Optimal production run length with imperfect production processes and backorder in fuzzy random environment

This article considers the economic production run time problem with imperfect production processes and allowable shortages. The elapsed time until the production process shifts is assumed to be a fuzzy random variable, and fuzzy random total cost per unit time model is constructed. The expectation theory and signed distance are employed to transform the fuzzy random model into crisp model. An effective approximate algorithm is developed to search for the optimal production run length. Furthermore, numerical examples are provided to illustrate the results of proposed model.     

An optimal production lot-sizing problem for an imperfect process with imperfect maintenance and inspection time length

This article develops an integrated model in considering the situations of an imperfect process with imperfect maintenance and inspection time for the joint determination of both economic production quantity (EPQ) and preventive maintenance (PM). This imperfect process has a general deterioration distribution with increasing hazard rate. Even with periodic PM, such a production system cannot be recovered as good as new. This means that the system condition depends on how long it runs. Also, the PM level can be distinct due to the maintenance cost. For convenience, it is assumed the age of system is reduced in proportional to the PM level. Further, during a production cycle, we need an inspection to see if the process is in control. This inspection might demand a considerable amount of time. In this article, we take PM level and inspection time into consideration to optimise EPQ with two types of out-of-control states. To see how the method works, we use a Weibull shock model to show the optimal solutions for the least costs.     

Optimal production run length in deteriorating production processes with fuzzy elapsed time

This paper investigates the optimal production run length in deteriorating production processes, where the elapsed time until the production process shifts is characterized as a fuzzy variable, also the setup cost and the holding cost are characterized as fuzzy variables, respectively. A mathematical formula representing the expected average cost per unit time is derived, and some properties are obtained to establish an efficient solution procedure. Since there is no closed-form expression for the optimal production run length, an approximate solving approach is presented. Finally, two numerical examples are given to illustrate the procedure of searching the optimal solutions.     

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.     

Optimal decision rules for determining the length of the production run

During the production period in some industrial processes, the process mean is shifted owing to the occurrence of an assignable cause. In other situations, simultaneous changes in process mean and process variance are experienced as time passes. When the changes are time dependent, the process mean and the process variance drift steadily as time goes on, and subsequently drive the process into an out-of-control state. Thus, at any point in the, a total change in product quality may result from drift or shift or both. This paper describes how to determine the optimal production run for a process under such conditions. The process is in control at the beginning of the production run and is shut down at the end for resetting. It is assumed that the process is subject to drift and/or shift. A cost function is developed that consists of the cost of resetting the process, the cost of rejected items, the lost product cost due to shutdown and the sampling cost. Optimal production run is determined by minimizing the cost function. A search algorithm as well as a graphical method are employed to locate the optimum solution.     

Lot sizing for an imperfect production process with quality corrective interruptions and improvements, and reduction in setups

The just-in-time (JIT) management philosophy advocates the elimination of waste or activities that add cost and not value to the product. Eliminating waste in the production process could be attained through smaller batch (lot) sizes and reduction of in-process inventory, where concepts such as setup reduction and increased quality are fundamental. In a JIT environment workers are authorized to stop production if a quality or a production problem arises, e.g., the production process going out-of-control. In such a case, the production process is interrupted for quality maintenance to bring the process in control again. This paper investigates the lot sizing problem for reduction in setups, with reworks, and interruptions to restore process quality. This paper assumes the rate of generating defects to benefit from any changes for eliminating the defects, and thus reduces with each quality restoration action. A mathematical model is developed and numerical examples are provided with results discussed.     

Inventory models for imperfect production and inspection processes with various inspection options under one-time and continuous improvement investment

This study investigates both internal and external effects of defective production and delivery from imperfect production and inspection processes in a stable production and inventory system, and subsequent defective returns and dispositions. We first develop profit-maximizing imperfect-quality inventory models for various inspection options (sampling inspection, entire lot screening, and no inspection) under one-time improvement investment in production and inspection reliability. We then present the models under continuous improvement (CI) investments over multiple periods, which have not been explored before. In a CI environment, we further propose an inspection alternative of changing an inspection option from entire lot screening to no inspection and vice versa. We develop an algorithm for finding the optimal inspection policy yielding a superior profit, among inspection option change between entire lot screening and no inspection and those without option change. Based on the analytical models along with numerical and simulation analyses, we provide important managerial implications to practicing managers and future research directions.     

Optimal lot sizing with maintenance actions and imperfect production processes

Porteus (1986) explored an economic order quantity model with imperfect production processes that the approximate lot size is derived. Basically, he dealt with the lot size problem is rather meaningful. However, for mathematical simplicity, he adopted a truncated Taylor series expansion to present the approximate expected total cost function that results in overvalue of expected total cost. In this paper, we extend Porteus (1986) to present the optimal lot size model for defective items with a constant probability when the system is out-of-control and taking the maintenance cost into account. We show that there exists a unique optimal lot size such that the expected total cost is minimised. In addition, the bounds of optimal lot size are provided to develop the solution procedure. Finally, numerical examples are given to illustrate the theoretical results and compare optimal solutions obtained by using our approach and Porteus's approach. Numerical results show that our approach is better.     

