Imperfect Production Process Research Articles

Setup cost reduction EMQ inventory system with probabilistic defective and rework in multiple shipments management

This paper considers an economic manufacturing quantity (EMQ) model for defective products with imperfect production processes and rework, in which the setup cost is logarithmic function of capital investment. In this study, fixed quantity multiple installments of the finished batch are delivered to customers at a fixed interval of time. We also consider three types of continuous probabilistic defective function to find the associated cost. The way our basic business operations like decision making, marketing strategies, financial management, etc. are done are being reformed with the use of computers and mathematics. In view of that the mathematical modeling and computational algorithm are employed in this study for optimizing the replenishment lot-size and setup cost simultaneously with the objective of minimizing total cost of the EMQ system. The long-run average cost function is derived, its convexity is proved via differential calculus. A computer code using the software Matlab is developed to derive the optimal solution and present numerical examples to illustrate the model.

An integrated supply chain model for deteriorating items considering delay in payments, imperfect quality and inspection errors under inflationary conditions

In this article, an integrated production–distribution model is presented for a manufacturer and retailer supply chain under inflationary conditions, permissible delay in payments, deterioration, imperfect production process and inspection errors. We assume that the first-stage inspection of the manufacturer is not perfect and makes inspection errors of Type 1 and Type 2. The second-stage inspection of the manufacturer is at the end of production period without inspection errors. Also, the demand is linear function of time. Once the retailer receives the lot, a 100% screening process of the lot is conducted without inspection errors, and the screening process and demand proceed simultaneously. The main objective is to determine the optimal inspection time and the optimal number of cycle such that the present value of the total cost is minimized. Finally, a numerical example and sensitivity analyses are provided to illustrate the proposed model using a proper algorithm.

A reverse logistic inventory model for imperfect production process with preservation technology investment under learning and inflationary environment

A reverse logistic inventory model for imperfect production process with preservation technology investment under learning and inflationary environment

EPL models for complementary and substitute items under imperfect production process with promotional cost and selling price dependent demands

This paper considers a multi-item, imperfect economic production lot-size (EPL) model with advertisement/promotional cost and selling price dependent demand and partially rework under a budget constraint. The items are either complementary or substitute to each other. In the EPL models, defective production commences from the out-of-control state, after the passage of some time from production commencement. Its occurrence is random after the lapse of certain time and it is imposed here through a chance constraint. The set-up cost is partly production dependent. Unit production cost is also production dependent and a part of it is taken as environment protection cost. Defective rate is also assumed to be random and production dependent. The model is formulated as an average profit maximization problem subject to chance constraints and a budget constraint and solved using the generalized reduced gradient method (GRG). Several special cases are derived and numerical experiments are performed to illustrate the general and particular models. Some sensitivity analyses are presented against few model parameters.

Modified Imperfect Economic Manufacturing Quantity Model with Limited Investment Capital

Traditional economic manufacturing quantity model assumes that the perfect product for production. Recently, Teng proposes an imperfect production process with limited investment capital for determining the optimal investment cost and production run time. Teng assumes that the percentage of process defectives with uniform distribution is a decreasing function of the investment cost. However, Teng's model does not include the customer's used cost for the conforming product. In this study, the authors adopt another investment cost function, i.e., the exponential reduction of process mean and standard deviation as the function of quality investment cost, for formulating the modified Teng's model. Taguchi's quadratic quality loss will be used for measuring the product quality. Finally, the numerical example and sensitivity analysis of parameters are provided for illustration.

A Production: Inventory Model for Defective Items with Shortages Incorporating Inflation and Time Value of Money

This paper develops a production-inventory model of a single product with imperfect production process in which inflation and time value of money are considered under shortages. Demand rate has been considered to be a function of quadratic decreasing and exponential decreasing of selling price. The selling price of a unit is determined by a mark-up over the production cost. Unit production cost is considered incorporating several features like energy and labour cost, raw material cost, replenishment rate and other factors of the manufacturing system. The defective items which is a certain fraction of the total production or a random number are either reworked or refunded if those reach to the customer. Two scenarios have been considered in which defective items are refunded from the customer with penalty in scenario (a) and the defective items are repaired and sold to the customer as good items in scenario (b). Based on these two scenarios, three models have been developed in which defective items are certain fraction of the produced quantity in Model-I, a random number in Model-II, and are dependent in reliability parameter and time in Model-III. Considering all these phenomena optimum production of the product has been evaluated to have maximum profit. Finally, numerical examples are given to illustrate the results along with graphical analysis. Sensitivity analysis has also been carried out for different values of the parameter.

