Determining the optimal lot size for the finite production model with random defective rate,the rework process,and backlogging

This paper considers the effects of the reworking of defective items on the economic production quantity (EPQ) model with backlogging allowed. The classic EPQ model assumes that manufacturing facility functions perfectly during a production run. However, due to process deterioration or other factors, the production process may shift and produce imperfect quality items. In this study, a random defective rate is considered, and when regular production ends, the reworking of defective items starts immediately. Not all of the defective items are reworked, a portion of them are scrap and are discarded. Repairing and holding cost per reworked item and disposal cost per scrap item are included in the proposed mathematical modelling and analysis. The renewal reward theorem is utilized to deal with the variable cycle length, and the optimal lot size that minimizes the overall costs for the imperfect quality EPQ model is derived where backorders are permitted.     

DETERMINATION OF THE OPTIMAL PROCESS MEAN WHEN INSPECTION IS BASED ON A CORRELATED VARIABLE

Consider a production process where items are produced continuously. A lower limit is specified for the quality characteristic of interest, and an item is defective if its value of the quality characteristic is smaller than the specification limit. The process mean (target value) may be set higher to reduce the costs incurred by producing defective items. Using a higher process mean, however, results in a higher production cost when production cost is an increasing function of the quality characteristic. An inspection procedure is used to screen outgoing items from the defective ones. In this paper, we consider a situation where inspection is based on a surrogate variable instead of the quality characteristic of interest. A model is developed to jointly determine the most economical process mean and the inspection specification limit.     

Economic production order quantity and quality

The purpose of this study is to integrate a conventional production-inventory management approach and a process-quality design approach so as to promote quality and reduce costs. Because the integration of these two approaches into a single system is conducted under the influence of a deterioration process, estimated costs of production must be modified. Only then can these various costs be presented as a total cost for the present integrated system. This total cost includes: a setup cost for production reordering and process resetting, quality-related costs stemming from the loss of product quality along with a tolerance-related production process cost and a failure cost for product defects, backorder costs for production shortage, carrying costs generated by the storing and handling of inventory, and material costs for determining the process mean. The Taguchi quality loss function is introduced to assess quality loss in the system. The decision variables include the initial setting (process mean), process tolerance, and production order quantity. These variables need to be determined simultaneously to minimise the average total cost for a cycle time. An example is presented to demonstrate the proposed approach.     

Economic design of an attributes control system for a multistage serial production process

A model for the economic design of an np-control system integrated within a multiple stage serial production process is presented. The total expected quality control cost includes the costs of sampling, the costs of investigating an out-of-control alarm and possibly correcting an assignable cause(s), and the costs associated with the production of non-conforming items. The model is represented as a directed network with decision variables of sample size, rejection number and frequency of sampling occurring at each stage of the process. A combination of dynamic programming and direct search techniques is applied to determine the set of sampling policies which yield minimum total expected cost. Numerical examples and results of a sensitivity analysis are reported.     

Integrated production quality and condition-based maintenance optimisation for a stochastically deteriorating manufacturing system

This paper investigates the problem of optimally integrating production quality and condition-based maintenance in a stochastically deteriorating single- product, single-machine production system. Inspections are periodically performed on the system to assess its actual degradation status. The system is considered to be in ‘fail mode’ whenever its degradation level exceeds a predetermined threshold. The proportion of non-conforming items, those that are produced during the time interval where the degradation is beyond the specification threshold, are replaced either via overtime production or spot market purchases. To optimise preventive maintenance costs and at the same time reduce production of non-conforming items, the degradation of the system must be optimally monitored so that preventive maintenance is carried out at appropriate time intervals. In this paper, an integrated optimisation model is developed to determine the optimal inspection cycle and the degradation threshold level, beyond which preventive maintenance should be carried out, while minimising the sum of inspection and maintenance costs, in addition to the production of non-conforming items and inventory costs. An expression for the total expected cost rate over an infinite time horizon is developed and solution method for the resulting model is discussed. Numerical experiments are provided to illustrate the proposed approach.     

