Abstract
While in multi-periodic inventory control problems the usual assumption are that the orders are placed at the beginning of each period (periodic review) or depending on the inventory level they can happen at any time (continuous review), in this research, we relax these assumptions and assume that the periods between two replenishments of the products are independent and identically distributed random variables. Furthermore, assuming the purchasing price are triangular fuzzy variables, the quantities of the orders are of integer-type and that there are space, budget and service level constraints, incremental discount is considered to purchase products and a combination of back-order and lost-sales are taken into account for the shortages. We show that the model of this problem is a fuzzy mixed-integer nonlinear programming type and in order to solve it, a hybrid method of fuzzy simulation and genetic algorithm approach is used. At the end, a numerical example is given to demonstrate the applicability of the proposed methodology in real world inventory control problems.
Highlights
In multi-periodic inventory control models, the continuous review and the periodic review are the major vastly used policies
The user has the freedom to act at anytime and replenish orders based upon the available inventory level
The multi-periodic inventory control problems have been investigated in depth in different research
Summary
In multi-periodic inventory control models, the continuous review and the periodic review are the major vastly used policies. Five main specifications of the proposed model of this research that have led to its novelty are the stochastic period length, the allowance of multiproducts multi-constraint, the purchasing price being fuzzy variable, incorporating discounts to purchase products and the fact that the decision variables are integer. By deploying these conditions simultaneously, the problem becomes more realistic and the created model is different from the other models in the periodic review literature. We need to identify the inventory levels in each cycle such that the expected profit is maximized
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