Economic production quantity (EPQ) models under an imperfect production process with shortages backordered

In this paper, we develop economic production quantity (EPQ) models to determine the optimal production lot size and backorder quantity for a manufacturer under an imperfect production process. The imperfect production process is characterised by the fraction of defective items at the time of production γ. The paper considers different cases of the EPQ model depending on (1) whether γ is known with certainty or is a random variable, and (2) whether imperfect items are drawn from inventory (a) as they are detected, (b) at the end of each production period or (c) at the end of each production cycle. Straightforward convexity results are shown and closed-form solutions are provided for the optimal order and backorder quantities for each of the cases we considered. We provide two numerical examples: one in which the defective probability follows a uniform distribution and the second which we assume follows a beta distribution, to illustrate the effects of yield variability and timing of the withdrawal of defectives on the optimal solutions. We obtain similar results for both numerical examples, which show that both the yield variability and the withdrawal timing are not critical factors.     

A two-warehouse inventory model with imperfect quality production processes

One of the weaknesses of some production-inventory models is the unrealistic assumption that all items produced are of good quality. But production of defective units is a natural phenomenon in a production process. Defective items should be treated as a result of imperfect quality production. On the other hand, the classical inventory models usually assume the available warehouse has unlimited capacity. In many practical situations, there exist many factors like temporary price discounts making retailers buy a capacity of goods exceeding their own warehouse. In this case, retailers may rent other warehouses for the need of business. A lot of researchers studied inventory models with two warehouses and inventory models with imperfect quality separately. Compared with previous models, based on Salameh and Jaber [Salameh, M. K., Jaber, M. Y. (2000). Economic production quantity model for items with imperfect quality. International Journal of Production Economics, 64, 59–64.], this paper tries to incorporate the above concepts to establish a new inventory model with two warehouses and imperfect quality simultaneously. The mathematical model by maximizing the annual total profit and the solution procedure are developed and numerical examples are provided to illustrate them.     

Mining association rules for the quality improvement of the production process

Academics and practitioners have a common interest in the continuing development of methods and computer applications that support or perform knowledge-intensive engineering tasks. Operations management dysfunctions and lost production time are problems of enormous magnitude that impact the performance and quality of industrial systems as well as their cost of production. Association rule mining is a data mining technique used to find out useful and invaluable information from huge databases. This work develops a better conceptual base for improving the application of association rule mining methods to extract knowledge on operations and information management. The emphasis of the paper is on the improvement of the operations processes. The application example details an industrial experiment in which association rule mining is used to analyze the manufacturing process of a fully integrated provider of drilling products. The study reports some new interesting results with data mining and knowledge discovery techniques applied to a drill production process. Experiment’s results on real-life data sets show that the proposed approach is useful in finding effective knowledge associated to dysfunctions causes.     

Optimal run lengths in deteriorating production processes in random fuzzy environments

This paper presents a random fuzzy economic manufacturing quantity (EMQ) model in a deteriorating process. It is assumed that the setup cost and the average holding cost are characterized as fuzzy variables and the elapsed time until shift is a random fuzzy variable. As a function of these parameters, the average total cost is also a random fuzzy variable, and the unimodality of its expected value is studied. To obtain the optimal run length and the minimum average cost, simultaneous perturbation stochastic approximation (SPSA) algorithm based on random fuzzy simulation is provided. Random fuzzy EMQ models with fuzzy deterioration, fuzzy linear deterioration and fuzzy exponential deterioration are presented, respectively. These models can be solved by the proposed algorithm. Numerical examples are presented in the end.     

Quasi-optimal integrated production, inventory and maintenance policies for a single-vendor single-buyer system with imperfect production process

In this paper we deal with the integrated supply chain management problem in the context of a single vendor-single buyer system for which the production unit is assumed to randomly shift from an in-control to an out-of-control state. At the end of each production cycle, a corrective or preventive maintenance action is performed, depending on the state of the production unit, and a new setup is carried out. Two different integrated production, shipment and maintenance strategies are proposed to satisfy the buyer’s demand at minimum total cost. The first one suggests that the buyer orders batches of size nQ and the vendor produces nQ and makes equal shipments of size Q. The second policy proposes that to satisfy the same ordered quantity, the vendor produces separately smaller batches of size Q, n times. The total integrated average cost per time unit corresponding to each strategy is considered as the performance criterion allowing choosing the best policy for any given situation.     

Optimal pricing, lot-sizing and marketing planning in a capacitated and imperfect production system

In the classical economic production quantity (EPQ) problem demand is considered to be known in advance. However, in the real-world, demand of a product is a function of factors such as product’s price, its quality, and marketing expenditures for promoting the product. Quality level of the product and specifications of the adopted manufacturing process also affect the unit product’s cost. Therefore, in this paper we consider a profit maximizing firm who wants to jointly determine the optimal lot-sizing, pricing, and marketing decisions along with manufacturing requirements in terms of flexibility and reliability of the process. Geometric programming (GP) technique is proposed to address the resulting nonlinear optimization problem. Using recent advances in optimization techniques we are able to optimally solve the developed, highly nonlinear, mathematical model. Finally, using numerical examples, we illustrate the solution approach and analyze the solution under different conditions.     

