Imperfect Production Process Research Articles

Development of optimal production, inspection and maintenance strategies with positive inspection time and preventive maintenance error

Preventive maintenance is performed after the inspection point is reached given an imperfect production process that is in an under-control state. The time length required for inspection and preventive maintenance are generally assumes to be neglected by most of inspection and maintenance policy models. This paper evaluates an integrated model of economic production quantity and preventive maintenance to take into account positive time length for inspection, and identifies influence of production strategies for number of times inspections, first inspection interval, production lot size, expected cost for inspection time lengths and level of maintenance error. Moreover, numerical analysis is performed employed to examine and analyze the optimization of production strategies.

An optimal production run for an imperfect production process with allowable shortages and time-varying fraction defective rate

The effects of an imperfect production process on the optimal production run by assuming that an elapsed time until the process shift is exponentially distributed have been studied. This problem was extended by assuming that the elapsed time until the process shift is arbitrarily distributed. The models, however, do not allow for shortages. This work has been generalized by assuming that shortages were allowed. The common assumption of all the above-mentioned models is that a fixed percentage of defective items are produced during the out-of-control period. This assumption may not be applicable in many industrial situations. Intuitively, the percentage of defective rate should increase with an increase in the duration of the out-of-control period. In fact, other research has considered an imperfect production process model with a variable rate of defective units produced when the process is in an out-of-control state. The defective rate is assumed to be a function of detection delay. The main purpose of this paper is to further generalize earlier work by introducing a time-varying percentage defective rate. This paper develops a model to determine the optimal production run for a deteriorating production system, with allowable shortages, and time-varying fraction defective rate. However, the elapsed time until the production process shift is assumed to be exponentially distributed. A unique optimal production run is found that minimizes the total expected cost. A numerical example is provided to illustrate the application of the model and to prove the convexity of the total cost function. A sensitivity analysis is also conducted to study the effects of various model parameters on the optimal production run and the total cost.

Optimization of maintenance, production and inspection strategies while considering preventative maintenance error

This investigation explores the influence of preventive maintenance error on production, inspection and cost. This study assumes that, given an imperfect production process, if preventive maintenance is performed after the inspection point is reached given a production process that is in an in-control state, correctness of maintenance performance will directly impact the inspection frequency, inspection interval, production quantity and cost benefit. In this study, numerical analysis is used to examine the influence of different levels of maintenance error with various non-conforming product rates on inspection frequency, inspection interval, production quantity and cost benefit, to optimize maintenance error values under different circumstances.

Optimal buffer inventory and preventive maintenance for an imperfect production process

In this paper we present a model to determine the optimal length of continuous production periods between maintenance actions and the optimal buffer inventory to satisfy demand during preventive maintenance or repair of a manufacturing facility. We include in the model the possibility of imperfect production. We consider that the duration and cost of the maintenance action depend on the state of the production facility.

Optimal production run length and capital investment in quality improvement with an imperfect production process

The paper studies the effects of an imperfect production process on the optimal production run length when capital investment in process quality improvement is adopted. The mathematical model is derived to determine the optimal production run length and capital investment under the assumption of logarithmic investment function such that the total annual cost is minimized. In addition, an efficient algorithm is provided to find both the optimal production run length and the optimal process quality. Therefore, the optimal lot sizing and capital investment are appropriately determined. A numerical example is provided to illustrate the results and to assess the cost savings realized by adopting capital investment. Furthermore, some managerial implications are also included.

Optimal lot-sizing problem with imperfect maintenance and imperfect production

In this paper, we develop an integrated model for the joint determination of both economic production quantity and level of preventive maintenance (PM) for an imperfect production process. This process has a general deterioration distribution with increasing hazard rate. The effect of PM activities on the deterioration pattern of the process is modelled using the imperfect maintenance concept. In this concept, it is assumed that after performing PM, the ageing of the system is reduced in proportion to the PM level. After a period of time in production, the process may shift to out-of-control states, either type I or type II. A minimal repair will remove the type I out-of-control state. If a type II out-of-control state occurs, the production process has to stop, and then restoration work is carried out. Examples of Weibull shock models are given to show that the use of PM reduces costs.

An EOQ model with process reliability considerations

The classical economic order quantity (EOQ) model assumes that items produced are of perfect quality and that the unit cost of production is independent of demand. However, in realistic situations, product quality is never perfect, but is directly affected by the reliability of the production process. In this paper, we consider an EOQ model with imperfect production process and the unit production cost is directly related to process reliability and inversely related to the demand rate. In addition, a numerical example is given to illustrate the developed model. Sensitivity analysis is also performed and discussed.