Product warranty and quality control

When a product is sold with a warranty, the manufacturer incurs additional costs in the form of warranty servicing costs. Owing to quality variations in manufacturing, some of the items produced do not meet the design specification and are labelled as defective (or non-conforming) items. The warranty servicing costs for such items are high and can be reduced through a weeding process. This paper deals with life testing as a means to weed out defective items being released, and examines the optimal testing period for three different types of warranties.     

Stochastic assessment considering process variation for impact of welding shrinkage on cost of ship production

Since ship hull blocks are constructed by assembling numerous intermediate parts, relatively small changes in their dimensions can easily accumulate to cause serious reworking during the block erection stage, as well as deteriorate the productivity in ship production industry. One of the major dimensional accuracy control activities in shipbuilding is shrinkage margin design, by which an optimal length of excess edge is assigned to plates, in order to compensate for welding shrinkage and thus minimise reworking due to shrinkage. This paper presents a stochastic methodology for a quantitative assessment procedure of welding shrinkage on production cost in shipbuilding. This reworking cost evaluation procedure includes not only the prediction of a nominal shrinkage profile, but also a statistical cost estimation process for shrinkage variation. The formulation to predict total rework cost is suggested to be a combination of nominal shrinkage profile, process variation and quality loss functions for each rework region. Also, this approach investigates the relationship between the shrinkage margin and the predicted rework cost, in case of different process variations for a 15?m?×?15?m ship block model. It also presents an optimal shrinkage margin calculation procedure for ship designers in order to minimise the impact of dimensional variation due to welding shrinkage, on productivity.     

Dynamic Programming Analysis of Special Multi-Stage Inspection Systems

A branch-compression dynamic programming approach is developed to investigate the degree of repeated inspection resulting in minimal expected quality control cost in a special class of nonserial production processes. The total cost includes inspection and reworking costs at each stage of the process, plus a penalty cost due to defective product which is not detected by the inspection scheme.     

An integrated EPQ model based on a control chart for an imperfect production process

The notion of quality control is introduced into the classic economic production quantity (EPQ) model. Based on previous research, this paper contributes to an integrated EPQ model combining the concepts of statistical process control and maintenance. An imperfect production process involving three different conditions is considered. A control chart is adopted to monitor the whole process with Taguchi's loss function estimating the quality cost of each condition. A corresponding maintenance policy is planned for the machine depending on what condition it runs in. Thus the proposed EPQ model takes quality-related costs and maintenance-related costs into account other than storage costs and ordering costs already considered in the classic model. The objective of this model is to minimise the total expected production cost per production cycle while simultaneously determining the optimal parameters of control chart design, the interval between sampling, the sample size and the maintenance decision policy. The pattern search method is used to solve the problem using the MATLAB toolbox. In addition, a case study, sensitivity analysis and comparison analysis are presented to demonstrate the application of the model.     

Optimal economic production quantity policy for a parallel system with repair,rework, free-repair warranty and maintenance

Hot standby redundancy maintains the working order of a system, repairs offer restoration in case of failure, and preventive maintenance (PM) prevents trouble. Warranties provide assurance to customers, and a superior warranty signifies higher product quality. The running costs of redundancy, maintenance and warranties influence decisions during product manufacture. Therefore, this paper presents an economic production quantity (EPQ) model for a parallel system with maintenance, production, and free-repair warranty (FRW) programmes. The production system begins with a basic unit and produces conforming items. PM is performed after the production run period and is classified as imperfect or perfect. If the basic unit fails, it is repaired and returned to operation after perfect PM; the spare unit is online only during the repair time of the basic unit. The spare will produce some number of defective goods, which are reworked in the same inventory cycle. The hot spare is minimally repaired if it fails in its standby or online mode. In this study, an inferior item is defined as one that satisfies specifications on inspection and is usable but is likely to incur postsale servicing costs when sold under an FRW. The total cost of this EPQ model includes setup, holding, PM, restoration, minimal repair, and warranty costs. The optimal production runtime is determined by minimising the total cost. Several cases are discussed in this paper, and the proposed model is illustrated using a numerical example and sensitivity.     

