Imperfect Production System Research Articles

Imperfect production system with rework of regular production with sales returns by customers and buffer stock

Jamal et al. (2004) proposed a model, which dealt with the optimum batch quantity in a single-stage system in which rework is done by addressing two different operational policies to minimise the total system cost but their models do not considered sales return by customers. A portion of defective items produced are not successfully screened out internally during the production process and passed on to customers, thereby causing defect sales returns and reverse logistic from customers back to the manufacturer. In this direction, this paper develops an economic production quantity inventory model with sales return by customers for determining the economic production quantity for a single product, which is manufactured in a single-stage manufacturing system that generates imperfect quality products and all these defective products are reworked in the same cycle. Mathematical model is developed and the optimal production lot size which minimises the total cost is derived.

Imperfect production system with rework of regular production with sales returns by customers and buffer stock

Imperfect production system with rework of regular production with sales returns by customers and buffer stock

An inventory model for imperfect production system with rework and shortages

An inventory model for imperfect production system with rework and shortages

Decision makings in discount pricing policy for imperfect production system

In this paper, we discussed the effects of discount price on demand and profit in a diminishing market. A production plan has been suggested for an imperfect production system. Here, demand is considered to be price sensitive and negative power function of the selling price. This problem is solved by optimization, using the Hessian matrix of order three. The main objective is to find the optimal expected average profit, optimal selling price, discount rate, backorder level, and lot-size. The recommendations are provided to offer a price discount for limited sale season on different occasions. A numerical example is presented to validate the model and is graphically illustrated accordingly.

Effects of product reliability dependent demand in an EPQ model considering partially imperfect production

In this article, an economic production quantity (EPQ) model with partially imperfect production system has been considered where both perfect and imperfect quality items are produced and demand of the product has been assumed as a function of selling price, reliability of the product and advertisement. Perfect quality items are ready for sale but imperfect quality items are reworked at a cost to become perfect one. Reworking cost, reliability of the product and reliability parameter of the manufacturing system can be improved by introducing the time dependent development cost and also by improving the quality of the raw material used in the production system. Under such circumstances, a profit function has been developed and maximised by optimising the reliability parameter of the manufacturing system, reliability of the product and duration of production. Finally, the model has been illustrated with some numerical examples.

An inventory model for imperfect production system with rework and shortages

This paper considers a production inventory model with planned backorders for a single product. The product is manufactured in a single stage manufacturing system. The manufacturing system generate...

Hybrid NSGA-II for an imperfect production system considering product quality and returns under two warranty policies

This study presents a new bi-objective mathematical model for an imperfect production system (IPS) that accounts for product returns and quality levels under two different warranty policies. We considered uncertain customer demand as stochastic behavior and product price as a function of return compensation, product quality level, and warranty-period length. We simultaneously looked at the pro rata warranty and free replacement/repair warranty policies and assumed that customers can choose the desired policy. A return policy for an online distributor was also included and two objective functions were used to address the problem. The first objective function maximized the total expected revenue, and the second objective function maximized customer satisfaction. The non-dominated sorting genetic algorithm (NSGA-II) and two others, the basic bee metaheuristic and teaching-learning-based optimization algorithms, were used to generate the initial solution for use in the NSGA-II algorithm. The results from the hybrid algorithms revealed that the proposed method improves the performance of the NSGA-II algorithm. Finally, several specific sensitivity analyses were conducted to determine the effects of the problem parameters.

Integrated model of quality inspection, preventive maintenance and buffer stock in an imperfect production system

Abstract In this study, the influence of a quality inspection policy on an imperfect production system in which a percentage of the produced items is inspected is modelled. The inspection policy is imperfect, permitting type I and type II errors. Items are shipped for sale with a free minimal repair warranty policy. After each production cycle, preventive maintenance is performed. In case of failure in the production process before the cycle’s end, a minimal repair is indicated. A buffer stock is established to meet demand while preventive maintenance is performed. We also considered that defective items detected on inspection are sent for reworking. The model is formulated with the objective of minimizing the total cost expected per item while considering an average outgoing quality constraint. Subsequently, we present a numerical experiment to illustrate the proposed model. The results indicate that the probability of type I and type II inspection errors has a significant impact on optimal production and the percentage of items inspected.

A supply chain model for imperfect production system with stochastic lead time demand

This study deals an integrated manufacturer–buyer supply chain system for imperfect production under stochastic lead time demand. Here, defective rate has been followed as a function of production rate. Also, the produced units have been inspected in order to screen the defective units but screening rate is less than the production rate and greater than the demand rate. Buyer purchases the products from the manufacturer. Also, we assume that shortage during the lead time is permitted and demand during the shortage period is fully back-ordered. The objective is to derive the optimal production rate, ordering quantity and to maximize joint total profit. Basically, two different models for different probability distribution functions of stochastic lead time demand have been developed. Some numerical examples are provided to show the applicability of the proposed models comparing the optimum average profits. Finally, sensitive analysis, conclusion and future researches are presented.

