A stochastic production inventory model for deteriorating items with products’ finite life-cycle
Pal, Brojeswar1 ; Sana, Shib Sankar2 ; Chaudhuri, Kripasindhu3
1 Department of Mathematics, The University of Burdwan, 713104 Burdwan, India.
2 Department of Mathematics, Bhangar Mahavidyalaya, University of Calcutta, Bhangar, 743502 Kolkata, 24PGS (South), India.
3 Department of Mathematics, Jadavpur University, 700032 Kolkata, India.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 669-684.

The article deals with a production inventory system for deteriorating items where the production rate of the system is a random variable within a finite range and the unit production cost depends on production lotsize as well as the rate of production. In the model, the maximum life-cycle of the products is finite and all the products are totally expired at the end of the life-time of the product. Shortages are allowed and partially backlogged. The backlogging rate is depended on length of the waiting time for the next replenishment. The main objective is to find out the optimal production lot-size such that the average expected cost per unit time of the inventory system is minimum. The different cases according to the value of the product’s life-time, production run-time and cycle length of the system are discussed analytically and numerically. A numerical example and its sensitivity analysis along with its managerial insights are presented to illustrate the behavior of the proposed production-inventory model.

DOI : 10.1051/ro/2016047
Classification : 90B05
Mots-clés : Flexible manufacturing systems, cost benefit analysis, backlogged, deterioration, products life cycle
Pal, Brojeswar 1 ; Sana, Shib Sankar 2 ; Chaudhuri, Kripasindhu 3

1 Department of Mathematics, The University of Burdwan, 713104 Burdwan, India.
2 Department of Mathematics, Bhangar Mahavidyalaya, University of Calcutta, Bhangar, 743502 Kolkata, 24PGS (South), India.
3 Department of Mathematics, Jadavpur University, 700032 Kolkata, India. 
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Pal, Brojeswar; Sana, Shib Sankar; Chaudhuri, Kripasindhu. A stochastic production inventory model for deteriorating items with products’ finite life-cycle. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 669-684. doi : 10.1051/ro/2016047. http://www.numdam.org/articles/10.1051/ro/2016047/

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