Imperfect Production Research Articles

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.

An imperfect quality items with learning and inflation under two limited storage capacity

Article history: Received February 2 2013 Received in revised format May 28 2013 Accepted June 22 2013 Available online June 26 2013 In this paper, we develop a two-warehouse imperfect production model under two cases: (i) model starts with shortages (ii) model ends with shortages. Most of the researchers proposed the models for perfect items but we develop for imperfect quality items, which is very realistic. Demand is taken as time dependent and dependent on the production. Holding cost in rented warehouse (RW) is greater than own warehouse (OW). Deterioration is taken as Weibull distribution in both OW and RW. Shortages are allowed and partially backlogged. The effect of learning on production cost is also considered. Learning from one cycle to other cycle, improve the efficiency of the organization. A numerical example including the sensitivity analysis is given to validate the results of the production-inventory model. © 2013 Growing Science Ltd. All rights reserved

Combined production-maintenance decisions in situations with process deterioration

This article addresses an imperfect production system with process deterioration and how best to maintain the system. In the system there is a constant percentage to produce defective products in the ‘in-control’ state and a higher percentage to produce defective products in the ‘out-of-control’ state. The production process may shift randomly from an in-control state to an out-of-control state during a production run; i.e. system process deterioration. This article considers both preventive maintenance and corrective maintenance. The objective is to determine the optimal production run time and preventive maintenance frequency while still minimising the total annual cost. We provide two efficient algorithms for solving the problems when considering the preventive maintenance frequency as discrete and continuous, respectively. Finally, we apply a numerical analysis to study the effects of changing parameter values on the optimal solutions and to point out some management implications.

EPQ model with learning consideration, imperfect production and partial backlogging in fuzzy random environment

The article scrutinises the learning effect of the unit production time on optimal lot size for the uncertain and imprecise imperfect production process, wherein shortages are permissible and partially backlogged. Contextually, we contemplate the fuzzy chance of production process shifting from an ‘in-control’ state to an ‘out-of-control’ state and re-work facility of imperfect quality of produced items. The elapsed time until the process shifts is considered as a fuzzy random variable, and consequently, fuzzy random total cost per unit time is derived. Fuzzy expectation and signed distance method are used to transform the fuzzy random cost function into an equivalent crisp function. The results are illustrated with the help of numerical example. Finally, sensitivity analysis of the optimal solution with respect to major parameters is carried out.

Optimizing inventory decisions in a two-level supply chain with order quantity constraints

A fundamental assumption in traditional inventory models is that all of the ordered items are of perfect quality. A two-level supply chain is considered consists of one retailer and a collection of suppliers that operate within a finite planning horizon, including multiple periods, and a model is formulated that simultaneously determines both supplier selection and inventory allocation problems in the supply chain. It is supposed that the ordered products dependent on the suppliers include a certain percentage of imperfect quality products and have different prices. In this paper, we study the impact of the retailer’s financial constraint. On the other hand, suppliers have restricted capacities and set minimum order quantity (MOQ) policy for the retailer’s order amount happened in each period. So, the problem is modeled as a mixed integer nonlinear programming. The purpose of this model is to maximize the total profit. The nutrients, fishery and fruitage industries give good examples for the proposed model. A numerical example is presented to indicate the efficiency of the proposed model. Considering the complexity of the model, a genetic algorithm (GA) is presented to solve the model. We demonstrate analytically that the proposed genetic algorithm is suitable in the feasible situations.

A study on negative binomial inspection for imperfect production systems

Production systems continuously deteriorate with age and usage due to corrosion, fatigue, and cumulative wear in production processes, resulting in an increasing possibility of producing defective products. To prevent selling defective products, inspection is usually carried out to ensure that the performance of a sold product satisfies the customer requirements. Nevertheless, some defective products may still be sold in practice. In such a case, warranties are essential in marketing products and can improve the unfavorable image by applying higher product quality and better customer service. The purpose of this paper is to provide manufacturers with an effective inspection strategy in which the task of quality management is performed under the considerations of related costs for production, sampling, inventory, and warranty. A Weibull power law process is used to describe the imperfection of the production system, and a negative binomial sampling is adopted to learn the operational states of the production process. A free replacement warranty policy is assumed in this paper, and the reworking of defective products before shipment is also discussed. A numerical application is employed to demonstrate the usefulness of the proposed approach, and sensitivity analyses are performed to study the various effects of some influential factors.

