An inventory system with postponed and renewal demands

This paper deals a continuous review inventory system with postponed demands. We generalise the existing models in the literature of postponed inventory system by assuming arbitrary demand distributions for the inter-arrival times. The inventory is replenished according to a (s, S) policy and the replenishing times are assumed to follow an exponential distribution. The demands that occur during stock-out periods enter a pool of infinite capacity. The demands in the pool are selected one by one, if the replenished stock is above some prefixed level. The inter-selection time is distributed as exponential. Using the matrix geometric method, the stationary joint probability distribution of the number of customers in the pool and the inventory level is calculated. The measures of system performance in the steady state are derived and the total expected cost rate is also calculated. We employ artificial intelligence techniques to find the optimal values. The sensitivity of system costs and parameters on the optimal values are studied numerically.