Imperfect Production Research Articles

An imperfect production inventory model with advance payment and credit period in a two-echelon supply chain management

This paper presents an integrated imperfect production inventory model under two layer supply chain management. To ensure the orders, manufacturer convinces the retailer to pay a percentage of the purchasing cost prior to replenish the products and offers the facilities such as (i) delay in payment on the remaining part of the purchasing cost and (ii) free transportation on the basis of advance payment amount. Time dependent development cost is incurred to maintain the reliability of the production system and as a result it reduces the imperfectness of the product during production. Under such circumstances, an integrated profit function has been developed to find the optimum number of production cycle, optimum number of replenishment cycle and hence reliability parameter of the manufacturing system, replenishment quantity for the retailer which maximize the integrated profit. Branch and Bound technique is used to obtain the integer solutions. Furthermore, we derived some useful lemmas and algorithms to obtain the optimum solution. Finally, the model has been illustrated with some numerical examples exploring the sensitivity analysis with respect to some parameters and obtains some managerial insights.

Quality Inspection Plan for Imperfect Production System with Assembly Configuration

In this study, the model concerning a negative binomial sampling inspection plan is proposed and applied to an imperfect production system with assemble-to-order configuration, where the production system is subject to a Weibull deteriorating process and is operated under an in-control or an out-of-control state. The proposed model of this study contributes to developing an approach which can effectively integrate the considerations of the production system status, the defective rate, the working efficiency of employees, and the market demands with an aim to determine the optimal number of conforming items for inspection with minimum total cost, and the results can be practically applied to the assembly of products in various industries, especially for the prevalent Industry 4.0 in manufacturing.

A Sustainable Inventory Model with Imperfect Products, Deterioration, and Controllable Emissions

Maintaining product quality and environmental performance are emerging concerns in modern competitive and transparent businesses. Many retailers separate perfect products from imperfect ones to ensure product quality and endeavor to achieve carbon dioxide (CO2) reduction through green technology investments and sustainable inventory planning. Product deterioration often badly hampers the retailing business; hence, suitable preservation technologies are used. In this study, we examined the optimization model of the selling price, investment, and replenishment planning to maximize the total profit. The proposed model considered the effect of a greater deterioration rate and discount price of imperfect products. Due to the high uncertainty in demand, a realistic holding cost was deliberated with a variable and constant part. Every time the retailer transports purchased items, greenhouse gases (GHGs), including CO2, are produced. Government regulations on CO2 minimization and customer awareness for greener products stimulate retailers to invest in energy-efficient green technology. This study simultaneously showed a harmonious relationship among the attributes of preservation technology, green technology investment, and discounts on defective items. Theoretical derivations were performed with numerical analysis.

Shipment Policy for an Economic Production Quantity Model Considering Imperfection and Transportation Cost

Determining replenishment lot size and number of shipments in a traditional production setup has been of great interest among researchers during the last decades. In order to survive modern competition, the manufacturer has to make good decisions about the lot size that is to be shipped to the retailer. Recently, several researchers have developed mathematical models for modelling different real-world situations; however, these models are lacking due to a combination of imperfection in process and shipment lot sizing. Therefore, in the proposed research, shipment policy for an imperfect production setup has been developed with transportation costs taken into consideration. The model analyzed lot sizing for manufacturers and retailers with imperfections in terms of equally sized shipments. Furthermore, an all-unit-discount policy for shipment is considered in the proposed research, and at the end, numerical computation and sensitivity analyses are carried out to gain more insight into the specifications of the model.

Optimal price and quality decisions of a supply chain game considering imperfect quality items and market segmentation

Imperfect production processes are frequently investigated in supply chain literature. Many recent articles assume that items that do not meet the quality requirements can be sold on a secondary market at a reduced price. Due to simplification, these papers ignore the demand of the secondary customers and assume instead that all imperfect quality items are salable. In this paper, we show that this ignorance can lead to unrealistic results as an unrestricted secondary market may reduce the manufacturer’s incentive for an error-free production process. By introducing a price- and quality-dependent demand for both the primary and secondary markets, we obtain the following main insights: (i) a restricted secondary market leads to more realistic results compared with the unrestricted case; the secondary demand is only ignorable under certain conditions; (ii) quality decisions are mainly influenced by the market parameters of both market segments as well as quality cost parameters; (iii) in some cases, it is advantageous not to serve the secondary market and to concentrate the sales process on primary customers.

