Imperfect Production System Research Articles

Integrated multistage supply chain inventory model of multiple retailers with imperfect production and inspection systems

An integrated multistage supply chain inventory model containing a single manufacturer and multiple retailers is proposed to consider deteriorating raw materials and finished products with imperfect production and inspection systems. The main purpose is to jointly determine the manufacturer’s production and delivery strategies and the retailers’ replenishment strategies to maximize the integrated total profit. First, the individual total profit functions of the manufacturer and multiple retailers are established and are integrated to form the total profit function of the supply chain system. Then, to address the model complexity, an algorithm is proposed to obtain the optimal solution. Several practical numerical examples are presented to demonstrate the solution procedure, and a sensitivity analysis is performed on the major parameters. From the numerical results, several findings that differ from those in the previous literature were observed. First, retailers with larger market scale, better cost control, and/or inspection capabilities guarantee higher individual and integrated total profits. Second, increasing the deterioration rates of raw materials and finished products has different effects on the order quantity of raw materials. Third, the manufacturer’s shipping strategy is rigid and not easily changed except for significant changes (increase or decrease by 20%) to the production rate or selling price. The performance of the proposed model has several meaningful management implications.

Coordination and defect management strategy for a two-level supply chain under price and sales effort-sensitive demand

This paper presents a single-manufacturer single-retailer supply chain model with an imperfect production system at the manufacturer. The manufacturer meets the order quantity of the retailer in unequal-sized shipments. After receiving each delivery, the retailer performs an inspection process that is erroneous and results in misclassification errors (Type-I and Type-II errors). Defective items are returned to the manufacturer, who conducts a rigorous screening to classify the defective items into repairable, design-flawed and non-repairable ones. The manufacturer incurs carbon emissions cost due to transportation and disposal of scrap items to get one step closer to sustainability. Customers at the retailer are influenced by retail price and sales effort. Optimal shipment policy, pricing and inventory decisions are determined in both the decentralised (based on the Stackelberg leader-follower gaming approach) and the centralised scenarios. A trade credit mechanism and wholesale price discount contract are employed and a fair profit-sharing strategy is implemented based on the supply chain member's bargaining power. The conditions for participating in these coordination mechanisms are examined from the point of view of each supply chain member. Finally, a numerical experiment along with sensitivity analysis is carried out to illustrate the applicability of the proposed coordination mechanisms and defect management policy.

Minimizing mission cost for production system with unreliable storage

Considerable research efforts have recently been devoted to the reliability analysis and optimization of production systems with product storage. The existing models, however, failed to address a crucial design factor of cost. This paper makes contributions by modeling the expected mission cost (EMC) of an imperfect production system with storage subject to failures during uploading and downloading processes. To perform a successful mission, the system must meet a certain demand during a specified mission time. The EMC modeled encompasses operation and standby cost of the production unit, downloading and uploading cost of the storage, cost of losses associated with the failure of the production unit and storage, as well as penalty cost associated with the mission failure. The optimal EMC problem is formulated and solved, which determines the scheduled storage uploading time to minimize the EMC. A detailed case study of a coal feeding system is conducted to demonstrate the proposed probabilistic evaluation method and influences of different model parameters on the mission success probability and EMC as well as on the optimization solutions. The advantage of using the production storage is also illustrated through a comparison to a dual-production unit system without storage.

Carbon-emission and waste reduction of a manufacturing-remanufacturing system using green technology and autonomated inspection

Environmental-friendly technology helps to reduce waste and carbon emissions of an imperfect production system. In general, the defective products generated during the “out-of-control” state are treated as waste. The single-stage manufacturing-remanufacturing system effectively depletes such defective spare parts within the same cycle but causes a tremendous amount of carbon. In such a circumstance, green technology to reduce carbon emissions is highly recommended. Also, the autonomated inspection makes defective detection more reliable and is ultimately helpful for waste reduction. Hence, in this study, we optimize the production plan along with the investments for applying green technology and autonomated inspection in an assembled product manufacturing-remanufacturing system. The numerical result shows that the appropriate green technology decreases carbon emissions up to 2.81% and autonomated inspection reduces the waste up to 2.37%, along with a reduction of entire production cycle cost up to 18.26%. In addition, the setup cost reduction is considered due to the characteristics of assembled product production.

