حل مسئله دوهدفه زمان‌بندی چندحالته پروژه با درنظرگرفتن برنامه‌ریزی پرداخت و منابع محدود با استفاده از الگوریتم NSGA-II

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد مهندسی صنایع، گروه مهندسی صنایع، دانشکده مهندسی صنایع و مکانیک، واحد قزوین، دانشگاه آزاد اسلامی، قزوین، ایران.

2 دانشیار، گروه مهندسی صنایع، دانشکده مهندسی صنایع و مکانیک، واحد قزوین، دانشگاه آزاد اسلامی، قزوین، ایران.

چکیده

     این پژوهش به بررسی مسئله زمان‌بندی چند­حالته پروژه با در­نظر­گرفتن برنامه‌ریزی پرداخت و منابع محدود پرداخته می‌شود؛ به‌طوری‌که در مسئله پیشنهادی برای هر چه بیشتر در­نظر­گرفتن شرایط حاکم در دنیای واقعی، منابع تجدیدپذیر (از جمله نیروی انسانی، ماشین‌آلات و تجهیزات) و همچنین منابع تجدیدناپذیر (از جمله مصرفی و پول) هم‌زمان در نظر گرفته می‌شوند. در ادامه پژوهش نیز مبحث زمان‌بندی و برنامه‌ریزی پرداخت پروژه با اهداف افزایش NPV پروژه و کاهش زمان اتمام پروژه در مسئله بررسی می­ شود. به همین دلیل ابتدا بر اساس فرضیه ­های مطرح‌شده در فضای مسئله، مدل برنامه‌ریزی غیرخطی ریاضی برای فرموله­ سازی مسئله ارائه می‌شود؛ سپس برای اعتبارسنجی مدل، چندین مسئله نمونه در ابعاد مختلف طراحی می‌شود و سپس توسط نرم‌افزار GAMS و روش محدودیت اپسیلون حل می‌شود. برای حل مسئله در ابعاد بزرگ نیز از روش الگوریتم NSGA-II بهره ­گیری شده و کارایی آن از طریق مقایسه با روش محدودیت اپسیلون سنجیده می‌شود.

کلیدواژه‌ها

عنوان مقاله [English]

Solving a Bi-Objective Multi-Mode Project Scheduling Problem with Regard to Payment Planning and Constrained Resources using NSGA-II Algorithm

نویسندگان [English]

  • Ebrahim Gholizadeh 1
  • Behrouz Afshar Najafi 2
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.
چکیده [English]

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.

کلیدواژه‌ها [English]

  • Multi-Mode Project Scheduling
  • NPV
  • Project Payment Scheduling
  • ε-Constraint Method
  • NSGA-II Algorithm

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