This thesis is concerned with the analysis of a continuous review (s,S) inventory system with a constant lead time and a compound Poisson demand process dependent upon environment.
For the environmental-dependent compound Poisson demand process, the intensity parameters ($λx_t$) are considered subject to variant environment, where the environment index processes ($x_t$) satisfy Markov property, and demand size processes are i.i.d. discrete valued random variables for each given environment index. Along with such demand processes, various cost parameters are assumed in a corresponding (s,S) inventory system such as fixed ordering cost, constant purchasing cost per unit, constant carrying cost per unit time, and constant backlogging cost per unitㆍtime.
To analyze such inventory system, it was proved that the limiting distribution of net inventory situation exists if the limiting distribution of inventory position exists and the environment process is irreducible recurrent. Thence, a longrun average expected function was formulated to determine the optimal s and S. Furthermore, it was found that the limiting distribution of net inventory situation can be derived explicitly from any given environmental-dependent demand process when the sojourn time distribution of Markovian environment process is determined.
A finite environmental-dependent Markovian demand process with three-state was treated.
