EPQ model with learning consideration, imperfect production and partial backlogging in fuzzy random environment

Abstract

The article scrutinises the learning effect of the unit production time on optimal lot size for the uncertain and imprecise imperfect production process, wherein shortages are permissible and partially backlogged. Contextually, we contemplate the fuzzy chance of production process shifting from an ‘in-control’ state to an ‘out-of-control’ state and re-work facility of imperfect quality of produced items. The elapsed time until the process shifts is considered as a fuzzy random variable, and consequently, fuzzy random total cost per unit time is derived. Fuzzy expectation and signed distance method are used to transform the fuzzy random cost function into an equivalent crisp function. The results are illustrated with the help of numerical example. Finally, sensitivity analysis of the optimal solution with respect to major parameters is carried out.

Keywords:

• inventory
• learning effect
• process shifting
• fuzzy random variable
• fuzzy expectation

Acknowledgements

The authors wish to thank the anonymous referees for their valuable comments and suggestions that improved the quality of the paper to a great extent.

Additional information

Notes on contributors

Ravi Shankar Kumar

Ravi Shankar Kumar is working as a Research Scholar at the Department of Mathematics, Indian Institute of Technology Kharagpur, India under the supervision of Prof. A. Goswami. He received his Master degree in Mathematics from Department of Mathematics, Ranchi University, India. His research interests include inventory management, supply chain management and fuzzy optimisation.

A. Goswami

A. Goswami is a Prof. of Mathematics at Indian Institute of Technology Kharagpur, India. He received his MSc and PhD from Jadavpur University, India in 1985 and 1992, respectively. His research interests focus on fuzzy inventory control/optimisation, fuzzy database systems, distributed databases, object oriented databases, data-mining techniques and network security. He has published articles in Journal of the Operational Research Society, European Journal of Operational Research, International Journal of Production Economics, Computers and Mathematics with Applications, Computers & Industrial Engineering, Production Planning and Control, OPSEARCH, International Journal of Systems Science, Journal of Medical Systems, The Journal of Fuzzy Mathematics, Journal of Information & Knowledge Management, Expert Systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Journal of Applied Mathematics & Computing, International Journal of Computers & Applications, International Journal of Data Analysis Techniques and Strategies, etc.