عنوان مقاله [English]
There are two methods for inventory control, the continuous review and periodic system. The continuous method is employed for important items, while periodic system is used for items whose importance is on average level. In this paper, we present two models for a constrained multi-product inventory control problem with stochastic demand under periodic review policy. The objective of the model is to minimize the total cost. The total cost is the sum of holding cost, shortage cost and set-up cost. In the model, shortage is allowed. In the first model, shortages are completely backordered and in the second model, we consider lost sale for shortages. We have considered stochastic constraints, such as warehouse space and restriction on order quantity and in hand budget. The stochastic constraints are more reliable than exact case and it is compatible to real world. Also, the resources of constraints (right hands) are assumed as random variable. We have employed the service levels for products as a constraint. The problems have modelled as nonlinear integer models and we have employed genetic and particle swarm optimization algorithms for solving models. The inputs of these algorithms are tuned by response surface methodology and if we set these properly, the speed of the algorithms will grow up. We have compared employed algorithms both stochastic and MADM bases. The stochastic comparison is done by t test, and the methods have compared statistically while time of execution and objective value are criteria in MADM comparison. In fact, two criteria are considered simultaneously in MADM, but they are considered individually in statistical comparison. TOPSIS, as a popular method, has employed for MADM comparison. Finally, we have reported the efficiency of the algorithms effectively.