Applying Game Theory to Competitive Production-Inventory Models with Vendor's Imperfect Production Processes and the Condition of Buyer's Exemption from Inspection

This study establishes the competitive production-inventory models with vendor’s imperfect production processes by using game theory. The imperfect production processes can be improved by capital investment which is shared out between the vendor and the buyer jointly. In addition, the inspection process is assumed to be imperfect and Type I and Type II inspection errors occur during product quality inspection. We first develop the total cost per unit time of the buyer and vendor, respectively and then seek the optimal buyer’s order quantity, vendor’s shipping times and defective rate of the product where the system achieves a Nash equilibrium. The necessary and sufficient conditions of the existence and uniqueness of the optimal solutions for the buyer and the vendor respectively are shown. Furthermore, we develop a algorithm to find the optimal solutions. Finally, an numerical example are presented to demonstrate the solution procedure.

Managing risk and disruption in production-inventory and supply chain systems: A review

This paper presents a literature review on risk and disruption management in production-inventory and supply chain systems. The review is conducted on the basis of comparing various works published in this research domain, specifically the papers, which considered real-life risk factors, such as imperfect production processes, risk and disruption in production, supply, demand, and transportation, while developing models for production-inventory and supply chain systems. Emphasis is given on the assumptions and the types of problems considered in the published research. We also focus on reviewing the mathematical models and the solution approaches used in solving the models using both hypothetical and real-world problem scenarios. Finally, the literature review is summarized and future research directions are discussed.

Dynamic lot-sizing with rework of defective items and minimum lot-size constraints

In most production processes, defective items may result from an imperfect production system and the need of reworking them is inevitable in many production environments. Despite the great importance of rework in real-world manufacturing, the body of literature is very limited. This paper deals with the effects of defective items and rework on the Capacitated Lot-Sizing Problem (CLSP). We present a mixed-integer programming formulation of the CLSP with rework of defective items and minimum lot-size constraints on production lots. The formulation describes an imperfect production process that leads to a fraction of defective items that have to be reworked before they can be sold to customers. Detailed numerical experiments show that while the occurrence of defective items significantly increases the computational times, reasonably sized minimum lot-size constraints, besides their practical importance, can be a good strategy to accelerate the solution process.

An EMQ inventory model for defective products involving rework and sales team’s initiatives-dependent demand

This paper investigates the issue of an economic manufacturing quantity model for defective products involving imperfect production processes and rework. We consider that the demand is sensitive to promotional efforts/sales teams’ initiatives as well as the setup cost can be reduced through further investment. It also assumes that fixed quantity multiple installments of the finished batch are delivered to customers at a fixed interval of time. The long-run average cost function is derived and its convexity is proved via differential calculus. An effective iterative solution procedure is developed to achieve optimal replenishment lot-size, setup cost and the initiatives of sales teams so that the total cost of system is minimized. Numerical and sensitivity analyses are performed to evaluate the outcome of the proposed solution procedure presented in this research.

A multi-item EPQ model with imperfect production process for time varying demand with shortages

In this paper, economic production quantity(EPQ)models for break- able or deteriorating items are developed with time dependent linear variable demands. Here rate of production and holding cost are time dependent and unit production cost is a function of both production reliability indicator and production rate. Set-up cost is also partially production rate dependent. Here two models are developed in optimal control framework considering the effect of time value of money and inflation. Shortages are allowed for both the models. The problems are solved using Eulers-Lagrangian function based on variational calculus and applying generalized reduced gradient method using LINGO 13.0 software to determine the optimal reliability indicator (r) and then corresponding production rates and total profits. Numerical experiments are performed for both the models to illustrate the models both numerically and graphically.

Contract Types and Supplier Incentives for Quality Improvement

When firms outsource production to suppliers, a key concern is how to control product quality and to motivate the supplier to invest in quality improvement. In practice, several kinds of quality management contracts are commonly used, such as subsidizing the supplier’s quality investment, setting a defect rate target, and a combination of both. This paper analyzes and compares the effectiveness of these approaches in a stylized two-echelon supply chain with deterministic market demand and imperfect batch production process. We show that the appropriateness of a contract form depends on the supplier’s initial quality level as well as the information structure about this level.

Joint determination of process quality level and production run time for imperfect production process

Chung and Hou develop a deteriorating production system with allowable shortage for determining the optimal production run time. The rework cost of the defective products is included in their model. However, they did not consider the quality cost of non-defective products. In this study, the author proposes a modified Chung and Hou’s model for obtaining the optimal production process parameters (process quality level and production run time) under the minimization of the expected total relevant cost of product per unit time. Taguchi’s asymmetric quadratic quality loss function is used for measuring the product quality.

