Single-stage Manufacturing System Research Articles

Investigation of a Fuzzy Production Inventory Model with Carbon Emission using Sign Distance Method

Reducing costs associated with inventory is the primary goal of conventional inventory models like the models of economic order quantity and economic production quantity. However, these models fall short of addressing defective goods or revising them. Imperfections in the manufacturing process result in flawed products alongside the final goods. To convert these flawed components into finished goods, rework is necessary. In manufacturing and reworking process produces carbon emissions which are harmful for the earth. To determine the optimal quantity for a single product manufactured in a single-stage manufacturing system that yields partially defective products that are reworked in the same cycle, is determined in real-life situations, where the inventory characteristics and objectives are not exact. Such a type of uncertainty may be characterized by fuzzy numbers. A pentagonal fuzzy number has been used to define the cost parameters. Due to fuzzy parameters, the model becomes a fuzzy quantity, and it is defuzzied by the sign distance method. this article formulates a model of manufacturing inventories with planned backorders. Furthermore, a closed form for the inventory’s system total cost is determined, and a range of actual values for defective products for which an appropriate method exists is also provided. A proper mathematical model is created to accomplish the goal, and the manufacturing lot size that reduces the overall cost is determined. The ideal amount of a production batch to reduce total cost is established in to attain this goal using an appropriate mathematical model. While formulating and solving the relevant model, the necessary and sufficient conditions for a single globally optimal solution have been determined. Examples used as visualizations are given and confirmed by data.

An inventory model for imperfect production system with rework and shortages

This paper considers a production inventory model with planned backorders for a single product. The product is manufactured in a single stage manufacturing system. The manufacturing system generate...

Imperfect production system with rework of regular production with sales returns by customers and buffer stock

Jamal et al. (2004) proposed a model, which dealt with the optimum batch quantity in a single-stage system in which rework is done by addressing two different operational policies to minimise the total system cost but their models do not considered sales return by customers. A portion of defective items produced are not successfully screened out internally during the production process and passed on to customers, thereby causing defect sales returns and reverse logistic from customers back to the manufacturer. In this direction, this paper develops an economic production quantity inventory model with sales return by customers for determining the economic production quantity for a single product, which is manufactured in a single-stage manufacturing system that generates imperfect quality products and all these defective products are reworked in the same cycle. Mathematical model is developed and the optimal production lot size which minimises the total cost is derived.

Optimal decision-making for a single-stage manufacturing system with rework options

ABSTRACTThis study investigates a manufacturing system with a single-stage production system that sometimes produces imperfect items. In this system, we assume that the rework process can start after the regular production process (immediate rework) or when the inventory of perfect goods is equal to zero (delayed rework). Also, we assumed non-zero set-up time for rework. Two models are presented for manufacturing systems with re-workable goods. The first model deals with non-zero set-up time for immediate rework and the second model deals with non-zero set-up times for delayed rework. We also investigate special cases associated with these models wherein the set-up times are zero. A general and aggregated model that included those two models is considered. The novelty of this research lies in selecting for a decision-maker the best approach based on system conditions and solutions. This paper provides a framework for rework policies to minimise the total cost of the system, which includes the cost of manufacturing cost, set-up cost for rework and regular production, holding cost for perfect and imperfect items, and the cost of rework. Finally, we solve the aggregated model by using an exact solution algorithm, and the optimal value of production in each period is obtained.

Single stage queueing/manufacturing system model that involves emission variable

Queueing is commonly occured at every industry. The basic model of queueing theory gives a foundation for modeling a manufacturing system. Nowadays, carbon emission is an important and inevitable issue due to its huge impact to our environment. However, existing model of queuing applied for analysis of single stage manufacturing system has not taken Carbon emissions into consideration. If it is applied to manufacturing context, it may lead to improper decisisions. By taking into account of emission variables into queuing models, not only the model become more comprehensive but also it creates awareness on the issue to many parties that involves in the system. This paper discusses the single stage M/M/1 queueing model that involves emission variable. Hopefully it could be a starting point for the next more complex models. It has a main objective for determining how carbon emissions could fit into the basic queueing theory. It turned out that the involvement of emission variables into the model has modified the traditional model of a single stage queue to a calculation model of production lot quantity allowed per period.

