FUZZY OPTIMIZATION MODEL OF PROJECT NETWORK WITH UNCERTAINTY

Abstract

Cost-time trade-off is a major problem in project network analysis because reducing project duration generally increases project costs, while minimizing costs may extend project completion time. Existing studies on project crashing and multi-objective optimization mainly focus on deterministic optimization or represent uncertainty using fuzzy input parameters, which often increase computational complexity. This study proposes a Fuzzy Multi-Objective Linear Programming (FMOLP) model based on Zimmermann's fuzzy goal programming framework to obtain a balanced compromise solution between project duration and cost. Unlike approaches that model fuzzy activity durations or costs, the proposed model represents fuzziness through decision-maker satisfaction levels using linear membership functions constructed from the best and worst values of each objective. The model is applied to a project network optimization problem with two objectives: minimizing project cost and minimizing project duration. Individual optimization produces extreme solutions, namely a minimum cost of Rp. 142.226.975 with a duration of 156 days and a minimum duration of 135 days with a total cost of Rp. 146.480.100. The proposed FMOLP model generates a compromise solution with a project duration of 141 days and a total cost of Rp. 143.243.125, including an additional acceleration cost of Rp. 1.016.150. These findings demonstrate that the proposed approach pro vides a computationally simple and practical framework for balancing conflicting project objectives under uncertainty.