Joint quality control and preventive maintenance strategy for imperfect production processes

In this paper, we develop a joint quality control and preventive maintenance policy for a production system producing conforming and nonconforming units. The considered system consists of one machine which must supply another production line operating on a just-in-time basis. Each lot produced by the machine is subject to a quality control. According to the proportion l of nonconforming units observed and compared to a threshold value l _m , one decides to undertake or not maintenance actions on the system. In order to palliate perturbations caused by the stopping of the machine for preventive and corrective maintenance actions of random durations, a buffer stock h is built up to ensure the continuous supply of the subsequent production line. The proposed strategy is modelled using simulation and experimental design. This approach allows to generate a second order response surface allowing to easily determine the optimal rate, l_m^*{l_{m}^*}, of nonconforming units on the basis of which preventive maintenance actions should be performed, and the optimal size, h*, of the buffer stock to be built. These values minimize the total cost per time unit which includes the costs related to maintenance, quality and inventory.     

A volume flexible economic production lot-sizing problem with imperfect quality and random machine failure in fuzzy-stochastic environment

An “economic production lot size” (EPLS) model for an item with imperfect quality is developed by considering random machine failure. Breakdown of the manufacturing machines is taken into account by considering its failure rate to be random (continuous). The production rate is treated as a decision variable. It is assumed that some defective units are produced during the production process. Machine breakdown resulting in idle time of the respective machine which leads to additional cost for loss of manpower is taken into account. It is assumed that the production of the imperfect quality units is a random variable and all these units are treated as scrap items that are completely wasted. The models have been formulated as profit maximization problems in stochastic and fuzzy-stochastic environments by considering some inventory parameters as imprecise in nature. In a fuzzy-stochastic environment, using interval arithmetic technique, the interval objective function has been transformed into an equivalent deterministic multi-objective problem. Finally, multi-objective problem is solved by Global Criteria Method (GCM). Stochastic and fuzzy-stochastic problems and their significant features are illustrated by numerical examples. Using the result of the stochastic model, sensitivity of the nearer optimal solution due to changes of some key parameters are analysed.     

Joint production and maintenance strategy for economic production quantity model with imperfect production processes

In this study, an economic production quantity (EPQ) model is generalized by considering maintenance and production programs for an imperfect process involving a deteriorating production system with increasing hazard rate. There are two types of preventive maintenance (PM), namely imperfect PM and perfect PM. The probability that perfect PM is performed depends on the number of imperfect maintenance operations performed since the last renewal cycle. Following a failure, the delayed repair performs some restorations and reduces production rate to restore the system into an operating state (in-control state), but leaves its lower production rate until perfect PM is performed. That is, the production run period not always starts in normal production rate. This study considers backorders, as well as loss of inventory due to the lower production rate. For the EPQ model, the optimum run time, which minimizes the total cost, is discussed. Various special cases are considered, including the maintenance learning effect. Finally, a numerical example is presented to illustrate the effects of PM ability, repair cost and production decreasing rate on total costs and production period.     

Optimal buffer allocation of serial production lines with quality inspection machines

Using Taylor series expansion and probability generating function technique, we present an approximation method for the analysis of the average steady state throughput of serial production lines with unreliable machines, finite buffers and quality inspection machines. Employing the approximation method, we propose an analytic method for the optimal buffer allocation to achieve a desired throughput. The proposed methods are validated by computer simulations.     

Simulation of partially observed Markov decision process and dynamic quality improvement

Computer simulation is used to compare three quality policies. The first policy is ‘do-nothing’. The second is an appraisal policy. The third policy includes prevention that leads to process quality improvement. The simulation model is based on a Partially Observed Markov Decision Process (POMDP). The unobserved states of the process depend on the failure rate, λ. The observed process output is the number of conforming and nonconforming products. The process performance is measured by quality costs per unit. The simulation language used is SLAM II. The power of using computer simulation to model the dynamics of process quality improvement is discussed.     

A mathematical model on EPQ for stochastic demand in an imperfect production system

In the paper, we develop an EPQ (economic production quantity) inventory model to determine the optimal buffer inventory for stochastic demand in the market during preventive maintenance or repair of a manufacturing facility with an EPQ (economic production quantity) model in an imperfect production system. Preventive maintenance, an essential element of the just-in-time structure, may cause shortage which is reduced by buffer inventory. The products are sold with the free minimal repair warranty (FRW) policy. The production system may undergo “out-of-control” state from “in-control” state, after a certain time that follows a probability density function. The defective (non-conforming) items in “in-control” or “out-of-control” state are reworked at a cost just after the regular production time. Finally, an expected cost function regarding the inventory cost, unit production cost, preventive maintenance cost and shortage cost is minimized analytically. We develop another case where the buffer inventory as well as the production rate are decision variables and the expected unit cost considering the above cost functions is optimized also. The numerical examples are provided to illustrate the behaviour and application of the model. Sensitivity analysis of the model with respect to key parameters of the system is carried out.