Imperfect and variable production cost in three-layer supply chain system incorporating deterioration and screening effect

This paper develops a three-layer supply chain for defective and non-defective types of produced items by supplier and manufacturer. The condition of the chain that without any financial liability on the manufacturer, defective items will be sent back to the supplier after screening. In the subsequent stage, the retailer accepts the non-defective items produced by the manufacturer after the screening and sends back the defective items to the manufacturer. Hence the retailer receives the perfect quality items for selling to the customers, but the retailer considers the effect of the deterioration of items. This model also considers the impact of several business strategies such as; optimal order size of raw materials, production rate, unit production cost, idle time costs of the supplier, and manufacturer in a collaborative marketing system, etc. to determine the optimum average profit of the integrated model. This study discusses the selling price of the retailer, demand rate of the customer, purchase cost of supplier and holding cost, which can be a significant breakthrough in expanding the profit of the business in real terms. Numerical example and sensitivity analysis are presented to illustrate the phenomenon of theoretical study and demonstrate the managerial implication of the model.

Autonomated Inspection Policy for Smart Factory—An Improved Approach

The proposed model focuses on an imperfect production process (IPP) in which, during long-term production, the system may change to an “out-of-control” state from an “in-control” state and produce some imperfect products because of a long production run length. Brand image and industry reputation are affected by product defectiveness. To increase the profit of any industry and improve reputation and brand image, inspection of the production system is required. However, this inspection is subjected to human error, which negatively affects the assessment of production systems. Herein, an error-free inspection is performed with the help of an autonomation policy, in which each product is inspected via a machine instead of a human, facilitating an error-free inspection and converting the production system to a smart production system. Moreover, in reality, product demand cannot always be constant. Therefore, in this model, a selling-price-dependent demand is considered along with a variable production rate to enhance model applicability. Moreover, total system profit is optimized and optimal values for production run time, inspection scheduling, selling price, buffer inventory, and production rate are determined. Finally, for model validation, some numerical examples along with special cases are provided. The concavity of the optimal function is also proven through graphical illustration. The sensitivity of the key parameters of the presented model is explored and the significance is explained.

Optimizing an Imperfect Production Model with Varying Setup Cost, Price Discount, and Lead Time Under Fuzzy Demand

This article considers the two-tier supply chain based on the single setup multiple delivery (SSMD) policy between a single vendor and a single buyer. The entire production process is performed in a single setup and the logarithmic reduction function is employed to reduce the expense of this setup. As the machine switches from the in-control stage to the out-of-control stage, the output of the manufactured item is found to be defective. Continuous investment has been made to reduce this imperfect production by improving the quality of the item. Furthermore, this model takes into account incomplete product restructuring. In some cases, due to certain issues, such as lead time, the order quantity may not be received on time. The buyer’s lead time duration is controlled by adding the crashing cost. The purpose of this research is to achieve optimum setup cost and defective item percentage with minimum total supply chain cost under a triangular fuzzy demand. Two numerical examples have been considered to evaluate this model. Moreover, sensitivity analysis, graphical representation, and managerial insights are given. Finally, the model obtains the minimum supply chain cost with decision variables as demonstrated by the numerical study.

A single-stage cleaner production system with random defective rate and remanufacturing

This paper investigates an impact of random defective rates in an imperfect production system with multiple products and planned backorders in a single-stage production system. The purpose of this study is to control a single-stage cleaner production system with a random defective rate for multiple products. Considering these, the model becomes a non-linear constraint problem. Based on different distribution functions of random defective rates, to eliminate the defective items from the system, five special cases for effective system management are considered. A non-linear optimization technique is utilized to solve the model and obtain the global optimum solution of cleaner production system with multiple products and a global optimum solution. Numerical examples, graphical representations, and sensitivity analysis are given to illustrate the model. Numerical studies prove that the cost related with a Chi-square distribution gives the least cost and cost related with a beta distribution gives the maximum cost, whereas the literature shows a triangular distribution gives the minimum cost.

An Optimal Two-level Supply Chain Model for Small and Medium-sized Enterprises with a rework for New Products and Price-Dependent Demand

The advent of new technologies, globalization of markets, customers' varied needs, and increasingly fierce competition, is making SMEs seek to improve engagement with their suppliers and cost management practices in order to survive. Thus, SMEs clearly need to focus on the interests of the entire supply chain by enacting win-win policies. In this study, we investigate a two-level inventory model featuring a manufacturer and a buyer in the competitive market with the policy of producing new products. Imperfect quality products and the capacity to rework are also considered in the model. In other words, because of the competitive nature of the market, any increase in price leads to a decrease in demand. The mathematical model is proposed over two scenarios: a scenario where shortage can occur, and one with no possibility of shortage. The objective function of the mathematical model revolves around the central goal of maximizing the total profit of the supply chain considering both independent and joint optimization by the supply chain members. A new algorithm is proposed to solve the mathematical model whose applicability is evaluated by giving a numerical example to the analysis software MATLAB. The final results are analyzed and discussed using sensitivity analysis approach.

