Optimality of an \((s,S)\) policy with compound Poisson and diffusion demands: a quasi-variational inequalities approach. (English) Zbl 1194.93215

Benkherouf, Lakdere; Bensoussan, Alain

SIAM J. Control Optim. 48, No. 2, 756-762 (2009).

Summary: This paper revisits the paper of Bensoussan, Liu, and Sethi where they proposed a single item continuous-time inventory model where demand is a mixture of a diffusion process and a compound Poisson process. They showed that in a continuous review setting an \((s,S)\) policy is optimal when the jump sizes are exponentially distributed. However, the case where the jump sizes are general was not solved completely. This paper solves this case.

MSC:

93E20	Optimal stochastic control
49J40	Variational inequalities
65C30	Numerical solutions to stochastic differential and integral equations
90B05	Inventory, storage, reservoirs
49N25	Impulsive optimal control problems

Keywords:

inventory control; impulse control; quasi-variational inequality