Development of a production inventory model with uncertainty and reliability considerations

This paper addresses a problem of an imperfect production system under fuzzy demand and inventory holding cost. Production process reliability is considered because of the imperfect production process. In this problem, reliability of the system in regards to producing defective and non-defective items is considered as a decision variable. The objective is to maximize the graded mean integration value (GMIV) of the expected average profit while considering revenues as well as any other relevant costs. The developed model belongs to the class of a geometric programming. We have developed a simple mathematical methodology to solve the model. Genetic algorithm and simulated annealing algorithms are also applied to solve and validate the results. A numerical example has been presented to interpret the solutions.

An imperfect multi-product production system with rework

This study develops an imperfect, multi-product production system with rework. Our objective is to minimize the joint total cost of the system, subject to service level and budget constraints. Since the objective function in the problem is convex, the existence of global optimality is assured. A solution procedure is proposed and numerical examples are provided to demonstrate the applicability of the model in real-world manufacturing problems. Finally, sensitivity analyses are provided to provide managerial insights, as well as to investigate the interdependency of the parameters.

An EPQ model for imperfect production systems with rework and incorporating a multi-delivery policy

In manufacturing firms, the EPQ model is commonly used for determining the optimal replenishment batch size that minimizes total production-inventory costs for items produced. The classical EPQ model assumes that all items manufactured are of perfect quality. However, real-life production systems, due to various controllable and/or uncontrollable factors, the generation of defective items during a production run seems to be inevitable and they should be reworked or repaired with additional cost. A portion of non-conforming items produced is considered to be scrap, while the rest are assumed to be repairable and are reworked in each cycle when regular production ends. Finished items can only be delivered to customers if the whole lot is quality assured after rework. This paper incorporates a multi-delivery policy into an imperfect EPQ model with scrap and rework 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 and number of deliveries such that the finished items are delivered by request to customers at a fixed interval of time that minimizes 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 results in this model was coded in Microsoft™ Visual Basic 6.0.

Optimal production lot with imperfect production process under permissible delay in payments and complete backlogging

The traditional economic production quantity (EPQ) model assumes that the production products are all perfect. It is not always true in the real production system, due to imperfect production process or other factors, imperfect quality items may be produced. Furthermore, it is well-known that the total production-inventory costs can be reduced by reworking the imperfect quality items produced with a relatively smaller additional reworking and holding costs. In addition, the permissible delay in payments offered by the supplier is widely adopted in the practical business market. In this study, we explore the effects of the reworking imperfect quality items and trade credit on the EPQ model with imperfect production processes and complete backlogging. A mathematical model which includes the reworking and shortage costs, interest earned and interest charged is presented. Besides, an arithmetic-geometric mean inequality approach is employed and an algorithm is developed to find the optimal production policy. Furthermore, some numerical examples and sensitivity analysis are provided to demonstrate the proposed model.

Production-inventory models for a damageable item with variable demands and inventory costs in an imperfect production process

In this paper, economic production quantity (EPQ) models for breakable or deteriorating item are developed with variable demands, being dependent on time or on-hand stock. Here rate of production and holding cost are time dependent, unit production cost is a function of both production reliability indicator and production rate. Set-up cost is also partially production rate dependent. The production process produces some imperfect quantities which are instantly reworked at a cost to bring back those units to the perfect ones. The production process ultimately depends on both time and reliability indicator. The models are formulated as optimal control problems and the total profit functions with effect of inflation and time-value of money are expressed as finite integrals over the finite planning horizon. The problems are solved using Euler–Lagrange function based on variational calculus and Newton–Raphson method to determine the optimal production reliability indicator (r) and then corresponding production rates and total profits. In some cases, results of the models for deteriorating item are obtained as particular cases from those of breakable item models. Similarly, results of simple EPQ models (without damageability) are deduced as particular cases. Numerical experiments are performed to illustrate the models both numerically and graphically.

Effects of maintenance policy on an imperfect production system under trade credit

The traditional production model development assumed that all products are perfect quality and did not consider maintenance, which is far from reality. In practice, the production process may shift randomly from an in-control state to an out-of-control state during a production run, i.e. process deterioration. This paper considers both preventive maintenance and corrective maintenance which are used to increase the system reliability. The objective of this paper is to determine the optimal production run time and maintenance frequency while minimising the total cost under process deterioration and trade credit. This paper develops a theorem and an algorithm to solve the problem described, provides numerical analysis to illustrate the proposed solution procedure, and discusses the impact of various system parameters. A real case of hi-tech manufacturer is used to verify the model. It predicts a 10.36% decrease in total cost if the preventive maintenance decision is considered.

