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.