Optimal and simple algorithms to solve integrated procurement-production-inventory problem without/with shortage

This research work deals with an imperfect production system considering the purchasing of raw materials in order to study the economic production quantity (EPQ). This manufacturing system produces perfect and defective finished products; defectives are considered as scrap. A single product is manufactured from multiple raw materials which are purchased from outside suppliers. In the integrated procurement-production-inventory (IPPI) model, one of the principal decisions, in addition to determining the optimal lot size to produce, is to define the number of optimal orders of each raw material with respect to rate of consumption in the manufacturing of finished product. Two cases are considered: without shortage (first model) and with shortage (backordering, second model). In the first model, the purpose is to determine jointly the optimal lot size to manufacture and the optimal number orders of each raw material in order to minimize the total cost. The second model obtains the optimal number of orders of each raw material, the optimal lot size to manufacture and the optimal shortage level with aim to minimize the total cost. This research also shows that both of the proposed inventory models are a convex programming problem, so exact algorithms to solve these inventory problems are proposed.

Lost sales reduction and quality improvement with variable lead time and fuzzy costs in an imperfect production system

This article investigates the effects of lost sales reduction and quality improvement in an imperfect production process under imprecise environment with simultaneously optimizing reorder point, order quantity, and lead time. This study assumes that the demand during lead time follows a mixture of normal distributions and the cost components are imprecise and vague. Under these assumptions, the aim is to study the lost sales reduction and the quality improvement in an uncertainty environment. The objective function in fuzzy sense is defuzzified using Modified Graded Mean Integration Representation Method (MGMIRM). For the defuzzified objective function, theoretical results are developed to establish optimal policies. Finally, some numerical examples and sensitivity analysis are provided to examine the effects of non-stochastic uncertainty.

Economic production quantity with the presence of imperfect quality and random machine breakdown and repair based on the artificial bee colony heuristic

This article considers a production-inventory system consisting of a single imperfect unreliable machine. The items manufactured by the system are either perfect items or imperfect items, which require a rework to be restored to perfect quality. The rework rate is permitted to be different from the production rate if the rework process is different from the main manufacturing process. The fraction of the number of imperfect items is random following a general distribution function. The time to failure of the machine is random, following a general distribution function. If the machine fails before the lot is completed, the production is interrupted and the machine repair is started immediately. A random machine repair time is assumed, with a general distribution function. Unlike a common assumption in the literature, after the repair of the machine is completed, the production resumes. During the machine repair, a shortage can occur. A single-variable expected average cost function is derived to find the optimal lot size. Because of the complexity in the model, the ABC heuristic is proposed and implemented to find a near optimal value for the lot size. The article also provides a sensitivity analysis of the model's key parameters. It has been observed that the lot interruption-resumption policy leads to smaller lot sizes. • An imperfect production system has a random time to failure and a random time to repair. • Shortages are permitted during the machine repair. • The model determines the optimal production lot size. • The lot interruption-resumption strategy leads to smaller lot sizes. • The lot size reacts significantly to changes in the machine failure rate and the repair rate.

Integrated production, quality control and condition-based maintenance for imperfect production systems

This paper considers an integrated problem of production lot sizing, quality control and condition-based maintenance for an imperfect production system subject to both reliability and quality degradations. The system produces a single type of product to meet constant demand. To provide protection to the stock against uncertainties, a make-to-stock production policy is employed. The condition-based maintenance policy consists in carrying out inspections at the end of production runs to evaluate system condition and performing imperfect preventive maintenance if detected degradation level exceeds the threshold. The quality control is performed by using 100% inspection policy to obtain the proportion of defectives. Based on the quality information feedback, an overhaul action is conducted once the proportion reaches a given threshold during production runs. The aim of this paper is to jointly optimize the lot size, the inventory threshold, the preventive maintenance and overhaul thresholds such that the total cost per unit time is minimized. A stochastic mathematical model is formulated and solved by a simulation-based optimization approach coupling Monte Carlo Simulation and Response Surface Methodology. Finally, an illustrative example and sensitivity analyses are provided to demonstrate the proposed model.

Green logistics under imperfect production system: A Rough age based Multi-Objective Genetic Algorithm approach

Abstract Imperfect economic production lot size (EPL) models are considered with time dependent defective rate. Here, defective production starts after the passage of some time from production commencement. Produced defective units are partially reworked and sold as fresh units. Under the environmental regulation, a cost (carbon tax) is charged by the government to mitigate global warming by reducing carbon emission (CE). Management also uses carbon trading when upper limit of carbon emission is given by the government. These costs bring a contradiction to a production manager. For more profit, if more production is decided, then CE and tax due to that are more. The models are formulated as single- and multi-objective profit maximization problems and solved using Rough age based single- and multi-objective Genetic Algorithms (RMOGAs). Numerical experiments are performed and graphical presentation of the results are depicted to illustrate the models. An algorithm with example for a firm management to achieve the maximum profit is also presented.