An integrated multi-stage supply chain inventory model with imperfect production process

This paper deals with an integrated multi-stage supply chain inventory model with the objective of cost minimization by synchronizing the replenishment decisions for procurement, production and delivery activities. The supply chain structure examined here consists of a single manufacturer with multi-buyer where manufacturer orders a fixed quantity of raw material from outside suppliers, processes the materials and delivers the finished products in unequal shipments to each customer. In this paper, we consider an imperfect production system, which produces defective items randomly and assumes that all defective items could be reworked. A simple algorithm is developed to obtain an optimal production policy, which minimizes the expected average total cost of the integrated production-inventory system.

Manufacturing system with immediate rework and partial backordering

This paper extends a manufacturing system with manufacturing capacity limitation, immediate rework, imperfect production processes and partial backordering in a multi–product single–machine manufacturing system. The primary aim of this research is to minimise the total cost by deriving the optimal periodic length, backorder, and order quantities. The objective function of the proposed model is proved to be convex, and two numerical examples are used to illustrate the proposed method. Finally, sensitivity analysis is performed to demonstrate the applicability of the proposed model in the real world environments and to provide some managerial insights for practitioners.

Optimal production lots for items with imperfect production and screening processes without using derivatives

Complicated traditional computing processes take the first and second order derivatives to obtain the EOQ/EPQ formula that are difficult to understand. This study proposes an EPQ model for imperfect items, which utilises a simple computing method without using derivatives and considers different screening rates to obtain the optimal production lots. The analytical method for sensitivity analysis is examined. A numerical example is provided to illustrate the proposed model. Using the proposed model, researchers who are unfamiliar with calculus may be able to find a solution to procedures with inventory problems more easily.

Optimal production run length for an imperfect production process with allowable shortages in fuzzy random environments

In this article, we develop a model to determine the economic production run length for a deteriorating production system and allowable shortages in fuzzy random environments. Based on the credibility measure of fuzzy event, the economic production quantity model with fuzzy random elapsed time can be transformed into a crisp model when deriving the expected total cost per unit time. The optimal production run length is proved to exist and be unique. Bounds for the optimal production run length are provided. Furthermore, the bisection method searching for the optimal production run length is designed. The relevant applications of the model are outlined. Finally, a numerical example is given to confirm the proposed model.

EPQ model for imperfect production processes with rework and random preventive machine time for deteriorating items and trended demand

Economic production quantity (EPQ) model has been analyzed for trended demand, and units in inventory are subject to constant rate. The system allows rework of imperfect units, and preventive maintenance time is random. A search method is used to study the model. The proposed methodology is validated by a numerical example. The sensitivity analysis is carried out to determine the critical model parameters. It is observed that the rate of change of demand, and the deterioration rate have a significant impact on the decision variables and the total cost of an inventory system. The model is highly sensitive to the production and demand rate.

A production-inventory model with imperfect production process and partial backlogging under learning considerations in fuzzy random environments

In this paper, we investigates the learning effect of the unit production time on optimal lot size for the imperfect production process with partial backlogging of shortage quantity in fuzzy random environments. It is assumed that the setup cost, the average holding cost, the backorder cost, the raw material cost and the labour cost are characterized as fuzzy variables and the elapsed time until the machine shifts from "in-control" state to "out-of-control" state is characterized as a fuzzy random variable. As a function of these parameters, the average total cost is also a random fuzzy variable. Based on the credibility measure of fuzzy event, the fuzzy random total cost function is transformed into an equivalent crisp function. We propose an algorithm to determine the optimal solution. Furthermore, the model is illustrated with the help of numerical example. Finally, sensitivity analysis of the optimal solution with respect to major parameters is carried out.

An EPQ model with imperfect items using interval grey numbers

The classic economic production quantity (EPQ) model has been widely used to determine the optimal production quantity. However, the analysis for finding an EPQ model has many weaknesses which lead many researchers and practitioners to make extensions in several aspects on the original EPQ model. The basic assumption of EPQ model is that 100% of manufactured products are non-defective that is not valid for many production processes generally. The purpose of this paper is to develop an EPQ model with grey demand rate and cost values with maximum backorder level allowed with the good quality items in units under an imperfect production process. The imperfect items are considered to be low quality items which are sold to a particular purchaser at a lower price and, the others are reworked and scrapped. A mathematical model is developed and then an industrial example is presented on the wooden chipboard production process for illustration of the proposed model.