Maximising profits for an EPQ model with unreliable machine and rework of random defective items

This article deals with an economic production quantity (EPQ) model in an imperfect production system. The production system may undergo in ‘out-of-control’ state from ‘in-control’ state, after a certain time that follows a probability density function. The density function varies with reliability of the machinery system that may be controlled by new technologies, investing more costs. The defective items produced in ‘out-of-control’ state are reworked at a cost just after the regular production time. Occurrence of the ‘out-of-control’ state during or after regular production-run time is analysed and also graphically illustrated separately. Finally, an expected profit function regarding the inventory cost, unit production cost and selling price is maximised analytically. Sensitivity analysis of the model with respect to key parameters of the system is carried out. Two numerical examples are considered to test the model and one of them is illustrated graphically.

Mathematical Modeling and Algebraic Technique for Resolving a Single-Producer Multi-Retailer Integrated Inventory System with Scrap

This study uses mathematical modeling along with an algebraic technique to resolve the production- distribution policy for a single-producer multi-retailer integrated inventory system with scrap in production. We assume that a product is manufactured through an imperfect production process where all nonconforming items will be picked up and scrapped in each production cycle. After the entire lot is quality assured, multiple shipments will be delivered synchronously to m different retailers in each cycle. The objective is to determine the optimal replenishment lot size and optimal number of shipments that minimizes total expected costs for such a specific supply chains system. Conventional method is by the use of differential calculus on system cost function to derive the optimal policy (Chiu et al., 2012c), whereas the proposed algebraic approach is a straightforward method that enables practitioners who may not have sufficient knowledge of calculus to understand and manage more effectively the real-life systems.

Effects of Lot-Sizing Integration and Learning Effect on Managing Imperfect Items in a Manufacturer-Retailer Chain

An optimal supply chain performance requires the execution of a precise set of actions, including coordination of the movement of materials, products, and information flows among suppliers, manufacturers, distributors, retailers, and customers. However, a supply chain usually involves several members who are primarily concerned with optimizing their own objectives. This self-serving focus often results in poor channel performance. The present study used the Nash game and the cooperation game in an imperfect production system to investigate the combined effects of lot-sizing integration, learning effect, and an imperfect production process on a manufacturer-retailer channel. This paper also developed a search procedure to solve the problem described, and the optimal properties and a numerical study were conducted to seek structural and quantitative insights into the relationship between the upstream and downstream entities of the supply chain. Numerical results indicated that the cooperation game policy created a higher cost reduction under a wide range of parameter settings.

Three stage supply chain model with two warehouse, imperfect production, variable demand rate and inflation

Three stage supply chain model with two warehouse, imperfect production, variable demand rate and inflation

Integrated imperfect production inventory model under permissible delay in payments depending on the order quantity

The aim of this paper is to develop an improved inventory modelwhich helps the enterprises to advance their profit increasing and costreduction in a single vendor-single buyer environment with permissible delayin payments depending on the ordering quantity and imperfect production.Through this study, some numerical examples available in the literature areprovided herein to apply the permissible delay in payments depending on theordering quantity strategy. Furthermore, imperfect products will cause thecost and increase number of lots through the whole model. Therefore, formore closely conforming to the actual inventories and responding to thefactors that contribute to inventory costs, our proposed model can be thereferences to the business applications. Finally, results of this studyshowed applying the permissible delay in payments can promote the costreduction; and also showed a longer trade credit term can decrease costs forthe complete supply chain.

Two Storage Production Model with Imperfect Quality for Decaying Items Under Preservation

In this paper, an imperfect inventory model with two separate warehouses called owned warehouse/show-room (OW) and rented warehouse (RW) is developed. The proposed model of this paper also considers a realistic assumption regarding the storage capacity of the rented warehouse. Production of defective units is a natural phenomenon in a production process. Defective items should be treated as a result of imperfect quality production. Inflation is also considered in this model. A solution procedure is presented to determine an optimal replenishment cycle, production cost, inspection cost, damaged item cost and preservation technology cost such that the total cost per unit time is minimized. A numerical example and sensitivity analysis are presented to illustrate the model.

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.

Stochastic inventory model for imperfect production processes

Production/inventory decisions for imperfect production process are considered in this paper. The process is in the in-of-control state when it starts a production run. However, it may shift to the out-of-control state at any point in time during the production cycle. The time until the shift from the in-control state to the out-of-control state is modelled by a Weibull random variable with increasing hazard. It is assumed that when the process is in the out-control state, it stays in that state until the next setup where it is brought to as-good-as new conditions. While in the out-of-control state, the process produces a fixed fraction on non-conforming items which are scrapped with no salvage value. Unlike the existing models in the literature, the demand is stochastic and is modelled by a normal probability distribution. Two cases are considered, the first of which is for a predetermined service level case. The other case is when the service level is a decision variable. The cost function is developed and minimised to find the optimal lot size using a simple and efficient algorithm.