Fuzzy opportunity cost for EOQ model with quality improvement investment

The cost of capital (i.e. opportunity cost) is one of the key factors that will influence the inventory and investment decisions. Previously, the classical EOQ model has been extended to include an imperfect production process and quality improvement investment, where the opportunity cost rate (interest rate or discounted rate) for evaluating the cost of capital investment is known with certainty. However, in some practical situations, the opportunity cost rate probably incurs disturbance due to the unstable environments. To capture this reality, this paper attempts to combine the statistical technique and fuzzy sets concept to deal with the unstable opportunity cost rate, so as to modify the aforementioned inventory/investment model. We derive the optimal lot size and the optimal process quality level in the fuzzy sense utilizing the logarithmic investment cost function. A numerical example is provided, and the results are compared with those obtained from a crisp opportunity cost rate model.

Integrated production-inventory models for imperfect production processes under inspection schedules☆

This paper deals with inventory models that unify the inventory problems of raw materials and finished products for a single product imperfect manufacturing system. The product is manufactured in batches, and raw materials are jointly replenished from outside suppliers. The system is assumed to deteriorate during the preduction process. As a result, some proportion of defective items is produced. The defective items are reworked at some cost either before or after a sale. Periodic inspections at equally spaced times and restorations of the production process are used to operate the system. The objective is to minimize the expected total cost for the system. A solution procedure is developed to find a near optimal solution for the basic model. The analysis is extended to various cases where the defect rate is a function of the setup cost, the proportion of defective items is not constant, or the inventory system has a limited capacity for raw materials.

Changing the values of parameters on lot size reorder point model

The Just-In-Time (JIT) philosophy has received a great deal of attention. Several actions such as improving quality, reducing setup cost and shortening lead time have been recognized as effective ways to achieve the underlying goal of JIT. This paper considers the partial backorders, lot size reorder point inventory system with an imperfect production process. The objective is to simultaneously optimize the lot size, reorder point, process quality, setup cost and lead time, constrained on a service level. We assume the explicit distributional form of lead time demand is unknown but the mean and standard deviation are given. The minimax distribution free approach is utilized to solve the problem and a numerical example is provided to illustrate the results. .

Optimal lot-sizing, quality improvement and inspection errors for multistage production systems

We develop multistage lot-sizing models for imperfect production processes. The effect of inspection errors in screening non-conforming items at various stages has been incorporated. Inspection and restorstion of the processes at all stages have also been considered. Numerical examples are presented to illustrate various aspects of the models developed. It is shown that when inspection and restoration are introduced, lower costs are incurred and larger lot sizes are produced because of reductions in quality control costs.

Determining the optimal production–maintenance policy with inspection errors: using a Markov chain

Lee and Park examine the effects of an imperfect production process on the optimal production-inventory policy. They consider an imperfect production process which can go out of control after an exponentially distributed production time and then produce some proportion of defective items. The defective item cost is equivalent to the reworking cost and the warranty cost. Some maintenance-inspection mechanisms are introduced to monitor and restore the process to enhance process reliability and thereby lower the number of defective items produced. However, in many situations, a deteriorating production system possesses an increasing failure rate. In general, such a process will not be as good as new after maintenance but will be younger than its real age. Besides, Lee and Park did not investigate the possibility of imperfect inspection based on consideration of type I and type II errors. In this paper, we consider the effects of general time to shift distributions, two types of process inspection errors and general repair policy on the optimal production/inspection/maintenance policy. A mathematical model representing the expected average cost is developed using a Markov chain to jointly determine the production cycle, process inspection intervals, and maintenance level. An optimal production/inspection/maintenance policy is determined by minimizing the expected average cost. A numerical example is given to illustrate the use of the method. Based on this proposed Markov structure model, some process-related assumptions such as maintenance that can cause the system to go out of control and that the random results of general repairs can also be easily relaxed, and they are described in the section of model extensions. An extended production–maintenance model for a deteriorating production system is established. Scope and purpose There are numerous production situations which may cause a production facility to shift from an “in-control” state to an “out-of-control” state due to aging of equipment. Once the process shifts to an “out-of-control” state, an increased number of defective items will be produced until a maintenance–inspection is performed to return the process to an “in-control” state. To reduce the risk that a shift to an out of control state will occur, lot sizing, periodic inspection and maintenance of the process are needed. These tasks also enhance the economical operation of the system. In this study, we investigate a production/inspection/maintenance model under the assumptions that the production process is subject to random deterioration, and that the process can be monitored through inspections, so that the lot size, inspections and maintenance policy are subject to control. Uncertainty probabilities associated with inspections are also considered, i.e., inspection is assumed to be imperfect. Our objective is to determine the optimal production/inspection/maintenance policy under the effect of process inspection errors. A mathematical model which presents the expected average cost is developed. An optimal production/inspection/maintenance policy is found by minimizing the expected average cost. Since this problem arises in many practical situations, the results may be helpful to production managers in developing approaches to control production systems economically.

Economic lot scheduling problem with imperfect production processes and setup times

Deteriorating production processes are common in reality. Although every production process starts in an ‘in-control’ state to produce items of acceptable quality, it may shift to an ‘out-of-control’ state, owing to ageing, at any random time and produce defective items. In the present article, we study the Economic Lot Scheduling Problem (ELSP) with imperfect production processes having significant changeovers between the products. The mathematical models are developed for the ELSP using both the common cycle approach and the time-varying lot sizes approach, taking into account the effects of imperfect quality and process restoration. Numerical examples are cited to illustrate the solution procedures and to compare the performances of the solution methodologies adopted to solve the ELSP.

