A multi-objective multi-product multi-period inventory control model considering inflation rate, total discount and stochastic demand

This research is a multi-product multi-period inventory control model, with inventory costs (including holding, ordering, shortage, and purchasing costs) which is provided under inflation and general discount policy with a randomized demand and has shortcomings (lost sales and lost backorder), and there are some limited and well-known programming periods. Also, the demand for different samples varies in different periods, so the ordering of a product in a particular period must reduce the number of deficiencies, and the shortage must also be allowed. This model also has some limitations in which the budget and storage space are limited. And the examinations are instantaneous. In this paper, a three-objective non-linear complex integer programming model including minimizing total inventory costs and total storage space and maximizing the level of assurance of inventory is introduced simultaneously. Then, multi-objective optimization algorithm of non-dominated sorting genetic algorithm and multi-objective is proposed to solve the problem. a numerical example is presented , which are used for small-size issues and obtaining the exact answer from the Lingo benefit program , And then the problem is executed in larger dimensions than the calculations of the meta-heuristic algorithms NSGAII in MATLAB software, and the computational results are obtained after the algorithm is applied to the sample problem.