This thesis considers a continuous review (s, S) inventory model in which stochastic lead times are allowed. The objective of this thesis is to determine the optimal system parameters s and S that minimize the long-run overall expected average inventory system cost. The model assumes that at most one order is outstanding and demands occur in Poisson processes.
The model is analyzed by applying the Markov Renewal theory to derive the steady-state probabilities of the inventory levels upon which the long-run overall expected average inventory system cost functions and relevant constraints are derived. The cost functions are further investigated to characterize the optimal solution, for which computational procedures are exploited.
The structure of this thesis includes several extensions of the (s, S) model to incorporate practical situations described in the following four areas:
First, the thesis considers an extension of (s, S) model to a single commodity inventory problem where unsatisfied demands are lost.
Second, it handles another extension to a single commodity inventory model with limited backlogging levels where unsatisfied demands are backlogged. However, a partial backlogging is allowed such that if backlogging sales exceed a limited level, the exceeding sales are then lost. In the problem, a limited backlogging level ought to be determined along with s and S.
Third, the extension is continued to the inventory model where each customer's yes-or-no decision on backlogging allowance can be made for unsatisfied demand, so that some customers allow backlogging but others not. Demands from the first (yes) and second (no) types of customers occur in two independent Poisson processes.
As the final extension, an inventory model is investigated where a service constraint is imposed and unsatisfied demands are backlogged. In the model, the steady-state probability distributions of inventory levels are used to determine the fill-rate (measured as fraction of demands satisfied directly with on-hand stock) as a service constraint.