Sustainable optimal production policies for an imperfect production system with trade credit under different carbon emission regulations

Sustainable optimal production policies for an imperfect production system with trade credit under different carbon emission regulations

Trade Credit Policies for Supplier, Manufacturer, and Retailer: An Imperfect Production-Inventory System with Rework

In this study, we developed a trade credit policy for a three-layer supply chain consisting of a supplier, a manufacturer and a retailer. We propose an optimal production rate and selling price for the manufacturer and the retailer under an imperfect production system. The suggested coordination policy optimizes the profit of each supply chain member. Two models were formulated for two real-life strategies respectively. The first one is a collaborative (integrated) system and the second one is a Stackelberg leadership system. Both strategies were analyzed for various credit periods, respectively offered by the supplier to the manufacturer, by the manufacturer to the retailer, and by the retailer to the customers, by considering price-sensitive demand and a certain replenishment rate. Finally, we concluded which strategy will be better for inventory management under the given restrictions in the form of propositions. The concavity property for the net profit function was established with respect to the selling price and the production rate, which was also described graphically and analyzed by numerical examples.

Optimizing the maximum filling level of perfect storage in system with imperfect production unit

Reliability of production systems with storage has recently attracted lots of research attentions. While the existing works have assumed certain maximum capacity of the storage, no models are available to examine the effects of the storage's maximum filling level Cmax on the mission success probability (MSP). This paper contributes by modeling two-sided effects of Cmax on the MSP of an imperfect production system subject to repairs and preventive maintenance (PM) during the specified mission time. In particular, a larger value of Cmax enables the storage to supply the system demand during a longer time when the production system is under repair or PM (enhancing the MSP); on the other hand, it leads to longer operation periods and consequently more frequent failures of the production system (reducing the MSP). To balance these conflicting effects, we formulate and solve the optimal storage filling problem, which determines the optimal value of Cmax to maximize the MSP. The optimization solution encompasses a new probabilistic model-based numerical algorithm proposed for the MSP evaluation. A case study of a water pump system is performed to demonstrate the influences of several system parameters and their interactions on the MSP and optimized Cmax.

Optimum buffer stock during preventive maintenance in an imperfect production system

The paper investigates a production‐inventory model where regular preventive maintenance starts at the end of production for smooth functioning in the next cycle. During production run time, the manufacturing system may shift from “in‐control” state to “out‐of‐control” state after a certain time. The manufacturing system produces imperfect quality products during “in‐control” state and “out‐of‐control” state with different rates, and these imperfect quality products are reworked at costs in parallel system. The whole items are sold with free minimal repair warranty if any fault arises after sale. This study extends and corrects the Sana's production‐inventory model and derives optimal buffer inventory to minimize the expected costs per unit item. A numerical illustration with its sensitivity analysis of the key parameters is studied to justify the proposed model.

Optimal inventory strategies for an imperfect production system with advertisement and price reliant demand under rework option for defectives

Every industrial sector emits carbon emissions during production, which is always a major concern for environmental practitioners. To resolve this, innovative and smart ways are required that are not only cost-effective but also environmentally savvy. Moreover, the production processes are also prone to various imperfections, and thus the production of defectives is quite pragmatic. The handling of such defective products varies from industry to industry and type of products. The present study constructs an inventory model to handle the defective products via a proficient rework strategy that makes the product fit to be sold at the primary price. Here, the demand for the product is assumed to be dependent on the selling price and advertisements. The model also considers the energy usage during the production and the cost of carbon emissions while optimizing the production batch size and selling price. Optimality is proved graphically by using the software Mathematica 11.3.0. A comprehensive sensitivity analysis for all the parameters is performed to impart managerial insights and robustness to the model.