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.

Optimum ordering policy for an imperfect single-stage manufacturing system with safety stock and planned backorder

Manufacturing industries prefer to produce extra units as safety stock especially when demand for these units varies. The phenomena of producing additional units is also observed when processes are imperfect and production managers are sure that product can be consumed in market. In addition, customer is also willing to wait for demands to be backordered in the case of shortages. However, inventory carrying and backordering costs may play vital role if products are produced in relatively large amount. Therefore, a mathematical model is needed that can define the ordered quantity taking safety stock and planned backordering into consideration with imperfect production setup. This paper is an attempt towards development of such mathematical model that considers safety stock, lot size, and planned backorders for a single-stage imperfect production setup. Mathematical model is developed based on minimization of total average cost function. Three decision variables including order quantity, safety stock, and planned backorders have been optimized simultaneously using classical optimization approach. Numerical examples are used to illustrate the proposed model for calculation of decision variables. Impact of changes in processes imperfection, holding costs, and backordering costs over variables have been numerically computed to highlight model significance in daily industrial life. Results prove that safety stock and planned backorder reduce the total cost significantly.

Performance comparison of multiple product kanban control systems

Kanban control systems have been around for decades and have been used to control work-in-process of manufacturing systems. Lately many variations of the basic control system have been developed; however, much of the work in the development and comparison of control systems has focused on a single-stage manufacturing system producing a single product type. In this research, we present procedures for optimising multiple product kanban control systems, namely Base Stock, Traditional Kanban Control System and Extended Kanban Control System (both dedicated and shared type). We then conduct a detailed simulation study to compare the performance of the systems using a common total cost measure. Numerical results show that the dedicated and shared-extended kanban control systems outperform the other two systems. The study also shows that in spite of their different schematics and contrary to conventional wisdom, the performance of dedicated and shared-extended kanban control systems doesn’t differ much.

An economic production quantity model with random defective rate, rework process and backorders for a single stage production system

This paper revisits the economic production quantity (EPQ) model with rework process at a single-stage manufacturing system with planned backorders. It is well known that any imperfect production system of real life has random defective rates. In this direction, this paper extends an inventory model to allow random defective rates. Basically, three different inventory models are developed for three different distribution density functions such as uniform, triangular, and beta. The analytical derivation provides closed-form solution for each inventory model. We have made comparison tables of optimal results among the distribution functions. Some numerical examples and sensitivity analysis are given to illustrate the inventory models.

Production inventory model with reworking of imperfect production, scrap and shortages

In traditional inventory models such as the economic order quantity and the economic production quantity models, the sole objective is to minimize the total inventory-related costs, typically the holding cost and the ordering cost. These models do not consider the presence of defective products in the lot or reworking them. In an imperfect manufacturing process, the defective items are produced with the finished goods. The rework process is necessary to convert those defective items into finished goods. This paper develops a production inventory model with planned backorders for determining the optimum quantity for a single product manufactured in a single stage manufacturing system that generates imperfect quality products where a proportion of the defective products are reworked in the same cycle. Additionally, a range of real values for the proportion of defective products for which there is an optimal solution is established, and a closed form for the total cost of the inventory system is obtained. To achieve this objective, a suitable mathematical model is developed and the optimal production lot size that minimises the total cost is derived. The relevant model is built and solved, and necessary and sufficient conditions for a unique and globally optimal solution are derived. Illustrative examples are provided and numerically verified. For validation of the results, this model was coded in Microsoft® Visual Basic 6.0.

