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The purpose of this study is to formulate two multi-product single-machine economic production quantity (EPQ) models by considering imperfect products. Two policies are assumed to deal with imperfect products: selling them at discount and applying a reworking process.

A screening process is used to identify imperfect items during and after production. Selling the imperfect items at a discount is examined in the first model and the reworking policy in the second model. In both models, demand during the production process is satisfied only by perfect items. Data collected from a case company are used to illustrate the performance of the two models. Moreover, a sensitivity analysis is carried out by varying the most important parameters of the models.

The case study in this research is used to demonstrate the applicability of the proposed models, i.e. the EPQ model with salvaging and reworking imperfect items. The models are applied to a high-tech un-plasticized polyvinyl chloride (UPVC) doors and windows manufacturer that produces different types of doors and windows. ROGAWIN Co. is a privately owned company that started in 2001 with fully automatic production lines. Finally, the results of applying the different ways of handling the imperfect items are discussed, along with managerial insights.

In real-world production systems, manufacturing imperfect products is unavoidable. That is why, it is important to make a proper decision about imperfect products to reduce overall production costs. Recently, applying a reworking strategy has gained the most interest when it comes to handling this problem. The principal idea of this research is to maximize the total profit of manufacturing systems by optimizing the period length under some capacity constraints. The proposed models were applied to a company of manufacturing UPVC doors and windows.

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.

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.

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.

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.

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.

Good management strives to align and corporate processes for more attention being paid to supply chain management. Firms realize that greater co-operation and improved coordination can help to manage the entire supply chain more efficiently. The imperfect quality item is one of the most important issues that affect the expected profit of green supply chain. The imprecise cost with screening process of poor quality items posed in supply chain is the subject of this study.

The present study explores production model for imperfect items having uncertain cost parameters with three-layer supply chain encompassing supplier, manufacturer and retailer. The model is considering the impact of business tactics such as order size, production rate, production cost and appropriate times in various sectors on collaborative marketing systems. Due to imprecise cost parameters, the pentagonal fuzzy numbers are set to fuzzify the total cost and defuzzifition by using graded mean integration.

This study offers an explicit condition in uncertain environment to manage the imperfect quality item to increase the potential profit of the supply chain. The influence of changes in parameter values on the optimal inventory policy under fuzziness is provided managerial insights.

This model makes a significant contribution to fuzzy inference. The results of the study provide a trading strategy for the industry to avoid losses. The prescribed study can be suitable for the industries like sculpture, jewelry, pottery, etc.

The purpose of this paper is to propose an economic production quantity (EPQ) inventory model considering imperfect items and probabilistic demand for a two-echelon supply chain. The production process is imperfect and the imperfect quality items are removed from the lot size. The demand rate of the inventory system is random and follows an exponential probability density function and the demand of the retailers is depending on the initiatives of the sales team.

Two approaches are examined. In the non-collaborative approach, any member of the supply chain can be the leader and takes decisions to optimize the profits, and in the collaborative system, all members make joint decisions about the production, supply, sales and inventory to optimize the profits of the supply chain members. The calculus approach is applied to find the maximum profit related to the members of the supply chain.

A numerical example is presented to illustrate the performance of the EPQ model. The results show that collaborative approach generates greater profits to the supply chain and the market’s demand represents the variable behavior and uncertainty that is generated in the replenishment of a supply chain.

The new and major contributions of this research are: the inventory model considers demand for products is random variable which follows an exponential probability distribution function and it also depends on the initiatives of sales teams, the imperfect production system generates defective items, different cycle time are considered in manufacturer and retailers and collaborative and non-collaborative approaches are also studied.

Develops a framework which provides a step towards better planning of production, scheming inspection and preventive maintenance. Studies the effects of an imperfect production process on the optimal production cycle time. The system is assumed to deteriorate during the production process and produce some proportion of defective items. Extends to the cases where the proportion of defective items and the cost of process restoration are not constant. Provides a comparative study of two monitoring policies where the preventive maintenance setting is used and not used in the deteriorating production process. These models are directly relevant to the management of the quality and reliability of the production process. When scheming inspection is adopted, it is shown that the optimal inspection intervals are equally spaced in the imperfect production process under the different policies, respectively. Provides a numerical example to illustrate the derivation of the optimal production cycle time in the models.

This study investigates a production process that requires N kinds of components for the production of a finished product. The producer orders the various kinds of components from different suppliers and receives the orders in lots at the beginning of each production cycle. Similar to situations often encountered in real life, the lead times are random variables with known probability distributions so that a production cycle starts whenever all N kinds of components become available. Each of the lots received at the start of a production run contains both perfect and imperfect quality components. Once all N kinds of components become available, the producer initiates a screening process to detect the imperfect components. The production of the finished product uses only perfect quality components. The imperfect components are removed from inventory whenever the screening process is completed. The percentage of components of perfect quality present in each lot is a random variable with a known probability distribution.

This production process is described and modeled mathematically and the optimal production/ordering policy is derived based on the mathematical model.

The formulated mathematical model resulted in the determination of the optimal policy consisting of the optimal number of finished items ordered to be produce during each production run, the number of components ordered from each supplier, and the reorder point. The derived closed form expression for the optimal lot size depends on the minimum of the number of perfect quality components in a lot, whereas the reorder point is determined based on the maximum lead time.

