### Research Article

Year : 2018 | Volume: 4 | Issue: 2 | Pages: 1-12

### A Model for Imperfect Production System with Probabilistic Rate of Imperfect Production for Deteriorating Products

DOI: 10.18831/djmaths.org/2018021001

Corresponding author

Department of Industrial & Management Engineering, Hanyang University.

• 1. Department of Industrial & Management Engineering, Hanyang University.

Revised on: 2018/02/20

Accepted on: 2018/02/24

Published on: 2018/03/01

• A Model for Imperfect Production System with Probabilistic Rate of Imperfect Production for Deteriorating Products, Muhammad Waqas Iqbal, Biswajit Sarkar., 2018/03/01, DJ Journal of Engineering and applied Mathematics. , 4(2): 1-12, https://dx.doi.org/10.18831/djmaths.org/12018021001.

Published on: 2018/03/01

### Abstract

Imperfection in a production process is inevitable. The rate of imperfect production does not remain constant but varies depending on several production parameters. Besides, some products, food products for example, have a tendency to deteriorate with time. The rates of deterioration of such products generally increase with time. For such an imperfect production system for deteriorating products, the decisions for the rate of production and planning horizon are very important. Keeping in view the importance, this study proposes an integrated production model of an imperfect production system for deteriorating products. The rate of imperfect production is taken as a random variable that follows normal, triangular, dual triangular, and beta distributions. The rate of deterioration is a function of maximum lifetime of the product and increases with time. The defective and the deteriorated items are separated and disposed through proper channel to fulfill environmental legislative requirements. Objective of the study is defined through a mathematical model for total cost per unit time, which is minimized by obtaining optimal values of the production rate and the cycle time. These variables are decided in such a way that the customer demand during the cycle is fulfilled by compensating the imperfect and deteriorated quantity. The proposed model is verified through some numerical examples.

### Keywords

Imperfect production system, Deterioration, Probabilistic rate, Time-varying rate, Non-linear programming.