A Genetic Algorithm for an inventory system under belief structure inflationary conditions

Nodoust, S.; Mirzazadeh, A.; Mohammadi, M.

RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 4-5, pp. 1027-1041.

The literature review on the inflationary inventory systems shows that a lot of researches have been made with considering the inflation as: (1) deterministic and constant; (2) deterministic and variable (time varying); (3) stochastic or (4) fuzzy. However, no attempt has been made to address the issue of how to deal with incomplete, imprecise and missing (ignorance) information in inflation, which is essentially inherent and sometimes inevitable in human being’s subjective judgments. The purpose of this paper is to develop a new method, on the basis of the evidential reasoning (ER) approach in order to handle various types of possible uncertainties that may occur in the determining of the inflation rate in the inventory decision making. It is capable of modeling various types of uncertainties using a unified belief structure in a pragmatic, rigorous, reliable, systematic, transparent and repeatable way. The evidential reasoning approach uses a systematic way to accumulate the incomplete data about inflation, which have been gathered from different decision makers. This approach causes interval inflation by accumulating information of all decision makers. Representing the inflation by an interval number and using the interval arithmetic, the objective function for cost is changed to corresponding multi objective functions. These functions are minimized and solved by NSGA- II approach of Multi-objective Genetic Algorithm. The algorithm parameters are tuned by Taguchi method and the mentioned parameter-tuned algorithm has been validated using several numerical examples by comparison with the optimal solution. The results show that the proposed GA takes less time than the classical model in solving the problem. This difference of times is more significant when we want to do a sensitivity analysis in a wide range of parameters.

Classification : 90B05, 90C27
Mots clés : Inventory system, genetic algorithm, inflation, Dempster–Shafer theory, evidential reasoning, belief structure

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