Determination of Economic Lot Size between Suppliers and Manufacturers for Imperfect Production System with Probabilistic Demand

This study aims to develop a combined economical lot size model between supplier and manufacturer for imperfect production processes with probabilistic demand patterns and constant lead times. The supplier side produces the product within a certain time interval then sent to the manufacturer with a certain amount of lot size. Imperfect supplier production systems are characterized by the probability of defective product (γ). The model decision variables are the lot size of the manufacturer's ordering, supplier lot size, and the reorder point of the manufacturer. The optimal decision variables are obtained by minimizing the total expected cost of the combined costs between the suppliers and the manufacturers borne by both parties. The model is built compared to the transactional partnership model, in which the supplier does not participate in the efficiency of its inventory system. A numerical example is given as an illustration of the JELS model and the transactional partnership model. Sensitivity analysis of the model is done by changing the parameters aimed at analyzing the behavior of the developed model.

A Model for Imperfect Production System with Probabilistic Rate of Imperfect Production for Deteriorating Products

A Model for Imperfect Production System with Probabilistic Rate of Imperfect Production for Deteriorating Products

An Imperfect Multi-Item Single Machine production system with Shortage, Rework, and Scrapped Considering Inspection, Dissimilar Deficiency Levels, and Non-Zero Setup Times

In this paper, we consider a deficient production system with permissible shortages. The production system consists of a unique machine that manufactures a number of products that a part of them are imperfect in form of rework or scrap. These defective products are identified by 100% inspection during production, then, they are whether reworked or disposed of after normal production process. Like real-world production systems, there are diverse kinds of errors creating dissimilar breakdown severity and rework. Moreover, reworks have non-zero setup times that makes the problem closer to real-world instances where machines require some preparations before starting a new production cycle. Thus, we introduce an economic production quantity (EPQ) problem for an imperfect manufacturing system with non-zero setup times for rework items. The rework items are classified into several categories based on their type of failure and rework rate. The aim of this study is to obtain optimum production time and shortage in each period that minimizes inventory system costs including setup costs in reworks, holding costs, production costs, inspection costs, disposal costs, and shortage. Finally, a numerical example is proposed to assess efficiency and validation of the proposed algorithm.

Imperfect production system with rework and scrap at a single stage manufacturing system and integrates cost reduction delivery policy

This paper deals with a production inventory model with reworkable defective items and integrates a cost reduction delivery policy. In this work, it is assumed that in each cycle the rework process of all defective items starts when the regular production process finishes. After the rework process, a portion of reworked items fails and this portion becomes scrap. In this paper, two models are developed, in the first model, the perfect finished items can be delivered to customers at the end of rework process and in the second model, integrates cost reduction delivery policy and finished items can only be delivered to customers at a fixed interval of time during production down time with the purpose of reducing holding cost. The objective is to derive the optimal production lot size, number of deliveries and the finished items are delivered by request to customers at a fixed interval of time that minimises total costs. The relevant model is built, solved and necessary and sufficient conditions for a unique and global optimal solution are derived. An illustrative example is provided and numerically verified. The validation of result in this model was coded in Microsoft Visual Basic 6.0.

Imperfect production system with rework and scrap at a single stage manufacturing system and integrates cost reduction delivery policy

This paper deals with a production inventory model with reworkable defective items and integrates a cost reduction delivery policy. In this work, it is assumed that in each cycle the rework process of all defective items starts when the regular production process finishes. After the rework process, a portion of reworked items fails and this portion becomes scrap. In this paper, two models are developed, in the first model, the perfect finished items can be delivered to customers at the end of rework process and in the second model, integrates cost reduction delivery policy and finished items can only be delivered to customers at a fixed interval of time during production down time with the purpose of reducing holding cost. The objective is to derive the optimal production lot size, number of deliveries and the finished items are delivered by request to customers at a fixed interval of time that minimises total costs. The relevant model is built, solved and necessary and sufficient conditions for a unique and global optimal solution are derived. An illustrative example is provided and numerically verified. The validation of result in this model was coded in Microsoft Visual Basic 6.0.

Promotional effort and quality sensitive two echelon production inventory model with partial backlogging

This study deals with the modelling aspect of a two echelon imperfect production system in the presence of the promotional effort of the retailer. The production cost of the system varies with both the ordering lot size and quality of product, and the demand of the product depends on the quality of the product. The inventory level for the manufacturer starts with shortages and new production and the inventory level for the retailer also begin with shortages and new product lot. The cycle ends for both the players with also backlogged inventory. The backlogging rate for each of the player is dependent on waiting time. The behaviour of the model under integrated system is analysed. In the decentralised structure, retailer Stackelberg model are also discussed. The sensitivity of the key parameters is examined to test feasibility of the model. Finally, a numerical example is provided to investigate the proposed model.