A mathematical model is developed for volume flexible production system taking into account the effect of imperfect quality products. At the start of the production of a lot, the whole system is adjusted so that the process is 'in-control' state and items produced are of acceptable quality. During high rate of production, the process shifts from the 'in-control' state to the 'out-of-control' state. In the 'out-of-control' state, the quality of products deteriorates resulting in defective items. The demand rate of some defective items which are suitable for sale at reduced price is considered as a function of reduction rate of selling price. The proposed model is graphically illustrated with numerical examples and optimised by Mathematica Software. Sensitivity analysis is undertaken and various issues regarding the sale of imperfect quality products are discussed. Copyright © 2007 Inderscience Enterprises Ltd.

S S SANA

K CHAUDHURI

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

&nbsp;

The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

&nbsp;

It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

On a volume flexible inventory model for items with an imperfect production system

International Journal of Operational Research

The article deals with an economic production lot size model in which the manufacturing process shifts from an 'in-control' state to an 'out-of-control' state after a certain time span which is exponentially distributed. Rapid production may cause such a type of shifting. During the 'out-of-control' state, defective items are accumulated and reworked immediately at some cost for maintaining the quality of the product. The demand of the product is assumed to be stochastic. Shortages are allowed and backlogged. Both partial backordering and complete backordering are studied separately and their comparisons are also done. Production cost, holding cost, backlogging cost, lost sale cost, reworked cost and selling price are taken together to construct the integrated expected average profit function, which is maximized to obtain the optimal production rate, optimal lot size and value of optimum expected average profit by using the calculus method. Six numerical examples with their graphical representation are provided to justify the proposed model. © 2013 The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

IMA Journal of Management Mathematics

An economic production lot size model for defective items with stochastic demand, backlogging and rework

This article deals with an economic production quantity (EPQ) model in an imperfect production system. The production system may undergo in out-of-control state from in-control state, after a certain time that follows a probability density function. The density function varies with reliability of the machinery system that may be controlled by new technologies, investing more costs. The defective items produced in out-of-control state are reworked at a cost just after the regular production time. Occurrence of the out-of-control state during or after regular production-run time is analysed and also graphically illustrated separately. Finally, an expected profit function regarding the inventory cost, unit production cost and selling price is maximised analytically. Sensitivity analysis of the model with respect to key parameters of the system is carried out. Two numerical examples are considered to test the model and one of them is illustrated graphically. © 2013 Copyright Taylor and Francis Group, LLC.

International Journal of Systems Science

Maximising profits for an EPQ model with unreliable machine and rework of random defective items

In the paper, we develop an EPQ (economic production quantity) inventory model to determine the optimal buffer inventory for stochastic demand in the market during preventive maintenance or repair of a manufacturing facility with an EPQ (economic production quantity) model in an imperfect production system. Preventive maintenance, an essential element of the just-in-time structure, may cause shortage which is reduced by buffer inventory. The products are sold with the free minimal repair warranty (FRW) policy. The production system may undergo "out-of-control" state from "in-control" state, after a certain time that follows a probability density function. The defective (non-conforming) items in "in-control" or "out-of-control" state are reworked at a cost just after the regular production time. Finally, an expected cost function regarding the inventory cost, unit production cost, preventive maintenance cost and shortage cost is minimized analytically. We develop another case where the buffer inventory as well as the production rate are decision variables and the expected unit cost considering the above cost functions is optimized also. The numerical examples are provided to illustrate the behaviour and application of the model. Sensitivity analysis of the model with respect to key parameters of the system is carried out. © 2012 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

Journal of Manufacturing Systems

A mathematical model on EPQ for stochastic demand in an imperfect production system

This article develops an integrated production-inventory model considering perfect and imperfect quality items, product reliability and reworking of defective items in the environment of supply chain management. Manufacturer, supplier and retailer are the members of the supply chain where supplier delivers raw materials to the manufacturer and sends back the defective raw materials after completion of inspection at a single lot with less market price. In this system, production starts to produce good items at the beginning of the production. The production system may undergo an "out-of-control" state from an "in-control" state, after a certain time that follows a probability density function. The density function varies with reliability of the machinery system that may be controlled by new technologies, investing more capital. The defective items produced in "out-of-control" state are reworked at a cost just after the regular production time. This model considers the impact of business strategies such as optimal order size of raw materials, production rate and unit production cost, and idle times in different sectors in a collaborating marketing system. An analytical method is employed to optimize the production rate and raw material order size for maximum expected average profit. A numerical example along with four graphical illustrations is considered and its sensitivity analysis is provided to test feasibility of the model. © 2012 Elsevier Inc. All rights reserved.

Applied Mathematics and Computation

Three-layer supply chain - A production-inventory model for reworkable items

This paper deals with an imperfect production system with allowable shortages due to regular preventive maintenance for products sold with free minimal repair warranty. Preventive maintenance is an essential factor of the just-in-time structure that results in a shutdown of the production process for a certain period of time. During such an interruption, a buffer stock is needed to adjust the market demand. The study includes the possibility of imperfect production and determines the optimum buffer level and production run time by trading off the holding cost, shortage cost, rework cost, repair cost for warranty, labour/energy costs, material cost and cost for maintenance so that the cost per unit product is minimised. © 2012 Copyright Taylor and Francis Group, LLC.

Journal	International Journal of Operational Research
Publisher	-
ISSN	1745-7645