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

作者：Roul J N; Maity K^*; Kar S; Maiti M

来源：International Journal of Production Research, 2015, 53(16): 4993-5016.

DOI：10.1080/00207543.2015.1012601

• reliability
• imperfect production control system
• rework for imperfect unit
• uncertain resource constraint
• chance constraint
• necessity & possibility measures

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.

• 出版日期2015-8-18