Imperfect Production Process Research Articles

A production model for ameliorating items with quality consideration

Most of the inventory models assume perfect production, but it is not necessary that all the units produced in manufacturing organisation are of excellent quality. This can be a mix of perfect and imperfect quality. This type of production is in the category of imperfect production process. In this article, we create a production model for ameliorating inventory system with time-varying demand. Here, the term ‘amelioration’ refers to improvement in the goods which causes value increase or benefit from the amount used at the time. The production cost per unit is considered as a function of the production rate. Mathematical expression for the expected profit is calculated and a numerical example is given to illustrate the model. Also, the effects of parameters involved in the modelling are examined with the help of sensitivity analysis.

The optimal production-run time for a stock-dependent imperfect production process

This paper develops an inventory model for a hypothesized volume flexible manufacturing system in which the production rate is stock-dependent and the system produces both perfect and imperfect quality items. The demand rate of perfect quality items is known and constant, whereas the demand rate of imperfect (non-conforming to specifications) quality items is a function of discount offered in the selling price. In this paper, we determine an optimal production-run time and the optimal discount that should be offered in the selling price to influence the sale of imperfect quality items produced by the manufacturing system. The considered model aims to maximize the net profit obtained through the sales of both perfect and imperfect quality items subject to certain constraints of the system. The solution procedure suggests the use of ?Interior Penalty Function Method? to solve the associated constrained maximization problem. Finally, a numerical example demonstrating the applicability of proposed model has been included.

An economic production quantity (EPQ) model for a customer-dominated supply chain with defective items, reworking and scrap

This paper investigates the production-inventory policy for a manufacturer operating in a supply chain environment where the manufacturer is not the chain leader. The chain leader dictates the size and the interval of the shipments. Large penalties set by the chain leader on short shipments preclude the permission of shortages. This might require the manufacturer to produce in larger, non-optimal lots to ensure that all orders are fulfilled as agreed upon with the chain leader. Larger lots, however, subjugate the manufacturer to the risk of an imperfect production process and reworks. A new mathematical model is developed that describes this situation and numerical results are discussed.

A production inventory model with fuzzy production and demand using fuzzy differential equation: An interval compared genetic algorithm approach

In this paper, a production inventory model, specially for a newly launched product, is developed incorporating fuzzy production rate in an imperfect production process. Produced defective units are repaired and are sold as fresh units. It is assumed that demand coefficients and lifetime of the product are also fuzzy in nature. To boost the demand, manufacturer offers a fixed price discount period at the beginning of each cycle. Demand also depends on unit selling price. As production rate and demand are fuzzy, the model is formulated using fuzzy differential equation and the corresponding inventory costs and components are calculated using fuzzy Riemann-integration. α-cut of total profit from the planning horizon is obtained. A modified Genetic Algorithm (GA) with varying population size is used to optimize the profit function. Fuzzy preference ordering (FPO) on intervals is used to compare the intervals in determining fitness of a solution. This algorithm is named as Interval Compared Genetic Algorithm (ICGA). The present model is also solved using real coded GA (RCGA) and Multi-objective GA (MOGA). Another approach of interval comparison–order relations of intervals (ORI) for maximization problems is also used with all the above heuristics to solve the model and results are compared with those are obtained using FPO on intervals. Numerical examples are used to illustrate the model as well as to compare the efficiency of different approaches for solving the model.

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.

ECONOMIC REPLENISHMENT PLAN WITH IMPERFECT PRODUCTION PROCESS AND BUSINESS-RETURN DEPENDENT DEMAND

This study considers the supplier's warranty return and the buyer's rebate policy as business-return policy in the supplier–buyer supply chain. The policy as well as the displayed stock level influences the behavior of the buyer. Distinct from the traditional single-stage inventory model, we investigate a two-stage replenishment policy model for deteriorating item considering the effect of imperfect production process, product design, stock level and business-return. A mathematical model utilizing the time weighted inventory (TWI) approach and two-variables fixed point optimization technique is developed to derive the optimal inspection starting time, the number of deliveries, the optimal delivery-time interval and the optimal business-return period. A numerical example is presented to illustrate the model developed. The result shows that the fixed demand rate, the unit holding cost and the unit inspection cost are the critical factors affecting the scheduling and performance of the two-stage supply chain.

Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns

In practice the items received in a lot may contain defective items, and during the screening process to eliminate the defective items, the inspector may incorrectly classify a non-defective item as defective (a Type I error) or incorrectly classify a defective item as non-defective (a Type II error). In this paper, we develop two economic production quantity models with imperfect production processes, inspection errors, planned backorders, and sales returns. A closed form solution is obtained for the optimal production lot size and the maximum shortage level for both models. We provide two numerical examples, one in which the defective probability and Type I and Type II inspection errors follow uniform distributions, and the second in which we assume they follow beta distributions. Sensitivity analyses are performed to see the impact of the defective probability, the probability of the Type I inspection error, the probability of the Type II inspection error, the holding cost, and the backordering cost on the optimal solutions. We obtain similar results on the sensitivity analyses for both numerical examples. The results show that the time factor of when to sell the defective items has a significant impact on the optimal production lot size and the backorder quantity. The results also show that if customers are willing to wait for the next production when a shortage occurs, it is profitable for the company to have planned backorders although it incurs a penalty cost for the delay.

An optimal production and inspection strategy with preventive maintenance error and rework

This study considers the integrated problem of production, preventive maintenance (PM), inspection, and inventory for an imperfect production process where rework and PM error exist. PM is performed when the process is in a controlled state. The correct implementation of PM results in a lower system failure rate, whereas a PM error results in the system shifting to the out-of-control state with a certain probability. The age of the system after PM is correlated with the level of PM performed. When the process in an out-of-control state produces a certain percentage of non-conforming items, we assume that a certain proportion of the non-conforming items can be reworked into conforming items. In a deteriorating production system, we determine the optimal inspection interval, inspection frequency, and production quantity that will yield the maximal unit expected profit. Numerical analyses are used to investigate the effectiveness of imperfect PM and to explore the effect of rework and PM error on profit.

Lot sizing and quality investment with quality cost analyses for imperfect production and inspection processes with commercial return

Abstract This study examines an imperfect production and inspection system with customer return and defective disposal. We develop an optimal lot sizing model with production and inspection quality investment, incorporating all the quality costs. We find the optimal lot size, rework frequency, defective proportion, and Type I and Type II inspection error proportions which minimize the total quality cost and maximize the total profit. We further analyze the solutions for no, partial, sequential and joint investment decisions on production and/or inspection processes in terms of quality costs using numerical analyses. The result provides important managerial insights into practice.

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 wit...

An integrated vendor–buyer cooperative inventory model in an imperfect production process with shortage backordering

In this paper, we develop an integrated inventory model for vendor–buyer coordination under an imperfect production process. The proportion of defective items in each production lot is assumed to be stochastic and follows a known probability density function. The vendor inspects the items while they are being produced and delivers good-quality items to the buyer in small lots over multiple shipments. We assume that shortages are permitted and are completely backordered. The expected annual integrated total cost is derived and a solution procedure is provided to find the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer. The results also show that if back orders are permitted, the expected integrated annual cost is less than that when back orders are not permitted. Therefore, if customers are willing to wait for the next shipment when a shortage occurs, it is profitable for the company to allow back orders although the delay incurs a penalty cost.

Optimal production policy with investment on imperfect production processes

The imperfect production processes always result in imperfect products and decrease the profit of the business. Improving the production processes by increasing the investment cost will decrease the percentage of defective items. The trade-off between the investment cost and the marginal improvement on products is a key problem. In this study, we develop an EPQ model of deteriorating items with investment on imperfect production processes. An algorithm is developed to derive a replenishment policy such that the expected unit time profit is maximized. Numerical examples are provided to illustrate the theory. Key words: Economic production quantity, imperfect quality, deterioration, investment.

An economic production lot-size (EPLS) model with rework and flexibility under allowable shortages

This paper develops a model to determine the optimal reliability and production rate that achieves the biggest total integrated profit for an imperfect production process under allowable shortage. This paper extends the paper of Sana (2010). Here, we consider two type of production process in a cycle time. One is 'in-control' state at the starting of the production which provides conforming quality items and second one is 'out-control' state after certain time due to higher production rate and production run time. In this study, we also consider that selling price of the units depends upon the unit production cost and screening cost of the items. The total cost function is illustrated by numerical examples and also its sensitivity analysis is carried out.

