International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2569

Full Length Research Paper

Optimal control of inventory-production systems with gumbel distributed deterioration

Md. Azizul Baten1* and Anton Abdulbasah Kamil2
  1Department of Statistics, School of Physical Sciences, ShahJalal University of Science and Technology, Sylhet-3114, Bangladesh. 2School of Distance Education, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia.
Email: [email protected]

  •  Accepted: 07 March 2011
  •  Published: 04 April 2011



This paper is concerned with the development of an inventory-production model for a special class of generalized extreme value, that is, gumbel distributed deterioration items. The production system with inventory-level-dependent demand is considered and Pontryagin maximum principle is used to determine the optimal control, which is the production rate that minimizes the optimal control model, while satisfying the system dynamics. The necessary optimality conditions are also derived in this case. It is then illustrated with the help of examples.


Key words: Inventory-production systems, gumbel distributed deterioration, optimal control, pontryagin maximum principle.