Reworkable Items Research Articles

Optimum production lot size for a perishable product under exponential demand with partial backordering and rework

The management of inventory significantly impacts an organization's profitability. Numerous researchers have developed the production model tailored for decaying items to boost sales and minimize inventory, thereby increasing turnover ratios. This study focuses on the EPQ model for reworkable items under exponential combined with inventory dynamics. The primary objective is to optimize the production plan to manage maintenance costs effectively, ensuring optimal Leveraging human and technological resources. The research determines the optimal cycle length, backordered quantities, and production quantities to minimize overall costs. Specifically, penalties are incurred for excessive production times during rework and non-rework phases. This model finds applications in industries such as printed circuit board assembly in semiconductor manufacturing, metal parts, and plastic molding. The study concludes with numerical examples comparing total costs under the proposed model, supplemented by sensitivity analyses that explore the impacts of parameter variations on decision-making.

An imperfect production-inventory model for reworked items with advertisement, time and price dependent demand for non-instantaneous deteriorating item using genetic algorithm

This article deals with an imperfect production inventory system with advertisement, price, and time-dependent demand for a non-instantaneous deteriorating item. Every manufacturing company aims to produce only perfect quality items, but this is not possible in reality. Firstly, the manufacturing system starts producing perfect items, but after some time, it starts producing imperfect items also, because of the manufacturing machine's long run. Perfect products are ready to sell, and some percentages of imperfect products are reworked to become perfect, and the remaining defective products are sold at a cheaper price. An efficiency cost is included to maintain the system efficiency. Considering these conditions, we developed a profit function. This profit function is highly nonlinear. Therefore, we employed a real coded genetic algorithm to obtain the optimum values of production rate, selling price of the perfect quality item, selling price of imperfect item, and inverse efficiency factor to maximise the profit. The model is demonstrated by using numerical example followed by sensitivity analysis.

Controllable Energy Consumption in a Sustainable Smart Manufacturing Model Considering Superior Service, Flexible Demand, and Partial Outsourcing

The waste of energy in the present era is a dangerous signal for the future. All categories of consumers should come forward to moderate energy use and prevent wastage. This study focuses on a controllable energy consumption-based sustainable inventory model incorporating variable production rates, improved service, partial outsourcing planning, defective production, restoring reworkable items, disposing of non-reworkable items, and energy-saving steps. Reducing unusual energy consumption in production systems reduces carbon emissions and maximizes the system’s profit. An improved service level attracts customers, increases demand, and improves product reputation. Separate holding costs of reworked, defective, and perfect-quality items are considered for every lot delivered and reworked. The demand in the market is related to price and service. A traditional optimization technique examines the global optimization for the profit function and decision variables. Numerical illustrations as well as concave 3D graphs validate the analytical results and provide a sensitivity analysis for different parameters. The model is validated through special cases and comparison graphs.

Solution of a pollution sensitive supply chain model under fuzzy approximate reasoning

This article develops a three-layer supply chain (SC) pollution dependent production transportation model with rework on fuzzy approximate reasoning approach. First of all, we develop a cost function of the model of reworkable items, in which pollution generates due to transportation of goods only. The aim of this study is to reduce the aggregated pollution level that simultaneously could optimize the integrated SC cost function under fuzzy approximate reasoning. Basically, the theory of two-tailed (randomized L-R fuzzy) approximate reasoning is introduced first time on demand rate in this model which is an extension of one-tailed (randomized L-fuzzy/R-fuzzy) approximate reasoning in the perspectives of the proposed model. An application of a new heart like approximate dual feasible region has also been utilized here also. However, a comparative study has been made taking numerical examples for crisp, general fuzzy, one- and two-tailed fuzzy approximate reasoning models exclusively. Finally, few numerical analyses with sensitivity and graphical discussions are done to legitimize the model.

