A fuzzy multi-objective model for solving project network problem with bonus and incremental penalty cost

• We develop multiobjective linear mathematical model for project network problem under fuzziness.
• We design a model supporting project managers to evaluate bonus and incremental penalty cost simultaneously.
• We compare the findings with different methods under various sets of weights.
• We demonstrate a real life case study to check the feasibility of the model.
• We observed that the trade-off between time & cost is significant and implementation of the proposed method may provide substantial savings.

Project management decisions require considering several conflicting constraints and objectives as well as uncertainties in the information over the planning period. The study aims to design a multi-objective linear programming model for solving project network problem under fuzzy environment. The developed model consists of three objectives such as minimizing total project completion time, minimizing total project completion cost and minimizing the earliest time of an event requiring special attention by taking into account several factors such as crash time, normal time, normal cost, crash cost, indirect cost as well as financial bonus and incremental penalty cost. In the study, a case study based on a real life problem is conducted to illustrate the validity and feasibility of the model. The study contributes to the project network literature by developing the fuzzy goal programming model and allows the project managers simultaneously evaluate financial bonus and incremental penalty cost with respect to total project time. In addition, the results of the sensitivity analysis highlight that the developed model can be used for helping the contractors make effective decisions.