Análise de modelos matemáticos para o problema de marketing direto com oferta de produtos

Abstract

The increasing complexity of modern business environments and the vast volume of data available make it necessary to use advanced models and computerized methods in organizations. With competitiveness increasing rapidly, organizations need to seek their differential and data are, often, the basis for calculations and simulations that support decision-making in a number of areas, including direct marketing. Direct marketing is a strategy that differentiates customers and exposes them to personalized information, seeking to supply individual needs and desires in the best possible way. The present research has the objective of analyze the behavior of mathematical models to solve the problem of direct marketing with product offer, whose purpose is to obtain the maximization of the problem, also considering the effect of cannibalism between products, comparing the quality of solutions obtained, GAP and computational time employed to obtain the results, thus, observing the performance of the commercial solver adopted. The method of study is based on Operational Research, especially in mathematical modeling. The mathematical models investigated, started from previous studies, exploring exact and heuristic methods to solve problems of direct marketing with offer of products. There were six executions of 324 instances for the problems No Cannibalism, M+, M+ Cannibalism, With Cannibalism, Dissimilarity and Similarity. The mathematical modeling in the Zimpl language generated LP files, later executed in the ILOG CPLEX Optimization Studio solver to solve the problems. The six exact methods performed in the present research, demonstrated good performance in the problems in which they were applied, since for the problem No Cannibalism 91.67% of the sets reached optimality, for the changes in the problem M+ Cannibalism and M+, 93.21% and 94.14% of the sets, respectively, obtained the optimal results. The problem With Cannibalism corresponded to 91.98% of optimal solutions, being that, the problem with Dissimilar pairs reached 95.37% and Similiridade 93.21%. The exact method applied proved be sufficient for the problems in question. It was verified the efficiency of the CPLEX solver for the problems already mentioned, since it provided the upper limits for all problems and in the majority, in the optimality, executing them in acceptable computational time. The files resulting from the application of the exact methods used in this research, are available at GitHub, aiming to foster new optimization research for problems of direct marketing with product offerings.