A profit jump inventory model for imperfect quality items with receiving reparative batch and order overlapping in dense fuzzy environment

This paper presents an economic order quantity (EOQ) inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a dense fuzzy environment Here, the imperfect items are identified by screening and are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterwards, the items are returned to the supplier to be reworked. Also, discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred to the buyer. The rework process is error free. An order overlapping scheme is employed so that the vendor is allowed to use the previous shipment to meet the demand by the inspection period. However, we assume the total monthly demand quantity as the dense fuzzy number because of learning effect. Moreover, first of all a profit maximization deterministic model is developed and solve by classical method. Fuzzifying the final optimized function via dense fuzzy demand quantity we have employed extended ranking index rule for its defuzzification. During the process of defuzzification we make an extensive study on the paradoxical unit square of the left and right deviations of dense fuzzy numbers. A comparative study is made after splitting the model into general fuzzy and dense fuzzy environment. Finally numerical and graphical illustrations and sensitivity analysis have been made for its global justifications.

Solving a hybrid batch production problem with unreliable equipment and quality reassurance

A hybrid batch fabrication plan involving an outsourcing option is often established to deal with the in-house capacity constraint and/or meet timely demand with a reduced cycle time. Besides, the occurrences of unpredictable equipment malfunction and imperfect product quality should also be effectively managed during in-house fabrication to meet the production schedule and the required quality level. To address these concerns, we examine a hybrid economic production quantity (EPQ) problem with an unreliable machine and quality reassurance; wherein, an outside provider helps supply a portion of the batch at a requested timing and desirable quality, but at the price of a higher than in-house unit cost. Corrective action is performed immediately when a Poisson-distributed breakdown occurs. Once the equipment repairing task completes, the interrupted lot’s fabrication resumes. Random nonconforming products are identified, and the re-workable items among them are separated from the scraps. A rework task follows the regular process in each cycle at an extra cost. A portion of reworked items fails and are scrapped. A model portraying the problem’s characteristics is built, and an optimization methodology is utilized to find the optimal runtime solution to the problem. A numerical example reveals our result’s applicability, and specific managerial implications are suggested.

An imperfect production-inventory model for reworked items with advertisement, time and price dependent demand for non-instantaneous deteriorating item using genetic algorithm

An imperfect production-inventory model for reworked items with advertisement, time and price dependent demand for non-instantaneous deteriorating item using genetic algorithm

Incorporating Outsourcing Strategy and Quality Assurance into a Multiproduct Manufacturer–Retailer Coordination Replenishing Decision

This study explores the multiproduct manufacturer-retailer coordination replenishing decision featuring outsourcing strategy and product quality assurance. Globalization has generated enormous opportunities. Consequently, transnational firms now face tough competition in global markets. To stay competitive, a firm should meet the client’s multi-item and quality requirements under capacity constraints and optimize the intra-supply chain system to allow the timely distribution of finished goods under minimum system cost. The outsourcing option is considered to release machine loadings and reduce cycle time effectively. All items fabricated are screened for quality, and reworkable and scrap items are separated. Any reworked items that fail the quality reassurance screening are discarded, whereas all outsourced products are quality-guaranteed by the provider. A fixed-quantity multi-shipment plan is used when the whole finished lot is quality-ensured to help present-day transnational firms gain competitive advantage by making efficient and cost-effective multiproduct manufacturing and delivering decisions. Mathematical modeling is built to portray the system’s characteristics, and conventional differential calculus is used to solve and derive the optimal operating policy for the proposed problem. Simultaneously, we find the optimal delivery frequency and common cycle time for the problem mentioned above. A simulated numerical example and sensitivity analysis demonstrate the research result’s capability and applicability. Our precise analytical model can reveal/highlight the impact of deviations in quality- and outsourcing-related features on the optimal operating policy and several performance indicators that help managerial decision-making.

A Fuzzy Inventory Model Considering Imperfect Quality Items with Receiving Reparative Batch and Order

This paper presents an inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a fuzzy environment by employing fuzzy triangular numbers. It is assumed that the imperfect items identified by Screening are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterward, the items are returned to the supplier to be reworked. Also, a discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred to the buyer. The rework process is error-free. An overlapping order scheme is employed so that the vendor is allowed to use the previous shipment to meet the demand by the inspection period. In the fuzzy model, the graded mean integration method is taken to defuzzify the model and determine its approximation of a profit function and optimal policy. In doing so, numerical examples are rendered to represent the model behavior, and, eventually, the sensitivity analysis is presented.

