Document Type : Original Article


1 MSc. Student, Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Islamic Azad University, Qazvin Branch, Qazvin, Iran.

2 Associate Professor, Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Islamic Azad University, Qazvin Branch, Qazvin, Iran.


This research studies the multi-mode project scheduling problem aiming to planning of payments considering limited resources. This model tries to propose a schedule as much as possible close to reality with taking the realistic assumptions into account. In the proposed model, renewable resources (including manpower, machinery, and equipment) as well as non-renewable resources (including consumption and money) are simultaneously considered. Then, the issues of scheduling and planning the project payment with the objectives of increasing the NPV of the project and reducing the completion time of the project in are examined. In doing so, a nonlinear mathematical programming model is presented based on the assumptions made in the problem space, to formulate the problem. Then, to validate the model, several random instances are designed in different dimensions and solved by GAMS software and ε-constraint method. To tackle the problem in large dimensions, we also proposed the NSGA-II algorithm. Finally, efficiency of the developed methodology is measured by comparing the results with ε-constraint method.


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