Joint Design of Control Chart, Production Cycle Length, and Maintenance Schedule for Imperfect Manufacturing Systems with Deteriorating Products under Stochastic Shift Size

This paper presents a hybrid model based on the integration of three interrelated topics including statistical process monitoring (SPM), production cycle length, and maintenance scheduling for imperfect production systems. The proposed model takes both process deterioration and product deterioration into account i.e., the process can go out of control and the products can deteriorate over time. In this regard, a nonuniform sampling strategy is presented for calculating the sampling intervals to avoid exceeding the hazard rate from a threshold value. Moreover, in order to make the model more adapted to real industrial systems, the shift magnitude in the mean parameter of quality characteristic is considered as a stochastic variable. To elaborate the model effectiveness, three comparative studies and a sensitivity analysis are presented. The first comparison shows that by using the variable sampling interval scheme instead of the fixed one, the ratio of in-control time interval to the whole production cycle increases dramatically. Moreover, the use of variable sampling interval scheme leads to a significant cost savings and decreases the out-of-control time interval. The second comparative study indicates that although using statistical considerations in establishment of the control chart imposes a higher cost on the manufacturer, both values of the in-control average run length ([Formula: see text]) and out-of-control average run length ([Formula: see text]) improve significantly. In other words, the use of economic-statistical model reduces the amount of non-conforming products as well as the risk of issuing a false alarm by the control chart. The third comparative study indicates that, in terms of total inventory holding cost, the proposed model performs better than the model without considering deterioration possibility due to the significant reduction in the deterioration cost.

An economic production quantity inventory model for multi-product imperfect production system with setup time/cost function

An economic production quantity inventory model for multi-product imperfect production system with setup time/cost function

Three-echelon supply chain model in an imperfect production system with inspection error, learning effect, and return policy under fuzzy environment

This article presents a three-echelon supply chain (SC) model, incorporating a single supplier, a single manufacturer, and a single wholesaler under fuzzy system. Three scenarios have been considered: (a) the learning effect (LE) of the employees on the production cost as well as the return contract (RC) between the supplier and an outside supplier and also between the manufacturer and the wholesaler, (b) without considering the LE on the manufacturing expenses and (c) without the RC between the SC players. The goal of this paper is to study the effect of the LE and the RC on total profit of the SC for centralised and decentralised cases. To adopt flexibility of the demand parameters of the entire process, we develop a fuzzy mathematical model of the proposed SC problem. To discuss the novelty of the proposed model, we insert a table of authors’ contribution and also perform numerical illustrations with the help of LINGO software and make a comparative study between the optimal results of the existing method and the proposed fuzzy approach. Sensitivity analysis and graphical illustrations have also been done for better realisation of the model followed by conclusion.

An Imperfect Production–Inventory Model with Mixed Materials Containing Scrap Returns Based on a Circular Economy

The implementation of scrap recovery activities has been shown to improve the financial performance of many firms, and this kind of circular economy (CE) is particularly evident in industries with green manufacturing (GM). In this paper, we consider an imperfect multiple-stage production system that manufactures paired products made from mixed materials containing scrap returns, in which the scrap returns are converted from defective products. The feed rates of scrap returns for two products are different, and the product with the higher feed rate is placed in the second order of the process to avoid unlimited accumulation of scrap returns. The proposed problem is formulated as a joint economic order quantity (EOQ) and economic production quantity (EPQ) model aimed at cost minimization. The decision variables of the proposed model include the production run time of two products, order quantity of new material, and the extent of investment in converted equipment. We also prove that the optimal solution exists uniquely and provide an algorithm for the computation of the optimal solution. Finally, a numerical example involving the pulp and paper manufacturing industry is provided to illustrate the solution process, and the results of its sensitivity analysis are also presented to show some managerial implications.

Work performance dependent screening process under preservation technology in an imperfect production system

ABSTRACT This study presents an EPQ inventory model which provides some imperfect quality products. Initially, due to the existence of all fresh sources, the system remains in good condition, i.e., in-control state. But, after a certain time of production, this system must produce some defective items with the perfect ones, i.e., the system goes into an out-of-control state. Here, the transition time from one state to another state has been considered as a random variable. Besides that, a generalized screening process has been proposed which is based on the work performance of a worker that also depends on time, this is the key contribution of this study. Also, we have considered a preservation investment cost in the manufacturing system to control the defective rate. A generalized stochastic demand function has been proposed. Finally, numerical implications, managerial implications, and conclusions are made for the justification of my proposed model.

