Introduce a Multi-product Multi-constraint inventory model with stochastic period length

Multi-periodic inventory control problems are mainly studied by two assumptions .Including the Continues Review assumption, in which order can happen at any time, depends on the inventory level and the other one is the Periodic Review assumption ,in which order can happen only at the beginning of each period .In this paper we discuss about a Multi-Period Inventory Control problem along with the proposal and analysis of a new assumption which none of the following assumptions are being used. The assumption are that periodic replenishment will happen totally stochastic and also the periods between two replenishments are independent and identically distributed random variables .indeed producer is encountered with customer in stochastic time .In this problem there are two kinds of constraints such as space and service level for each product. Also the decision variable has been chosen as an integer. In first model shortage will be back ordered and in second model shortage will be lost sale. Finally in third model combination of them will be considered. Three main specifications of the model which has led to be new are the stochastic period length, being multi-product and multi-constraint and the fact that the decision variables are integer. As this condition is deployed simultaneously therefore the created model is different from other models in the periodic review literature. The model of this problem is an integer nonlinear programming. Also for solving the model, the genetic algorithm is used and for analyzing the output of the algorithms a numerical example will be exhibited