An Inventory Control Model with (M/M/1) Queueing System and Lost Sales

In this thesis We investigate M/M/1/ - queuing systems with inventory management, continuous review, and lost sales. Demand is Poisson, service times and lead times are exponentially distributed. These distributions are used to calculate performance measures of the respective system. In case of infinite waiting room the key result is that the limiting distributions of the queue length processes are the same as in the classical M/M/1/ -system. We compute performance measures and derive optimality conditions under different order distributions. Although we can completely determine analytically the steady state probabilities for the system. We are able to derive functional relations for replenishment order size distributions that is in single server system with inventory. A computer programs were developed in this thesis to obtain the optimal policy.