An inventory model with reliability in an imperfect production process

The paper analyzes an economic manufacturing quantity (EMQ) model with price and advertising demand pattern in an imperfect production process under the effect of inflation. If the machine goes through a long-run process, it may shift from in-control state to out-of-control state. As a result, the system produces imperfect items. The imperfect items are reworked at a cost to make it as new. The production of imperfect quality items increases with time. To reduce the production of the imperfect items, the systems have to more reliable and the produced items depend on the reliability of the machinery system. In this direction, the author considers that the development cost, production cost, material cost are dependent on reliability parameter. Considering reliability as a decision variable, the author constructs an integrated profit function which is maximized by control theory. A numerical example along with graphical representation and sensitivity analysis are provided to illustrate the model.

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.

An imperfect production process for time varying demand with inflation and time value of money – An EMQ model

The paper deals with an economic manufacturing quantity (EMQ) model for time-dependent (quadratic) demand pattern. Every manufacturing sector wants to produce perfect quality items. But in long run process, there may arise different types of difficulties like labor problem, machinery capabilities problems, etc., due to that the machinery systems shift from in-control state to out-of-control state as a result the manufacturing systems produce imperfect quality items. The imperfect items are reworked at a cost to become the perfect one. The rework cost may be reduced by improvements in product reliability i.e., the production process depend on time and also the reliability parameter. We want to determine the optimal product reliability and production rate that achieves the biggest total integrated profit for an imperfect manufacturing process using Euler–Lagrange theory to build up the necessary and sufficient conditions for optimality of the dynamic variables. Finally, a numerical example is discussed to test the model which is illustrated graphically also.

A two-warehouse inventory model for items with imperfect quality and penalty costs under screening errors

This paper corrects an improper expression in the economic order quantity (EOQ) model with two-warehouses and imperfect quality developed by Chung et al. [2009. A twowarehouse inventory model with imperfect quality production processes. Computers & Industrial Engineering 56, 193–197]. The modified model yields a simple and corrected expression for the optimal order quantity and expected profit per unit time. This paper then extends the above idea to a case involving a 100% inspection process with screening errors that may occur under imperfect quality and two warehouses. A model, in which it includes two scenarios, with imperfect quality and penalty costs under screening errors (Type I and Type II error) is developed. The effects of percentage of defective items and screening errors on the optimal solution are investigated. A numerical example is provided for the developed model and its result reveals that the order lot size and expected total profit considering in this paper is less than Chung et al. [2009]. Managerial insights are also draw.

Optimal inventory policy with reliability consideration and instantaneous receipt under imperfect production process

As markets become more and more competitive, reliability has become a prevailing characteristic of the modern production systems operating in complex, dynamic and uncertain environments. Ensuring reliability for exceptional products requires stringent production control measures often with costs that are usually difficult to estimate. Yet not accounting for these in costs can lead to less efficient production systems. This paper suggests that the need to consider reliability and need for instantaneous receipt resembles an imperfect production process. The applicability of these factors is demonstrated in a simple reverse inventory model with an imperfect production process, where the unit cost of production is inversely related to reliability and directly related to demand. These objective functions are included to model the problem accurately. Under reasonable conditions, maximum positive cost savings are achieved when process reliability increases. Numerical examples and a sensitivity analyses are presented to illustrate the results of the proposed model and to draw managerial insights.

Imperfect production process with exponential demand rate, Weibull deterioration under inflation

In this research, an integrated production inventory model is developed from the perspective of both the manufacturer and the retailer. The model assumes exponential demand rate, production rate is demand dependent under the inflation, imperfect production process and multiple deliveries. We have assumed that the produced items deteriorates at a constant rate at the producer’s end due to the proper storages conditions, and as the items reaches the retailer’s end follows the Weibull deterioration. Shortages are allowed at the retailer’s part only and the unfulfilled demand is partially backlogged. A numerical example along with sensitivity analysis is given to illustrate the model. Integrated cost policy is compared with the independent decisions made by the manufacturer and the retailer’s and the necessary conclusions are made. Mathematica5.2 is being used to reach the optimal policies.

Determining optimal selling price and lot size with process reliability and partial backlogging considerations

In this article, we extend the classical economic production quantity (EPQ) model by proposing imperfect production processes and quality-dependent unit production cost. The demand rate is described by any convex decreasing function of the selling price. In addition, we allow for shortages and a time-proportional backlogging rate. For any given selling price, we first prove that the optimal production schedule not only exists but also is unique. Next, we show that the total profit per unit time is a concave function of price when the production schedule is given. We then provide a simple algorithm to find the optimal selling price and production schedule for the proposed model. Finally, we use a couple of numerical examples to illustrate the algorithm and conclude this article with suggestions for possible future research.