An Inventory Model based on Imperfect Production with Shortage Backorder

In this paper, we discussed about the imperfect items. In practice items may get damaged due to production or transportation conditions. Each lot receives some imperfect items. This model also considers the effects of business strategies such as optimal order size of raw materials, production rates and unit production costs, and idle time in different areas on the cooperation of marketing systems. The model can be used in industries such as textiles and footwear, chemicals, food. We develop an inventory model based on imperfect products and shortages. We consider demand is constant and continuous. Purpose of this study is not only to find the retailer`s optimal replenishment policies but also to minimize the total average cost. Finally, a numerical example is presented to illustrate the proposed model and sensitivity analysis of the optimal solution concerning parameters is carried out using the Mathematica 10.0 software.

Cooperative sustainable supply chain for deteriorating item and imperfect production under different carbon emission regulations

Operational adjustments in a supply chain and efficient inventory management, especially when demand is uncertain, can turn out to be an effective way in emission reduction. Different emission regulation strategies influence the firms to redesign their supply chain for sustainable management. This paper develops a sustainable supply chain inventory management (SSCIM) model for a single-manufacturer and a single-buyer’s integrated approach by considering item deterioration and imperfect production simultaneously. Rework facility of produced imperfect items is available. Carbon emissions through production, transportation, warehousing and disposal of the deteriorated items are considered. Our objective here is to implement different regulatory policies (mainly carbon tax, carbon cap-and-offset and cap-and-trade) of emission reduction which mitigate the effect of carbon emission by reducing its volume. We also focus on finding a trade-off between overall generated cost and carbon emission. Hence, the mathematical model of proposed SSCIM is formulated in bi-objective framework for the purpose to minimize the operational cost and carbon emission. Furthermore, fuzzy rule base approach, which is based on some existing survey records over the past years, is employed to predict the customers’ demand. The derived mathematical model and solution methodology are discussed and thereby illustrated with the help of numerical examples. Sensitivity analysis accounting to changes in the parameter values is also examined to highlight the managerial insights.

Analytics of an Imperfect Four-Layer Production Inventory Model Under Two-Level Credit Period Using Branch-and-Bound Technique

This paper explains an integrated production inventory supply chain model, which consists of a supplier, a manufacturer and a retailer under two-level credit period. One is manufacturer’s credit period offered by the supplier, and other is retailer’s credit period offered by the manufacturer. Here, the manufacturer replenishes raw materials from the supplier and produces non-deteriorating products in some cycles of equal length. It is noted that here four inventory structures have been considered to show the flow of the materials as either raw materials or finished products from supplier to retailer via manufacturer. Also in this model, manufacturer’s imperfect production has been considered. Here imperfect items are not repairable. The retailer receives good finished products from the manufacturer and sells these to his/her customers during some cycles of equal length in total time horizon. Our main objective is to find the optimal number of production and business cycles of the manufacturer such that the integrated system can get the maximum profit. The above discussed model is elaborated with the help of a numerical example, and a sensitivity analysis is done with respect to some parameters used in this model.

Inventory Control Policy for Imperfect Production Process on Various Demand and Fuzzy Nature: Latest Trend

Inventory Control Policy for Imperfect Production Process on Various Demand and Fuzzy Nature: Latest Trend

A Study and Comparison of Shipment Policies with Repair Options in a Two-Tier Supply Chain Model

Vendors often sell their products to buyers far away. Frequently, a few products in the lot are found to be imperfect, but because of the distance to the vendor, it is not cost-effective for the buyer to place another order to replace the imperfect products with good ones. These imperfect products are still valuable and can be repaired, so the buyer has them repaired at a nearby shop and restores them to the inventory. The buyer pays a repair charge plus a markup margin. A two-tier supply chain problem will be studied in this paper under the EOQ (Economic Order Quantity) model, considering the issues of a single buyer and a single vendor and aiming to minimize the total costs for both entities. Based on three supply-chain structures, this paper presents three models, providing engineering managers with guidelines for the selection of a cost-effective supply chain inventory system through analysis of different shipment policies. The shipment policies used for these models were, first, equal-sized, then geometric, and finally, geometric-then-equal-sized. The total expected cost per unit time under each policy is calculated and a proposal is developed for the solution procedure. The paper then proceeds to make a comparative analysis of the three shipment policies in the context of the two-tier supply chain problem. A discussion of the results is illustrated by a numerical example.

