Solving multi-period project selection problems with fuzzy goal programming based on TOPSIS and a fuzzy preference relation

• Project portfolio decisions are complex multi-objective problems.
• We propose a fuzzy goal programming model for project portfolio selection.
• The proposed model is based on TOPSIS and a fuzzy preference relation.
• TOPSIS is used to reduce the multi-objective problem into a bi-objective problem.
• A fuzzy preference relation is used to capture uncertain preferences toward fuzzy goals.

Project portfolio managers are multi-objective Decision-Makers (DMs) who are expected to select the best mix of projects by maximizing profits and minimizing risks over a multi-period planning horizon. However, project portfolio decisions are complex multi-objective problems with a high number of projects from which a subset has to be chosen subject to various constraints and a multitude of priorities and preferences. We propose a Goal Programming (GP) approach for project portfolio selection that embraces conflicting fuzzy goals with imprecise priorities. A fuzzy goal with an aspiration level and a predefined membership function is defined for each objective. The impreciseness in the priorities of the membership values of the fuzzy goals is modeled with fuzzy relations. This leads to type II fuzzy sets since fuzzy relations are organized between the membership values of the fuzzy goals which are themselves fuzzy sets. The proposed model is based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and fuzzy preference relations. TOPSIS is used to reduce the multi-objective problem into a bi-objective problem. The resulting bi-objective problem is solved with fuzzy GP (FGP). The fuzzy preference relations are used to help DMs express their preferences with respect to the membership values of the fuzzy goals. The proposed approach is used to solve a real-life problem characterized as a fuzzy Multi-Objective Project Selection with Multi-Period Planning Horizon (MOPS–MPPH). The performance of the proposed approach is compared with a competing method in the literature. We show that our approach generates high-quality solutions with minimal computational efforts.