scholarly journals A Single-Stage Manufacturing Model with Imperfect Items, Inspections, Rework, and Planned Backorders

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 446 ◽  
Author(s):  
Chang Wook Kang ◽  
Misbah Ullah ◽  
Mitali Sarkar ◽  
Muhammad Omair ◽  
Biswajit Sarkar
Keyword(s):  
Production System ◽  
Single Stage ◽  
Order Quantity ◽  
Lot Size ◽  
Defective Items ◽  
Long Run ◽  
Proposed Model ◽  
Imperfect Items ◽  
Inspection Process ◽  
Inspection Station

Each industry prefers to sell perfect products in order to maintain its brand image. However, due to a long-run single-stage production system, the industry generally obtains obstacles. To solve this issue, a single-stage manufacturing model is formulated to make a perfect production system without defective items. For this, the industry decides to stop selling any products until whole products are ready to fulfill the order quantity. Furthermore, manufacturing managers prefer product qualification from the inspection station especially when processes are imperfect. The purpose of the proposed manufacturing model considers that the customer demands are not fulfilled during the production phase due to imperfection in the process, however customers are satisfied either at the end of the inspection process or after reworking the imperfect products. Rework operation, inspection process, and planned backordering are incorporated in the proposed model. An analytical approach is utilized to optimize the lot size and planned backorder quantities based on the minimum average cost. Numerical examples are used to illustrate and compare the proposed model with previously developed models. The proposed model is considered more beneficial in comparison with the existing models as it incorporates imperfection, rework, inspection rate, and planned backorders.

scholarly journals Does the Autonomation Policy Really Help in a Smart Production System for Controlling Defective Production?

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1142 ◽  
Author(s):  
Mitali Sarkar ◽  
Li Pan ◽  
Bikash Koli Dey ◽  
Biswajit Sarkar
Keyword(s):  
Production System ◽  
Capital Investment ◽  
Single Type ◽  
Main Theme ◽  
Total System ◽  
Production Rates ◽  
Setup Cost ◽  
Defective Items ◽  
Long Run ◽  
Imperfect Items

This study explains about a serial smart production system where a single-type of product is produced. This system uses an unequally sized batch policy in subsequent stages. The setup cost is not always deterministic, it can be controllable and reduced by increasing the capital investment cost, and that the production rates in the system may vary within given limits across batches of shipments. Furthermore, as imperfect items are produced in long-run system, to clean the imperfectness autonomation policy is adopted for inspection, which make the process smarter. The shipment lot sizes of the deliveries are unequal and variable. In long-run production system, defective items are produced in “out-of-control” state. In this model, the defect rate is random with a uniform distribution which is clean from the system by autonomation. In addition, in the remanufacturing process, it is assuming that all defective products are repaired, and no defective products are scrapped. The main theme of developing this model is to determine the number of shipments and the optimal production lot size to adjust the production rates and decrease the total system cost under a reduced setup cost by considering the discrete investment and make a serial smart production system. A solution procedure along with an advanced algorithm was proposed for solving the model. Numerical examples with some graphical representations are provided to validate the model.

scholarly journals An EPQ inventory model considering an imperfect production system with probabilistic demand and collaborative approach

2019 ◽  
Vol 17 (2) ◽  
pp. 282-304
Author(s):  
Katherinne Salas-Navarro ◽  
Jaime Acevedo-Chedid ◽  
Gina Mora Árquez ◽  
Whady F. Florez ◽  
Holman Ospina-Mateus ◽  
...  
Keyword(s):  
Supply Chain ◽  
Production System ◽  
Inventory Model ◽  
Collaborative Approach ◽  
Lot Size ◽  
Defective Items ◽  
Content Type ◽  
Imperfect Production ◽  
Imperfect Items ◽  
Exponential Probability

Purpose The purpose of this paper is to propose an economic production quantity (EPQ) inventory model considering imperfect items and probabilistic demand for a two-echelon supply chain. The production process is imperfect and the imperfect quality items are removed from the lot size. The demand rate of the inventory system is random and follows an exponential probability density function and the demand of the retailers is depending on the initiatives of the sales team. Design/methodology/approach Two approaches are examined. In the non-collaborative approach, any member of the supply chain can be the leader and takes decisions to optimize the profits, and in the collaborative system, all members make joint decisions about the production, supply, sales and inventory to optimize the profits of the supply chain members. The calculus approach is applied to find the maximum profit related to the members of the supply chain. Findings A numerical example is presented to illustrate the performance of the EPQ model. The results show that collaborative approach generates greater profits to the supply chain and the market’s demand represents the variable behavior and uncertainty that is generated in the replenishment of a supply chain. Originality/value The new and major contributions of this research are: the inventory model considers demand for products is random variable which follows an exponential probability distribution function and it also depends on the initiatives of sales teams, the imperfect production system generates defective items, different cycle time are considered in manufacturer and retailers and collaborative and non-collaborative approaches are also studied.

