A Fuzzy Optimization Framework for COTS Products Selection of Modular Software Systems

In this paper, we discuss a decision-making situation under uncertainty related to software creation through Commercial-Off-The-Shelf (COTS) based modules. We propose a bi-objective fuzzy optimization model of the COTS selection problem. The proposed optimization model simultaneously maximize the weighted quality and minimize the total cost of a modular software system subject to many limitations including maximum threshold on delivery time of the software and incompatibility among COTS products. The coefficients of both the objective functions and the delivery time constraints are characterized by fuzzy restrictions with triangular possibility distributions. Analytical hierarchy process technique is used to assign weights to the various modules according to their access frequencies and also using preferences of the software developer regarding technical specifications of the software system. Using possibility theory, an auxiliary linear multiple objective 0-1 programming model parameterized by possibility (feasibility) level beta is obtained corresponding to the fuzzy COTS selection model. The resultant model is converted into an equivalent crisp 0-1 linear programming model using max-min approach employing linear membership functions for all the fuzzy sets and we solved the equivalent model using an interactive approach that provides fuzzy solutions corresponding to different possibility levels beta. A real-world case study of ERP software system is included for numerical illustrations to deal with many situations of the imprecise data in the fuzzy COTS selection model.