of this crucial issue on integrated vendor-buyer inventory model. Hence, in a specific imperfect manufacturing system, this paper, presents an integrated vendor-buyer inventory model wherein buyer's lead time demand is follows a normal distribution. As a consequence of demand uncertainty, a full backorder system for allowable shortage is considered. A solution procedure is proposed to find optimal joint strategy of both vendor and buyer and numerical example is presented to illustrate the results of the proposed model. This study, also, shows a respective probabilistic inventory model to be minimised is jointly convex in the decision variables. The proposed algorithm is coded by MATLAB 2012b.