A Fuzzy Inventory Model Considering Imperfect Quality Items with Receiving Reparative Batch and Order

This paper presents an inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a fuzzy environment by employing fuzzy triangular numbers. It is assumed that the imperfect items identified by Screening are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterward, the items are returned to the supplier to be reworked. Also, a discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred to the buyer. The rework process is error-free. An overlapping order scheme is employed so that the vendor is allowed to use the previous shipment to meet the demand by the inspection period. In the fuzzy model, the graded mean integration method is taken to defuzzify the model and determine its approximation of a profit function and optimal policy. In doing so, numerical examples are rendered to represent the model behavior, and, eventually, the sensitivity analysis is presented.

Synergic Effect of Reworking for Imperfect Quality Items with the Integration of Multi-Period Delay-in-Payment and Partial Backordering in Global Supply Chains

Abstract In intercontinental trade and economics goods are bought from a global supplier. On occasion, the expected lot may include a fraction of defective items. These imperfect items still have worth and can be sold to customers after repair. It is cost-effective and sustainable to rework such items in nearby repair workshops rather than return them. The reworked items can be returned from the workshop to the buyer when shortages are equal to the quantity of imperfect items. In the meantime, the supplier correspondingly deals a multi-period delay-in-payments strategy with purchaser. The entire profit has been maximized with paybacks for interim financing. This study aims to develop a synergic inventory model to get the most profit by making an allowance for reworking, multi-period delay-in-payments policy, and shortages. The findings of the proposed model augment inventory management performance by monitoring cycle time as well as fraction of phase with optimistic inventory for a supply chain. The results demonstrate that profit is smaller if the permitted period given by supplier to buyer is equal to or greater than the cycle time, and profit is greater if the permitted period is smaller than the cycle time. The algebraic method is engaged to make a closed system optimum solution. The mathematical experiment of this study is constructed to provide management insights and tangible practices.

A deterministic production inventory model with defective items, imperfect rework process and shortages backordered

The basic assumption of the conventional inventory models is that all items produced are of perfect quality. In practice, some defective items are produced due to process deterioration or other factors. This paper develops a mathematical model for an imperfect production inventory system. It is assumed that the defective items produced in the regular production process consist of scrap, imperfect quality and reworkable items. The rework process is accomplished immediately when the regular production process ends, and the rework process produces scrap, imperfect quality and as-good-as perfect items. A numerical example is provided to illustrate the developed model, and a sensitivity analysis is carried out. It was found that producing scrap and imperfect quality items through the reworking is crucial, since this assumption effects optimal policy. Managerial insights are also presented based on the numerical examples.

An EPQ model for deteriorating items with imperfect production, inspection errors, rework and shortages : a type-2 fuzzy approach

In this paper, a production inventory model is studied considering imperfect production and deterioration of item, simultaneously. Both the serviceable and reworkable items are assumed to deteriorate with time. A cost-minimizing model is developed incorporating both Type I and Type II inspection errors. Shortages are allowed that are completely backlogged. All the screened items are reworked at the end of the production process. To encounter a more practical situation, the deterioration rate is considered to be a type-2 fuzzy number. Such a situation arises when the vendor assigns, with similar priority, a number of experts to determine the rate of deterioration and the decision given by each expert is in linguistic term, which may be replaced by a fuzzy number. The aim of the proposed model is to calculate the maximum back-order quantity allowed and the optimal lot size that must be produced in order to minimize the overall inventory cost. The problem is solved for both the crisp and fuzzy models and a numerical example with practical application is also presented to exemplify the procedure. A novel method for solving a type-2 fuzzy optimization problem is developed which results in a set of Pareto optimal solutions for the proposed problem. It is followed by presenting a sensitivity analysis of various parameters involved on the decision variables and the cost function for a better illustration of the model.