The modeling approach and results of this study provide practical implications that may be beneficial to both production and supply chain managers as well as researchers.

This modeling approach that incorporates decision-making related to the logistics of acquiring the components and accounts for the probabilistic nature of the lead times and quality of components addresses a gap in the logistics/production literature.

This paper integrates condition-based maintenance (CBM) with production planning in a single-stage production system that deteriorates with usage during a specified finite planning horizon. The purpose of this paper is to develop an integrated production and maintenance model to minimize the expected total cost over the horizon.

A joint production planning and CBM model is proposed. In the model, a set of products must be produced in lots. The system degradation is a stationary gamma process and the degradation level is detected by inspection between production lots. Maintenance actions including imperfect preventive maintenance (PM) should be taken when the failure risk exceeds the maintenance threshold. A fix-iterative heuristic algorithm is proposed to address the joint model.

The proactive policy expressed as a prognosis maintenance threshold is introduced to integrate CBM with batch production perfectly. Experiments are carried out to conduct sensitivity analysis, which provides some insights to facilitate industrial manufacturing. The superiority of the proposed joint model compared with a separate decision method is demonstrated. The results show an advantage in cost saving.

Few studies have been made to integrate production planning and CBM decisions, especially for a multi-product system. Their maintenance decisions are usually based on a periodic review policy, which is not appropriate for batch production system. A prognosis maintenance threshold based on system condition and production quantity is suitable for the integrated decisions. Moreover, the imperfect PM is taken into consideration in this paper. A fix-iterative algorithm is developed to solve the joint model. This work forms a proactive maintenance for batch production.

The purpose of this paper is to develop an extensive economic production quantity (EPQ) model on the basis of previous research. Considering an imperfect three‐state production process, this paper makes contributions to an integrated model combining conceptions of quality loss and design of control chart based on EPQ model. The objective is to minimize the total production cost with the determination of EPQ and design parameters of control chart subjected to quality loss and other process costs.

In this paper, imperfect process is defined as a three‐state process, and the quality cost corresponding to each state contributes to the eventual total expected cost formulation. Control chart is used to monitor the shift from the target value within whole process and its control limits are set to be related to the quality cost.

The proposed integrated model conforms more closely to the real situation of production process considering the process shift as a random variable.

Numerical computation and sensitivity analysis through a case study are presented to demonstrate the applications of the model.

Few research efforts investigate an integrated model considering EPQ, control chart and quality loss simultaneously. In particular, compared with the former researches, the process shift, due to which the quality cost incurs, is considered as a random variable in this paper.

Lot-sizing is among the most important problems in the production and inventory management field. The purpose of this paper is to move one step forward in the direction of the real environment of the dynamic, multi-period, lot-sizing problem. For this purpose, a two-warehouse inventory system, imperfect quality and supplier capacity are simultaneously taken into consideration, where the aim is minimization of the system costs.

The problem is formulated in a novel continuous nonlinear programming model. Because of the high complexity of the lot-sizing model, invasive weed optimization (IWO), as a population-based metaheuristic algorithm, is proposed to solve the problem. The designed IWO benefits from an innovative encoding–decoding procedure and a heuristic operator for dispersing seeds. Moreover, sequential unconstrained minimization technique (SUMT) is used to improve the efficiency of the IWO.

Taking into consideration a two-warehouse system along with the imperfect quality items leads to model nonlinearity. Using the proposed hybrid IWO and SUMT (SUIWO) for solving small-sized instances shows that SUIWO can provide satisfactory solutions within a reasonable computational time. In comparison between SUIWO and a parameter-tuned genetic algorithm (GA), it is found that when the size of the problem increases, the superiority of SUIWO to GA to find desirable solutions becomes more tangible.

Developing a continuous nonlinear model for the concerned lot-sizing problem and designing a hybrid IWO and SUMT based on a heuristic encoding–decoding procedure are two main originalities of the present study.

Sets out to develop an integrated model that considers simultaneously inventory production decisions, PM schedule, and warranty policy for a deteriorating system that experiences shifts to an out of control state. The time to shift follows a general probability distribution with increasing hazard rate, so that time‐based PM is effective in improving the system reliability.

A profit function is used to model the production system. Optimization techniques are used to generate optimal solutions for the problem. Although global optimality cannot be guaranteed, empirical results show that global optimal solutions are obtained.

The integrated model provides decisions on inventory levels, production run length, and PM schedule simultaneously. It is illustrated through numerical examples that investment in PM can lead to savings in warranty claims for repairable products. As a result, the overall profit per unit, in certain cases, is higher with PM than without PM.

The production system is taken, numerical examples are presented and a sensitivity analysis is conducted to gain more insight into the developed model. In particular, the numerical analysis shows that a better PM program reduces warranty claims.

In addition to the joint optimization of production/inventory decisions and PM schedule, such models can be very useful in making resource allocation decisions between warranty and PM programs. It is clear from the numerical analysis that a better PM program reduces warranty claims.

The paper provides a joint optimization of production inventory decisions and the PM schedule for a system subject to a time to shift that follows a general probability distribution. Previous research considered only an exponential distribution and did not consider PM.