SIAM Journal on Control and Optimization, Vol.36, No.4, 1147-1170, 1998
Risk-sensitive production planning of a stochastic manufacturing system
This paper is concerned with long-run average risk-sensitive control of production planning in a manufacturing system with machines that are subject to breakdown and repair. By using a logarithmic transformation, it is shown that the associated Hamilton-Jacobi-Bellman equation has a viscosity solution. The risk-sensitive control problem has a dynamic stochastic game interpretation. Finally, a limiting problem is obtained when the rates of machine breakdown and repair go to infinity.
Keywords:HAMILTON-JACOBI EQUATIONS;VISCOSITY SOLUTIONS;DIFFERENTIAL-GAMES;UNIQUENESS;EXISTENCE;FORMULAS