Impacts of collaborative investment and inspection policies on the integrated inventory model with defective items

For an imperfect production system, to reduce quality-related costs, a manager may consider investing capital in quality improvement. In general, the investment expense in reducing the defective rate of items is often paid by the vendor. On the other hand, the buyer may inspect the product quality as the order is received which implies it incurs an inspection cost. In a supply chain integrated system, to accomplish global optimisation, the vendor and buyer can agree to jointly invest capital to improve the imperfect production processes, and the buyer can remove the inspection programme as the defective rate reaches a certain low-level. Hence, this paper investigates the impacts of collaborative investment and inspection policies on an integrated inventory model with defective items. The objective of this study is to seek the optimal order quantity, shipping times from the vendor to the buyer per production run, and the defective rate that minimise the joint total cost per unit time. An algorithm is developed to find the optimal solution. Several numerical examples are presented to demonstrate the proposed model and solution procedure, and then several management insights are obtained from the numerical examples.     

Minimizing Cost of Multiple Response Systems by Probabilistic Robust Design

In the design of products and processes, a methodology that helps adjust the means and tolerances of the design variables to both improve conformance and lower costs is a valuable tool. In this paper, the cost of a product at the manufacturing stage is the sum of the production cost, which includes known costs for tolerances, inspection, and so forth, plus any cost for scrapping or reworking products that do not conform to specifications. We call this added cost the so-called loss-of-quality cost and evaluate it as the probability of nonconformance (of the responses) times established scrap or rework costs. Accurate probability estimates are obtained using full distributions, limit-state functions, and first-order reliability methods (FORM). Probabilities are adjusted through probabilistic robust design. The production costs and the loss-of-quality cost are competing costs and thus their sum provides a single objective function in terms of the means and tolerances of the design variables. The need to satisfy the equations in both the product model and the workings of FORM introduce nonlinear equality constraints. The minimum of the objective function, hence the minimum cost, is obtained by solving a nonlinear, constrained, optimization problem. The design of a mechanism for controlling a grating diffraction spectroscope serves as a case study using the presented method. A minimum cost, the probability of conformance, and the respective parameter settings are found for both complete and zero inspection strategies.     

Economic development of specifications for 100% inspection based on asymmetric quality loss functions

As a means of providing protection for both the producer and the consumer, for example as in airport security, 100% inspection plays an important role in today's environment. The same is true for some industrial or other decision-making processes where the consequences of excessive deviations from target values are very high. Motivated by Deming's “all or none” inspection rule and associated philosophy for quality improvement, we develop an inspection strategy by considering the costs to both the producer and the customer, and thus to the whole system. A general optimization model is formulated to determine whether 100% inspection is to be performed or no inspection to be performed. If complete inspection is chosen then the optimal specification limits can be determined at the same time. Specifically, we consider two types of asymmetric quality loss functions for the “target the best” quality characteristic: the asymmetric quadratic quality loss function, and the asymmetric piecewise linear loss function. For each loss function, we propose an optimization model to determine the optimal process mean and specification limits. Numerical examples are given to illustrate the proposed models that can be used to improve the quality of the output of any process.     

An economic model for raw material selection

An economic model for raw material selection is presented and a case analysis is given. The model considers two decision factors: initial raw material cost and additional manufacturing costs incurred due to inappropriateness of raw material quality. This additional manufacturing cost may include items such as: extra operator cost, extra machine cost and extra quality cost.     

