Multi-item reliability dependent imperfect production inventory optimal control models with dynamic demand under uncertain resource constraint

J.N. Roul, K. Maity, S. Kar and M. Maiti

International Journal of Production Research, 2015, vol. 53, issue 16, 4993-5016

Abstract: In this paper, imperfect multi-item production inventory models are considered over a finite time horizon with known dynamic demands. The production rates are functions of time which are taken as control variables. In the production process, reliability plays an important role to improve the quality of products and to decrease the defective rate. The said defective units are partially or fully reworked. The unit production cost is a function of production rate and also dependent on raw material cost, development cost due to reliability and wear-tear cost. There is a constraint on the total production cost termed as budget constraint which is crisp/imprecise/random in nature. The objective of the present investigation is to fix the optimum reliabilities of the production system to have maximum return. Thus, the models are formulated as optimal control problems for the maximisation of profit and solved using Hamiltonian (Pontryagin’s Maximum Principle), fixed-final time and free-final state system, Kuhn–Tucker conditions and Generalised Reduced Gradient Method. Several particular cases are derived from the general model. The models are illustrated numerically and graphically and some managerial decisions are derived.

Date: 2015
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Citations: View citations in EconPapers (8)

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DOI: 10.1080/00207543.2015.1012601

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