Interval valued EOQ model with two types of defective items

In the classical inventory model, the issue of quality of the product is not considered. It is assumed that all the items procured are of perfect quality. However, in real life production environment it is observed that some of the items produced are defective. Here, we have considered an Economic Order Quantity (EOQ) model with imperfect quality items where the incoming lot has fractions of scrap and re-workable items. These fractions are considered to be known with a certain given percentage. The demand from customers end is met with the perfect and re-worked items and the scrap items are sold differently at a salvage cost in a secondary market. Also to represent the real life situations, the inventory parameters have been taken as interval numbers. The corresponding mathematical problem has been formulated as an un-constrained optimization problem and has been solved using Particle Swarm Optimization (PSO) technique. Finally, the model has been illustrated with a numerical example.

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.

Some Observations to: Lot Sizing with Non-zero Setup Times for Rework

Haji et al. (J Syst Sci Syst Eng 17(2):230–240, 2008) proposed a single machine multiproduct economic batch quantity for an imperfect manufacturing system that includes perfect and re-workable items. They assumed the setup time in rework process is non-zero. They presented two inventory models; one for a single product and one for the case that several products manufactured on a unique machine. However, in these inventory models, there exists the possibility that shortages occur. Therefore, this technical paper identifies some inconsistencies in the research paper of Haji et al. (2008). With a numerical example, it is shown that Haji et al. (2008)’s solution is not held for all instances. Furthermore, this technical paper provides some observations and corrections to the shortcomings in order to improve two solution procedures for single product and multi-product cases.

Joint determination of process mean, price differentiation, and production decisions with demand leakage: A multi-objective approach

The selection of an optimal process mean is an important problem in production planning and quality control research. Most of the literature in this area has focused on the single objective problem of maximizing the profit for a fixed exogenous price. However, it is known that considering multiple objectives (such as gross income from sales, profit, and expected product uniformity) while allowing process mean, production and pricing to vary can significantly improve the profitability and performance of a firm. This article addresses this multi-objective problem while allowing the firm to sell two classes of products at differentiated prices based on their quality characteristics. These products are sold at differentiated prices depending upon their quality characteristics into primary and secondary markets at full and discounted prices respectively. Any nonconforming items are reworked at an additional cost. Due to customers heterogeneity, the firm experiences demand leakage between the two market segments. The proposed joint decision control for the firm includes the joint determination of full and discounted prices, the process mean selection, and the production quantities for each of the two product classes along with expected reworked items. A mathematical formulation of the objectives is first provided and then the multi-objective problem is transformed into a goal-programming problem. A solution procedure is developed using simulation-based optimization to identify Pareto-optimal solutions. Some important characteristics of the solution procedure are discussed and the performance of the approach is corroborated through detailed numerical experiments.

Pricing and lot sizing for an EPQ inventory model with rework and multiple shipments

This paper deals with an economic production quantity (EPQ) inventory model with reworkable defective items when a given multi-shipment policy is used. 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. This portion becomes scrap and only the perfect finished items can be delivered to customers at the end of rework process. A profit function is derived to model the inventory problem and it is shown that the profit function is concave. Due to the complexity of the optimization problem, an algorithm is developed to determine the optimal values of manufacturing lot size and price such that the long-run average profit function is maximized. Furthermore, two special cases are identified and explained. Finally, a numerical example is given to illustrate the applicability of the proposed inventory model.

An imperfect quality economic order quantity with advanced receiving

Differing from previous studies on economic order quantity model with imperfect quality, this paper assumes that a lot received contains either good, re-workable, or scrap items where the re-workable items are stored at a warehouse until a subsequent lot arrives and then these are sent back to the supplier to rework. We propose an imperfect quality inventory model with overlapped and advanced receiving in which the supplier provides a discount rate of procurement cost to compensate the buyer for the additional holding cost and maintain a cooperative relationship. As we expected, a lot sizing policy with overlapped and advanced receiving is developed to generalize the current literature models. It should be noted that the classical EOQ model and Maddah et al’s work (Comput Ind Eng 58:691–695, 2010) are two special cases of our model. A numerical example is given to illustrate the proposed model. In addition, a sensitivity analysis is made to investigate the effects of five important parameters on the optimal lot size and the expected total profit per cycle. Managerial insights are also presented.