A study of an EOQ model with public-screened discounted items under cloudy fuzzy demand rate

2021 ◽  
pp. 1-12
Author(s):  
Suman Maity ◽  
Sujit Kumar De ◽  
Madhumangal Pal ◽  
Sankar Prasad Mondal
Keyword(s):  
Uncertain Demand ◽  
Order Quantity ◽  
Eoq Model ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Imperfect Items ◽  
Demand Rate ◽  
Computer Based ◽  
Fuzzy Degree ◽  
Graphical Illustration

This article deals with an economic order quantity inventory model of imperfect items under non-random uncertain demand. Here we consider the customers screen the imperfect items during the selling period. After a certain period of time, the imperfect items are sold at a discounted price. We split the model into three cases, assuming that the demand rate increases, decreases, and is constant in the discount period. Firstly, we solve the crisp model, and then the model is converted into a fuzzy environment. Here we consider the dense fuzzy, parabolic fuzzy, degree of fuzziness and cloudy fuzzy for a comparative study. The basic novelty of this paper is that a computer-based algorithm and flow chart have been given for the solution of the proposed model. Finally, sensitivity analysis and graphical illustration have been given to check the validity of the model.

scholarly journals Effect of Energy and Failure Rate in a Multi-Item Smart Production System

Energies ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 2958 ◽  
Author(s):  
Mitali Sarkar ◽  
Biswajit Sarkar ◽  
Muhammad Iqbal
Keyword(s):  
Energy Consumption ◽  
Production Rate ◽  
Failure Rate ◽  
Production System ◽  
Optimal Solution ◽  
Development Cost ◽  
Lot Size ◽  
Defective Items ◽  
Unusual Amount ◽  
Control State

To form a smart production system, the effect of energy and machines’ failure rate plays an important role. The main issue is to make a smart production system for complex products that the system may produce several defective items during a long-run production process with an unusual amount of energy consumption. The aim of the model is to obtain the optimum amount of smart lot, the production rate, and the failure rate under the effect of energy. This study contains a multi-item economic imperfect production lot size energy model considering a failure rate as a system design variable under a budget and a space constraint. The model assumes an inspection cost to ensure product’s quality under perfect energy consumption. Failure rate and smart production rate dependent development cost under energy consumption are considered, i.e., lower values of failure rate give higher values of development cost and vice versa under the effect of proper utilization of energy. The manufacturing system moves from in-control state to out-of-control state at a random time. The theory of nonlinear optimization (Kuhn–Tucker method) is employed to solve the model. There is a lemma to obtain the global optimal solution for the model. Two numerical examples, graphical representations, and sensitivity analysis of key parameters are given to illustrate the model.

Geometric process repair model for an unreliable production system with an intermediate buffer

2016 ◽  
Vol 231 (4) ◽  
pp. 747-759 ◽  
Author(s):  
Guoqing Cheng ◽  
Binghai Zhou ◽  
Ling Li
Keyword(s):  
Production System ◽  
Buffer Stock ◽  
Sensitivity Analyses ◽  
Cost Rate ◽  
Long Run ◽  
Proposed Model ◽  
Joint Policy ◽  
Traditional Assumption ◽  
Average Cost Rate ◽  
Continuous Demand

In this paper, we consider an unreliable production system consisting of two machines (M1 and M2) in which M1 produces a single product type to satisfy a constant and continuous demand of M2 and it is subjected to random failures. In order to palliate perturbations caused by failures, a buffer stock is built up to satisfy the demand during the production unavailability of M1. A traditional assumption made in the previous research is that repairs can restore the failed machines to as good as new state. To develop a more realistic mathematical model of the system, we relax this assumption by assuming that the working times of M1 after repairs are geometrically decreasing, which means M1 cannot be repaired as good as new. Undergoing a specified number of repairs, M1 will be replaced by an identical new one. A bivariate policy [Formula: see text] is considered, where S is the buffer stock level and N is the number of failures at which M1 is replaced. We derive the long-run average cost rate [Formula: see text] used as the basis for optimal determination of the bivariate policy. The optimal policies [Formula: see text] and [Formula: see text] are derived, respectively. Then, an algorithm is presented to find the optimal joint policy [Formula: see text]. Finally, an illustrative example is given to validate the proposed model. Sensitivity analyses are also carried out to illustrate the effectiveness and robustness of the proposed methodology.