A Sustainable Economic Recycle Quantity Model for Imperfect Production System with Shortages

Recycling of products has a great impact on contemporary sustainable business strategies. In this study, a sustainable recycling process in a production-inventory model for an imperfect production system with a fixed ratio of recyclable defective products is introduced. The piecewise constant demand rates of the non-defective items are considered under production run-time, production off-time with positive stock, and production off-time with shortages under varying conditions. Based on the production process, two cases are studied using this model. The first case does not consider recycling processes, while the second case picks up all defective items before sending these items to recycling during the production off-time; the recycled items are added to the main inventory. The aim of this study is to minimize the total cost and identify the optimal order quantity. The manufacturing process with the recycling process provides a better result compared to without recycling in the first case. Some theoretical derivations are developed to enunciate the objective function using the classical optimization technique. To validate the proposed study, sensitivity analysis is performed, and numerical examples are given. Finally, some managerial insights and the scope of future research are provided.

A deterministic economic production quantity model with partial backordering and outsourcing repair of non-conforming products

In this paper, an economic production quantity model for an imperfect production system with reparation of non-conforming products is studied. The system allows shortages and a proportion of the shortages are backordered, following a last-in/first-out (LIFO) policy. It is assumed that the repair of non-conforming products cannot be carried out in the manufacturer's production system. Therefore, the company decides to have the repairs carried out in a repair centre. Depending on the time when the consignment of reworked items returns to the manufacturer's stocks, this study identifies three cases. The paper shows the derivation of the optimal solution for each case. The required conditions for the initial value of the backordering rate are developed in order to achieve optimal partial backordering. The model is also compared with a modified version that includes not only outsourcing repair of non-conforming products but also full backordering. The numerical examples comparing full backordering with partial backordering indicate that partial backordering is more profitable than full backordering when return of the repaired items to the system leaves a negative inventory level; that is, when there is a shortage.

A production-repairing inventory model considering demand and the proportion of defective items as rough intervals

This paper explores a production inventory model in an imperfect production system under a rough interval environment. The occurrences of shortages are allowed and are fully backlogged. In this paper, two models are presented. In the first model, the demand of the product is considered as a rough interval. In the second model, both the demand and the defective rate are considered as rough intervals. In reality, these two factors cannot be assessed exactly due to a lack of available data. Moreover, there are few scenarios where the demand of the product is assessed in two-layer information. The inner layer demand is obvious, and it may extend up to the outer layer depending on the situation. Also, the same thing may happen for the defective rate of the product. In those cases, it is more reasonable to express the demand and the defective rate as rough intervals instead of fuzzy or interval numbers. Based on the expected value of rough intervals, the necessary and sufficient conditions are determined analytically to obtain the optimal inventory policies. The main advantage of this method is that the optimal profit and the optimal lot size are determined as crisp numbers rather than rough intervals. Obtaining a precise value for these two quantities is desirable for any production manager. Numerical examples for both models are provided to illustrate the solution methodology. Sensitivity analysis of the optimal solutions concerning the key parameters is conducted for identifying several managerial implications.

Sustainable inventory policy for imperfect production system with imperfect rework and defective sales return

Sustainable inventory policy for imperfect production system with imperfect rework and defective sales return

Sustainable Inventory Policy for Imperfect Production System with Imperfect Rework and Defective Sales Return

Over the last decade, environmental issues like global warming have become more critical to address. Thus, organisations are turning their attention towards tracking the carbon emissions of their processes. Further, despite technological advancements, industries even now face the problem of imperfect items during production. Thus, it gets imperative to screen the produced units before dispatching them to the retailer. Realistically, screening is prone to human errors. To enhance their customer's post-buying experience, the manufacturer allows the return of defective items. Towards his social responsibility, the manufacturer tries to reduce the environmental impact of the production process. Consequently, rework of the defective items has been undertaken. Moreover, rework process too is assumed to be imperfect. Further, carbon emissions during production, warehousing, rework and disposal have been considered. This study presents an inventory production model incorporating all the above-mentioned aspects. A closed-form solution along with an illustrative numerical example has been provided.

An integrated inventory model for imperfect production system incorporating marketing decisions with an investment in preservation technology

An integrated inventory model for imperfect production system incorporating marketing decisions with an investment in preservation technology