An economic manufacturing quantity model with probabilistic deterioration in a production system

Mitali Sarkar, Biswajit Sarkar

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73 Citations (Scopus)


This paper develops an economic manufacturing quantity (EMQ) model with deterioration and exponential demand in a production system over a finite time horizon under the effect of inflation and time value of money. The production rate is a dynamic variable (varying with time) in a production system. Due to a long run process, the machinery system is converted from in-control state to out-of-control state which results the production of improper items. The improper items are reworked at a fixed cost to make it as proper. With the increasing value of time, the production of improper item also increases. To reduce the production of the improper items, the systems have to be more reliable and with less amount of failure. In this direction, the model considers that the development cost, production cost, and material cost are dependent on the reliability parameter. The deterioration of the product is considered probabilistic to make the research a more realistic one. By considering the reliability parameter as a decision variable, we try to obtain the associated profit of the system which we have to maximize. To derive the maximization procedure, we use Euler-Lagrange formula from control theory. We outline some numerical examples along with graphical representations and sensitivity analysis to illustrate the model.

Original languageEnglish
Pages (from-to)245-252
Number of pages8
JournalEconomic Modelling
Issue number1
Publication statusPublished - 2013 Mar

Bibliographical note

Funding Information:
The authors want to acknowledge the reviewers for their constructive comments to revise the paper. They want to express their gratitude to Mr. Bhim Chandra Sarkar, Mrs. Prova Sarkar, Mr. Lal Bahadur Mondal, Mrs. Seva Rani Mondal for their encouragement during the research. The authors want to express their heartiest gratitude to Mr. Arnesh Sarkar for his valuable support during the research. This research is supported by the University Grant Commission, Delhi, India from the research grant of the Minor Project (no: 41-1433/2012(SR) ). The corresponding author wants to acknowledge the infrastructural assistance available at Vidyasagar University, West Bengal, India.

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


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