Quality improvement, setup cost and lead-time reductions in lot size reorder point models with an imperfect production process

This paper investigates the lot size, reorder point inventory model involving variable lead time with partial backorders, where the production process is imperfect. The options of investing in process quality improvement and setup cost reduction are included, and lead time can be shortened at an extra crashing cost. The objective is to simultaneously optimize the lot size, the reorder point, the process quality, the setup cost, and the lead time. We first assume that lead-time demand follows a normal distribution and develop an algorithm to find the optimal solution. Then, we relax the assumption of normality to consider a distribution-free case where only the mean and standard deviation of lead-time demand are known. We apply the minimax distribution-free procedure to solve this problem. Furthermore, two numerical examples are given to illustrate the results. Scope and purpose In past two decades, the Japanese successful experience of using just-in-time (JIT) production has received a great deal of attention. The underlying goal of JIT is to eliminate waste, which can be achieved through various efforts, such as shortening lead time, reducing setup cost, and improving quality. In a recent paper, Moon and Choi (Comput. Oper. Res. 25 (1998) 1007) studied the lead time reduction problem on a lot size, reorder point (continuous review ( Q, r)) inventory model in which the quality issue is ignored and the setup cost is fixed. In this article, we extend Moon and Choi's model to include the possible relationship between quality and lot size. We also investigate the joint effects of quality improvement and setup cost reduction in which the lot size, reorder point, process quality, setup cost, and lead time are decision variables.

The economic production lot-sizing problem with imperfect production processes and imperfect maintenance

This paper deals with an integrated model for the joint determination of economic production quantity and preventive maintenance (PM) level for an imperfect process having a general deterioration distribution with increasing hazard rate. The effect of PM activities on the deterioration pattern of the process is modeled using the imperfect maintenance concept. It is assumed that, after each PM, the age of the system is reduced proportional to the PM level. A numerical example is used to illustrate the effect of PM level on the cost of nonconforming items and restoration cost due to shift to the out-of-control state. It is found that performing PM will yield reductions in quality related costs. It is more economical to perform PM when the extra PM cost is compensated for by the reduction in quality related costs.

An optimal production run time with imperfect production processes and allowable shortages

This paper develops a model to determine an optimal run time for a deteriorating production system under allowable shortage. It is assumed that the elapsed time until the production process shift is arbitrarily distributed. We show that there exists a unique optimal production run time to minimize the total relevant cost function. Finally, bounds for the optimal production run time are provided to develop the solution procedure. Scope and purpose Rosenblatt and Lee [IIE Trans. 18 (1986) 48] study the effects of an imperfect production process on the optimal production run time assuming that an elapsed time until shift is exponentially distributed. Furthermore, Kim and Hong [Int. J. Prod. Econ. 58 (1999) 183] extend the problem of Rosenblatt and Lee by assuming that elapsed time until the process shift is arbitrarily distributed. Basically, their models do not allow for shortage. Consequently, the main purpose of this paper is to generalize Kim and Hong to assume that the shortage is allowed.

Economic Lot Scheduling Problem with Imperfect Production Processes

Economic Lot Scheduling Problem with Imperfect Production Processes

Economic lot scheduling problem with imperfect production processes

In this paper, we model the effects of imperfect production processes on the economic lot scheduling problem (ELSP). It is assumed that the production facility starts in the in-control state producing items of high or perfect quality. However the facility may deteriorate with time and shifts at a random time to an out of control state and begins to produce nonconforming items. A mathematical model is developed for ELSP taking into account the effect of imperfect quality and process restoration. Numerical examples are presented to illustrate important issues related to the developed model.

Quality improvement on lot size reorder point model with partial backorders based on limited information of demand

This paper considers a modified lot size reorder point model with imperfect production process, where the unsatisfied demand is assumed to be a mixture of backorders and lost sales. It investigates the effects of investing in process quality improvement on the model. Specifically, we discuss the case where only partial information of lead time demand is known, and solve the problem by applying the minimax distribution free approach. An algorithm procedure is established to obtain the optimal lot size, reorder point and process quality level. Numerical examples are provided to illustrate the results derived.

Impact of investing in quality improvement on (Q, r, L) model involving the imperfect production process

This paper investigates the impact of quality improvement on the modified lot size reorder point models involving variable lead time and partial backorders. The formulated models include the imperfect production process and an investing option of improving the process quality. The objective is simultaneously optimizing the lot size, reorder point, process quality level and lead time. We first assume that the lead time demand follows a normal distribution, then relax this assumption to consider the distribution-free case where only the mean and standard deviation of lead time demand are known. An algorithm procedure of finding the optimal solution is developed, and two numerical examples are given to illustrate the results.