Disruption management in a constrained multi-product imperfect production system

Over several decades, production and inventory systems have been widely studied in different aspects, but only a few studies have considered the production disruption problem. In production systems, the production may be disrupted by priorly unknown disturbance and the entire manufacturing plan can be distorted. This research introduces a production-disruption model for a multi-product single-stage production-inventory system. First, a mathematical model for the multi-item production-inventory system is developed to maximize the total profit for a single-disruption recovery-time window. The main objective of the proposed model is to obtain the optimal manufacturing batch size for multi-item in the recovery time window so that the total profit is maximized. To maintain the matter of multi-product, budget and space constraints are used. A genetic algorithm and pattern search techniques are employed to solve this model and all randomly generated test results are compared. Some numerical examples and sensitivity analysis are given to explain the effectiveness and advantages of the proposed model. This proposed model offers a recovery plan for managers and decision-makers to make accurate and effective decisions in real time during the production disruption problems.

Sustainable inventory policy for an imperfect production system with energy usage and volume agility

A sustainable production inventory model that addresses some of the pragmatic scenarios of the production process is developed. The production process is considered imperfect which results in the production of some imperfect quality items with known distribution. The imperfect products are managed through an efficient rework process that makes the items suitable to be vended at their original markup price only. The agile nature of the manufacturing process is considered. And, the energy usage and carbon emission in the production process is also considered. Undoubtedly, the fundamental nature of demand is sensitive to price. Thus, the model incorporates the demand to be price-contingent. The objective is to maximize the overall inventory turnover by conjointly optimizing the selling price, production rate, and production time. A numerical example is included to validate the model. Further, the sensitivity analysis unfolds valuable managerial insights for decision-makers. Findings suggest that the model with the insertion of volume agility effect performs better when compared with the one without the volume agility.

Disorder-dressed quantum evolution

The active harnessing of quantum resources in engineered quantum devices poses unprecedented requirements on device control. Besides the residual interaction with the environment, causing environment-induced decoherence, uncontrolled parameters in the system itself -- disorder -- remains as a substantial factor limiting the precision and thus the performance of devices. These perturbations may arise, for instance, due to imperfect sample production, stray fields, or finite accuracy of control electronics. Disorder-dressed quantum evolution means a unifying framework, based on quantum master equations, to analyze how these detrimental influences cause deviations from the desired system dynamics. This description may thus contribute to unveiling and mitigating disorder effects towards robust schemes. To demonstrate the broad scope of this framework, we evaluate two distinct scenarios: a central spin immersed in an isotropic spin bath, and a random mass Dirac particle. In the former scenario, we demonstrate how the disorder average reflects purity oscillations, indicating the time- and state-dependent severity of the disorder impact. In the latter scenario, we discuss disorder-induced backscattering and disorder-induced Zitterbewegung as consequences of the breakup of spin-momentum locking.

Effect of inspection errors on imperfect production inventory model with warranty and price discount dependent demand rate

This paper deals with selling price-discount and warranty period dependent demand in an imperfect production inventory model under the consideration of inspection errors and time dependent development cost. Normally, due to long-run, a production process deteriorates with time and here we assume that the process shifts from "in-control" to "out-of-control" state at any random time. A time dependent development cost has been constructed to increase the reliability of the production systemi.e., to decrease the deterioration of the system during the production process. As a result, a few items are rejected. Here, two types of inspection errors such as Type-I error and Type-II error, have been considered during the period of product inspection process. In Type-I error, an inspector may choose falsely a defective item as non-defective and in Type-II error an inspector may choose falsely a non-defective item as defective. Due to these phenomena, the inspection process would consist of the following costs: cost of inspection, cost of inspection errors. The purpose of this paper is to investigate the effects of time dependent development cost on the defective items, selling price-discount and warranty policy on the market demand and finally optimize the expected average profit under consideration of such inspection costs in infinite time horizon. Some numerical examples along with graphical illustrations and sensitivity analysis are provided to test the feasibility of the model.

An EPQ Model for Deteriorating Items With Imperfect Production, Two Types of Inspection Errors and Rework Under Complete Backordering

This paper presents an EPQ model which illustrates imperfect production and imperfect inspection processes for items that are subject to a constant rate of deterioration. The model considers two types of inspection errors, namely, Type I error of falsely screening out a proportion of nondefects, thereby passing them on for rework and Type II error of falsely not screening out a proportion of defects, thus selling those to customers which results in defect sales returns. The screened and returned items are then reworked and the proportion that could not be reworked successfully is scrapped. Shortages are allowed and are completely backlogged. Finally, we calculate the optimal production lot size and the optimal backordering quantity in order to minimize the total inventory cost per unit time. A numerical example is also considered to exemplify the obtained theoretical results which is followed by the complete sensitivity analysis of the involved parameters for even better managerial insights.