Framework of Cascade Quality Prediction Method Using Latent Variables for Multi-Stage Manufacturing

Prediction model in data mining context is the formulation that explains the relationship between predictor and response variables. In similar, quality prediction model in manufacturing context is the formulation that explains the relationship between manufacturing operation and quality variables. Quality prediction model, as the key to realize the real-time quality manufacturing process, has been developed using various data mining techniques. Unfortunately, most of quality prediction models are developed in single-stage manufacturing system (SMS) where the relationship between manufacturing operation and quality variables is straightforward. Previous studies show that single-stage quality system cannot solve quality problem in multi-stage manufacturing system due to the complex variable relationships. This conceptual study is intended to propose a framework to develop quality prediction model which is able to deal with the complex variable relationships in multi-stage manufacturing system (MMS). This framework, named Cascade Quality Prediction Method (CQPM), is developed based on the characteristics of multi-stage manufacturing system that have been explained in several studies. CQPM is expected to produce more accurate quality prediction model since it is able to explain all type of existed variable relationship in MMS. However further investigation regarding the performance of CQPM and the selection of the data mining technique to be employed is required

Cascade Quality Prediction Method Using Multiple PCA+ID3 for Multi-Stage Manufacturing System

Quality prediction model, as the key to realize the real-time online quality monitoring process, has been developed using various data mining techniques. However, most of quality prediction models are developed in single-stage manufacturing system, where the relationship between manufacturing operation and quality variables is straightforward. Previous studies show that single-stage quality system cannot solve quality problem in multi-stage manufacturing system due to the complex variable relationships. This study is intended to propose a data mining method to develop quality prediction model which is able to deal with the complex variable relationships in multi-stage manufacturing system. This method, named Cascade Quality Prediction Method (CQPM), is developed by considering the complex variables relationships in multi-stage manufacturing system. CQPM employs the combination of multiple Principal Component Analysis and Iterative Dichotomiser 3 algorithm. A case study in semiconductor manufacturing shows that the prediction model that has been developed using CQPM is performed better in predicting both positive and negative classes compared to others.

An alternative analysis and solution procedure for the EPQ model with rework process at a single-stage manufacturing system with planned backorders

This paper revisits the work by Cárdenas-Barrón (Cárdenas-Barrón, L. E., (2009). Economic production quantity with rework process at a single-stage manufacturing system with planned backorders. Computers and Industrial Engineering, 57(3), 1105–1113). The optimal solution condition is analyzed using the production time and the time to eliminate backorders as decision variables instead of the classical decisions variables of lot and backorder quantities. This new approach leads to an alternative inventory policy for imperfect quality items when the optimal production time is less than the optimal time. This is a new method that has not been explored before; it improves and complements the work by Cárdenas-Barrón (2009) and provides interesting managerial insights. An easy to apply solution procedure is provided to obtain the optimal policy. Finally, numerical examples are solved to illustrate our results.

Optimal production control of a service-oriented manufacturing system with customer balking behavior

The great challenge for service-oriented manufacturing (SOM) is how to cope with customer behavior while making decision on production planning and scheduling. In this paper, we consider a single-stage manufacturing system for SOM with impatient customers. In order to represent customer balking behavior caused by backlog, we employ a balking function, which is an arbitrary non-decreasing function of the backlog for characterizing the customer’s response to the backlog. The objective is to find the optimal production policy that minimizes the system cost. The problem is formulated as a Markov decision process. The optimal production policy is proved to be a base-stock policy. The effects of system parameters on the optimal base-stock level are analytically investigated, and the impact of customer balking behavior on the system is illustrated by numerical example in which linear balking function is employed. Numerical example shows that customer balking has a significant impact on the optimal control and the performance measures of the system under the optimal policy.