scholarly journals A Constrained Production System Involving Production Flexibility and Carbon Emissions

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 275 ◽  
Author(s):  
Asif Iqbal Malik ◽  
Byung Soo Kim
Keyword(s):  
Production Rate ◽  
Carbon Emissions ◽  
Production System ◽  
Ghg Emissions ◽  
Real Life ◽  
Lot Size ◽  
Setup Cost ◽  
Defective Items ◽  
Machine Failure ◽  
Decision Variables

The proposed study presents an economic lot size and production rate model for a single vendor and a single buyer setup. This model involves greenhouse gas (GHG) emissions from industrial sources. The carbon emissions in this model are considered as two types: direct emissions and indirect emissions. The production rate affects carbon emissions generation in production, i.e., generally, higher production rates result in more emissions, which is governable in many real-life cases. The production rate also impacts the process reliability and quality. Faster production deteriorates the production system quickly, leading to machine failure and defective items. Such reliability and quality problems increase energy consumptions and supply chain (SC) costs. This paper formulates a vendor-buyer SC model that tackles these issues. It considers two decision-making policies: integrated or centralized as well as decentralized, where the aim is to obtain the optimal values of the decision variables that give the minimum total SC cost. It includes the costs of setup, holding inventory, carbon emissions, order processing, production, reworking, and inspection processes. The decision variables are the production rate, lead time, order quantity, the number of shipments, and the investments for setup cost reduction. In the later sections, this paper compares the numerical outcomes of the two centralized and decentralized policies. It also provides sensitivity analysis and useful insights on the economic and environmental execution of the SC.

Optimal manufacturing lot size for a single-stage production system with rework in a fuzzy environment

2014 ◽  
Vol 27 (6) ◽  
pp. 3067-3080 ◽  
Author(s):  
Ehsan Shekarian ◽  
Christoph H. Glock ◽  
Seyyed Mehrdad Pourmousavi Amiri ◽  
Kurt Schwindl
Keyword(s):  
Production System ◽  
Single Stage ◽  
Lot Size ◽  
Fuzzy Environment

scholarly journals Integrated inventory model involving quality improvement investment and advance-cash-credit payments

2021 ◽  
Author(s):  
Chih-Te Yang ◽  
Chien-Hsiu Huang ◽  
Liang-Yuh Ouyang
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Decision Makers ◽  
Optimal Solutions ◽  
Order Quantity ◽  
Defective Items ◽  
Numerical Examples ◽  
Proposed Model ◽  
Production Inventory ◽  
Total Profit

This paper investigates the effects of investment and inspection policies on an integrated production–inventory model involving defective items and upstream advance-cash-credit payment provided by the supplier. In this model, retailers offer customers a downstream credit period. Furthermore, the defective rate of the item can be improved through capital co-investment by the supplier and retailer. The objective of this study was to determine the optimal shipping quantity, order quantity, and investment alternatives for maximizing the supply chain's joint total profit per unit time. An algorithm was developed to obtain the optimal solution for the proposed problem. Several numerical examples are used to demonstrate the proposed model and analyze the effects of parameters changes on the optimal solutions. Finally, management implications for relevant decision makers are obtained from the numerical examples.

scholarly journals Optimal inventory policies for imperfect inventory with price dependent stochastic demand and partially backlogged shortages

2012 ◽  
Vol 22 (2) ◽  
pp. 199-223 ◽  
Author(s):  
Jhuma Bhowmick ◽  
G.P. Samanta
Keyword(s):  
Stochastic Demand ◽  
Optimal Order ◽  
Partial Backlogging ◽  
Order Quantity ◽  
Inventory Policies ◽  
Defective Items ◽  
Proposed Model ◽  
Special Cases ◽  
Total Profit ◽  
Increasing Function

The paper investigates a single period imperfect inventory model with price dependent stochastic demand and partial backlogging. The backorder rate is a nonlinear non-increasing function of the magnitude of shortage. Two special cases are considered assuming that the percentage of defective items follows a truncated exponential distribution and a normal distribution respectively. The optimal order quantity and the optimal mark up value are determined such that the expected total profit of the system is maximized. Numerical example is given to illustrate the proposed model which is compared with the traditional model of perfect stock. Sensitivity analysis is performed to explain the behavior of the proposed model with respect to the key parameters.

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