Economic production quantity (EPQ) model with partial backordering and a discount for imperfect quality batches

Economic production quantity (EPQ) models are traditionally used in operations management. Despite the large number of papers that describe the models, the classic EPQ model does not consider either imperfect quality batches or shortages. However, some industries may be able to sell imperfect items for a lower price, reducing the total production cost. This paper proposes an EPQ model with partial backordering and discount for imperfect quality batches and an algorithm that returns optimal values for the problem. From a numerical example, it is possible to analyse how the changes in the variables affect each part of the total cost function, which provides a useful tool for strategic decision-making. We conclude that it is better to sell imperfect items as soon as possible because the savings in holding costs results in a total cost reduction. It is more profitable for the producer to have planned shortages considering that some costumers are willing to wait. Furthermore, the reduction of the goodwill cost does not necessarily reduce the total cost.     

Economic selection of sub-process mean values for a mixture production process

The problem of determining the most profitable sub-process means is considered for a production process where multiple ingredients are mixed. The quantities of the ingredients are controlled through the corresponding sub-processes. The values of the sub-process means directly affect the fraction defective and the costs of production, reworking, and scrap of the mixture process. Every item accepted through screening inspection is sold to a regular market at a fixed price, and any rejected item is scrapped. It is assumed that the quantities of the multiple ingredients are normally distributed with known variances. An economic model is constructed, which involves the selling price, production costs, inspection cost, and scrap and reprocessing costs. The goal is to determine the optimum sub-process mean values maximizing expected profit function. A solution procedure is provided, and an illustrative example for the case with two main ingredients is given.     

Economic evaluation of disassembly processes in remanufacturing systems

A model to deal with the disassembly processes in remanufacturing systems is presented with focus being on evaluating their economic consequences. More specifically, the model assists decisions such as to which degree and for the sake of which components should the returned items be disassembled. Consequently, using the economic values of recoverable items, the inventory holding costs of these items are obtained. This information is further used to determine the inventory control policy. To access such economic values, the above average cost approach is compared with the net present value method. The latter is often considered a more?‘correct’?way in remanufacturing systems from the viewpoint of inventory control. The results from the economic evaluation model are intended to aid companies in systematically evaluating current as well as projected remanufacturing systems.     

Economic Design And Control of Monitoring Mechanisms in Automated Production Systems

Monitoring production processes to assure product quality has been a major managerial and control problem. These processes are subject to shifts to “out-of-control” states, resulting in the production of defective items. Inspection as well as restoration capabilities are necessary to provide early detection and correction of these shifts in the process. This paper considers the costs of different policies for providing these detection and restoration capabilities. These policies amount to periodic or continuous inspection of the production process with perfect information, and continuous or periodic availability of maintenance facilities. The optimal operation of each policy is studied. Comparative analyses are conducted with different specifications of key parameters such as the rate of shift of the process and the cost of producing defective items. These analyses enable the derivation of the optimal policy when only ranges of the values of these parameters are known.     

Cutting optimization with variable-sized stock and inventory status data

Many production environments require economical cutting of one-dimensional items according to bills of materials from objects of several standard lengths. However, even with optimized cutting substantial trim loss may occur. This trim loss should not be regarded as waste. It is returned to store and can be reused in future optimizations. Optimization of packing linear items into standard lengths is presented for items that cannot be packed into available lengths from inventory status data. The core of the proposed optimization tackles the variablesized bin packing problem (VBPP). The article presents a hybrid genetic algorithm that packs items into both available objects from the inventory and variablesized objects from the stock. The algorithm tries to minimize waste. Large trimloss items are returned as remnants to the inventory for subsequent optimizations.     

Good quality at low cost: Trends in quality assurance

For as long as electronic devices have been produced the relationship between the costs and benefits of quality assurance has been discussed. At present this relationship is influenced by the increase in the complexity of integrated circuits and by the growing extent of automation in production. In this paper a way is presented showing how the cost of quality assurance can be decreased without loss of quality. Six steps to achieving this goal are described.