The economic production quantity with rework process in supply chain management

Cardenas-Barron [L.E. Cardenas-Barron, Economic production quantity with rework process at a single-stage manufacturing system with planned backorders, Computers and Industrial Engineering 57 (2009) 1105–1113] minimizes the annual total relevant cost T C ( Q , B ) to find the economic production quantity with rework process at a manufacturing system and assumes that T C ( Q , B ) is convex. So, the solution ( Q ̄ , B ̄ ) satisfying the first-order-derivative condition for T C ( Q , B ) will be the optimal solution. However, this paper indicates that ( Q ̄ , B ̄ ) does not necessarily exist although T C ( Q , B ) is convex. Consequently, the main purpose of this paper is two-fold: (A) This paper tries to develop the sufficient and necessary condition for the existence of the solution ( Q ̄ , B ̄ ) satisfying the-first-derivative condition of T C ( Q , B ) . (B) This paper tries to present a concrete solution procedure to find the optimal solution of T C ( Q , B ) .

Economic production quantity with rework process at a single-stage manufacturing system with planned backorders

In traditional inventory models such as the economic order quantity (EOQ) and the economic production quantity (EPQ) the sole objective is to minimize the total inventory-related costs, typically holding cost and ordering cost. These models do not consider the presence of defective products in the lot or rework of them. Recently, Jamal, Sarker, and Mondal (Jamal, A. A. M., Sarker, B. R., & Mondal, S., (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77–89) proposed a model, which dealt with the optimum batch quantity in a single-stage system in which rework is done by addressing two different operational policies to minimize the total system cost, but their models do not consider planned backorders. In this direction, this paper develops an EPQ type inventory model with planned backorders for determining the economic production quantity for a single product, which is manufactured in a single-stage manufacturing system that generates imperfect quality products, and all these defective products are reworked in the same cycle. We also establish the range of real values of the proportion of defective products for which there is an optimal solution, and the close form for the total cost of inventory system. The use of the inventory model is illustrated with numerical examples. The classical EOQ, EPQ inventory models with or without planned backorders and Jamal, Sarker and Mondal’s model (Jamal, A. A. M., Sarker, B. R., & Mondal, S., (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77–89) are shown to be special cases of the EPQ inventory model presented in this paper.

Optimal Release Times in Single-Stage Manufacturing Systems with Blocking: Optimal Control Perspective

This paper concerns a due-date matching problem in a single-stage manufacturing system. Given a finite sequence of jobs and their service order, and given the delivery due date of each job, the problem is to choose the jobs release (arrival) times so as to match as closely as possible their completion times to their respective due dates. The system is modelled as a deterministic single-server FIFO queue with an output buffer for storing jobs whose service is completed prior to their due dates. The output buffer has a finite capacity; when it is full, the server is being blocked. Associated with each job there is a convex cost function penalizing its earliness as well as tardiness. The due-date matching problem is cast as an optimal control problem, whose objective is to minimize the sum of the above cost functions by the choice of the jobs arrival (release) times. Time-box upper-bound and lower-bound constraints are imposed on the jobs output (delivery) times. The optimal-control setting brings to bear on the development of fast and efficient algorithms having intuitive geometric appeal and potential for online implementation.

A backward algorithm for computing optimal controls for single-stage hybrid manufacturing systems

This paper concerns optimal control problems in single-stage manufacturing systems. The control variables comprise parameters of the jobs' processing times, and the cost functional involves measures of both jobs' due dates and products' physical characteristics. The system is configured for processing a finite number of jobs in a given order, and it is modelled as a hybrid dynamical system cast in a deterministic setup. The paper identifies a necessary and sufficient optimality condition having an intuitive geometric appeal, and it develops an efficient, low-complexity algorithm for computing the optimal controls. Numerical experiments testify to the efficacy of the proposed algorithm.

Optimal Machining Speed and Tool Inventory Policies in Machining Economic Systems

This paper presents an integrated cost model that combines a tooling inventory control policy with a machining economics scheme in single-stage manufacturing systems. An algorithm is proposed for estimating simultaneously tool cutting speed, along with tool reorder points and safety levels. The behavior of the integrated model is investigated; numerical results are presented.