TITLE:
Production Planning of a Failure-Prone Manufacturing/Remanufacturing System with Production-Dependent Failure Rates
AUTHORS:
Annie Francie Kouedeu, Jean-Pierre Kenné, Pierre Dejax, Victor Songmene, Vladimir Polotski
KEYWORDS:
Stochastic Process, Optimal Control, Reverse Logistics, Production Planning, Numerical Methods
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.10,
June
6,
2014
ABSTRACT: This paper deals
with the production-dependent failure rates for a hybrid manufacturing/remanufacturing
system subject to random failures and repairs. The failure rate of the manufacturing
machine depends on its production rate, while the failure rate of the
remanufacturing machine is constant. In the proposed model, the manufacturing
machine is characterized by a higher production rate. The machines produce one
type of final product and unmet demand is backlogged. At the expected end of
their usage, products are collected from the market and kept in recoverable
inventory for future remanufacturing, or disposed of. The objective of the
system is to find the production rates of the manufacturing and the
remanufacturing machines that would minimize a discounted overall cost
consisting of serviceable inventory cost, backlog cost and holding cost for
returns. A computational algorithm, based on numerical methods, is used for
solving the optimality conditions obtained from the application of the
stochastic dynamic programming approach. Finally, a numerical example and
sensitivity analyses are presented to illustrate the usefulness of the proposed
approach. Our results clearly show that the optimal control policy of the
system is obtained when the failure rates of the machine depend on its production
rate.