inventory control model with stochastic period lneght and delayed payment

in classic inventory control system, we assume that purchasing cost should be paid at time of delivery. but sometimes in order to encourage retailer to increase his order, postpond payment is provided by supplier as an incentive policy for retailer. in this paper a periodic inventory control model is invetigated in which the period between two consecutive replenishmnet is a random variable. in fact the economic order quantity model under stochastic period lenght and postpond payment is developed. in this paper the concavity of profit function is prooved and situation under which the profit function of retalier is maximized, is determined. the aim of this researchis to determine the the maximum level of inventory such that the total profit is maximized. in continue in order to describe the model numerical examples and sensitivity analysis are introduced.