A MEMBERSHIP FUNCTION APPROACH FOR COST-RELIABILITY TRADE-OFF OF COTS SELECTION IN FUZZY ENVIRONMENT

The optimization techniques used in commercial-off-the-shelf (COTS) selection process faces challenges to deal with uncertainty in many important selection parameters, for example, cost, reliability and delivery time. In this paper, we propose a fuzzy optimization model for selecting the best COTS product among the available alternatives for each module in the development of modular software systems. The proposed model minimizes the total cost of the software system satisfying the constraints of minimum threshold on system reliability, maximum threshold on the delivery time of the software, and incompatibility among COTS products. In order to deal with uncertainty in real-world applications of COTS selection, the coefficients of the cost objective function, delivery time constraints and minimum threshold on reliability are considered fuzzy numbers. The fuzzy optimization model is converted into a pair of mathematical programming problems parameterized by possibility (feasibility) level α using Zadeh's extension principle. The solutions of the resultant problems at different α-cuts provide lower and upper bounds of the fuzzy minimum total cost which helps in constructing the membership function of the cost objective function. The solution approach provide fuzzy solutions instead of a single crisp solution thereby giving decision maker enough flexibility in maintaining cost-reliability trade-off of COTS selection besides meeting other important system requirements. A real-world case study is discussed to demonstrate the effectiveness of the proposed model in fuzzy environment.