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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.

This research work introduces an imperfect production system where the demand is assumed to be stochastic and it is influenced by random selling price. The shift time from an “in-control” state to an “out-of-control” state is exponentially distributed. The accumulated inventory contains both perfect and defective items which are all sold with a free repair warranty (FRW) offer. Complete back ordering of shortages are taken into account. The purpose of this paper is to determine the optimal selling price and hence the optimal production lot size such that the expected profit is maximized.

The general model is discussed separately for both types of uniformly distributed selling price-sensitive demand pattern: additive type and multiplicative type. Numerical examples and graphical representations of the optimal solutions are provided to illustrate the models.

This paper helps the manager to manage future situations and it may be considered as a base work for the researchers to work in this direction.

The main limitation of this model is to consider a single item for a single channel system. There are many correlated issues that need to be further investigated. The future study in this direction may include the consideration of multi-items, diverse demand pattern with different types of price distributions.

In the production inventory literature, plenty of articles are available considering imperfect production but none of them have considered selling price-sensitive stochastic demand where the sales price is random in character under an FRW offer.

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.

The purpose of this study is to develop a joint production, maintenance and quality control strategy involving a periodic preventive maintenance policy.

The proposed integrated policy is defined and modeled mathematically.

The paper focuses on finding simultaneously the optimal values of the preventive maintenance period, the buffer stock size, the sample size, the sampling interval and the control chart limits, such that the expected total cost per time unit is minimized.

The paper attempts to integrate in a single model the three main aspects of any manufacturing system: production, maintenance and quality. The considered system consists of one machine subject to a degradation process that directly affects the quality of products. The process and product quality control is carried out using an “x-bar” control chart. In the proposed model, a preventive maintenance action is performed every α inspections of product quality in order to reduce the shift rate to the “out-of-control” state. A corrective maintenance action is undertaken once the control limits are exceeded. In order to palliate perturbations caused by the stopping of the machine to undergo maintenance actions, a buffer stock is built up to ensure the continuous supply of the subsequent machine. The main goal of this work is to develop a model that captures the underlying link between the preventive maintenance policy, the buffer stock size and the parameters of an “x-bar” control chart used to control the quality of the product. Numerical experiments and a study of the effects of the input parameters variation on the obtained results are performed.

The existing models that simultaneously consider maintenance, inventory and control charts consist of a condition-based maintenance (CBM) policy. Periodic preventive maintenance (PM) has not been considered in such models. The proposed integrated model is original, in that it links production through buffer stocks, quality through a control chart and maintenance through periodic preventive maintenance (different practical settings and modeling approach than when CBM is used). Hence, this paper addresses practical situations where, for economic or technical reasons, only systematic periodic preventive maintenance is possible.

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.

The purpose of this paper is to develop a bottleneck-based opportunistic maintenance (OM) model for the series production systems with the integration of the imperfect effect into maintenance activities.

On the analysis of availability and maintenance cost, preventive maintenance (PM) models subjected to imperfect maintenance for different equipment types are built. And then, a cost-saving function of OM is established to find out an optimal OM strategy, depending on whether the front-bottleneck machines adopt OM strategy or not. A numerical example is given to show how the proposed bottleneck-based OM model proceeded.

The simulation results indicate that the proposed model is better than the methods to maintain the machines separately and the policy to maintain all machines when bottleneck machine reaches its reliability threshold. Furthermore, the relationship between OM strategy and corresponding parameters is identified through sensitivity analysis.

In practical situations, the bottleneck machine always determines the throughput of the whole series production system. Whenever a PM activity is carried out on the bottleneck machine, there will be an opportunity to maintenance other machines. Under such circumstances, findings of this paper can be utilized for the determination of optimal OM policy with the objective of minimizing total maintenance cost of the system.

This paper presents a bottleneck-based OM optimization model with the integration of the imperfect effect as a new method to schedule maintenance activities for a series production system with buffers. Furthermore, to the best of the knowledge, this paper presents the first attempt to considering the bottleneck constraint on system capacity and diverse types of machines as a means to minimize the maintenance cost and ensure the system throughput.

This paper aims to develop a dynamic civil facility degradation prediction model to forecast the reliability performance tendency and remaining useful life under imperfect maintenance based on the inspection records and the maintenance actions.

A real-time hidden Markov chain (HMM) model is proposed in this paper to predict the reliability performance tendency and remaining useful life under imperfect maintenance based on rare failure events. The model assumes a Poisson arrival pattern for facility failure events occurrence. HMM is further adopted to establish the transmission probabilities among stages. Finally, the simulation inference is conducted using Particle filter (PF) to estimate the most probable model parameters. Water seals at the spillway hydraulic gate in a Taiwan's reservoir are used to examine the appropriateness of the approach.

The results of defect probabilities tendency from the real-time HMM model are highly consistent with the real defect trend pattern of civil facilities. The proposed facility degradation prediction model can provide the maintenance division with early warning of potential failure to establish a proper proactive maintenance plan, even under the condition of rare defects.

This model is a new method of civil facility degradation prediction under imperfect maintenance, even with rare failure events. It overcomes several limitations of classical failure pattern prediction approaches and can reliably simulate the occurrence of rare defects under imperfect maintenance and the effect of inspection reliability caused by human error. Based on the degradation trend pattern prediction, effective maintenance management plans can be practically implemented to minimize the frequency of the occurrence and the consequence of civil facility failures.

This paper aims to demonstrate how the five phases of design for six sigma approach as defined by define-measure-analyse-design-validate (DMADV) are adopted towards the development of an optoelectronic product to address the unexplored development issues related to micron-scale tolerances of internal diameters in plastic moulded parts. In addition, the structured product development approach is used to address the critical-to-quality (CTQ) characteristics that define the quality of the final product.

In line with DMADV, the presented methodology used various tools at each development stage to address key requirements of critical concern in the project. This included the ideal use of computer-aided design (CAD) simulation tool to identify CTQ parameters, failure mode effect analysis as a predictive tool to identify the major defects, while adopting root-cause-analysis to identify the fundamental causes of the major defects, design of experiment, and statistical analysis using Minitab Software for data-driven decision-making.

The two major defects that hindered the mass production of quality products were eliminated, and the overall development of the product significantly improved. Additionally, a quality control strategy approach was implemented to “lock in” the quality.

The case study presented develops and adopts a structured approach from DMADV with the key focus of addressing a micron-scale tolerance conflict between the design and manufacturing tolerance requirements of an optoelectronic product. The uniqueness of the case study is the adoption and application of CAD simulation at the Define phase of the DMADV process to address the CTQ issue of the product developed.