مدل برنامه‌ریزی ریاضی مسئله زمان‌بندی پروژه چندحالته با منابع محدود و در نظر گرفتن معیارهای زیست محیطی

حمیدزاده, فرهاد; مختاری, هادی

doi:10.22034/sep.2025.2073888.1406

مدل برنامه‌ریزی ریاضی مسئله زمان‌بندی پروژه چندحالته با منابع محدود و در نظر گرفتن معیارهای زیست محیطی

مقالات آماده انتشار

نوع مقاله : پژوهشی

نویسندگان

فرهاد حمیدزاده ¹

هادی مختاری ²

¹ کارشناسی، گروه مهندسی صنایع، دانشکده مهندسی، دانشگاه کاشان، کاشان، ایران

² نویسنده مسئول: دانشیار، گروه مهندسی صنایع، دانشکده مهندسی، دانشگاه کاشان، کاشان، ایران

10.22034/sep.2025.2073888.1406

چکیده

مسئله زمان‌بندی پروژه‌ها با منابع محدود در پی یافتن توالی مناسبی برای انجام فعالیت‌های یک پروژه است، به‌نحوی‌که محدودیت‌های تقدم و تأخر شبکه پروژه و انواع مختلف محدودیت‌های منابع موجود در پروژه، به‌طور هم‌زمان ارضا و همچنین معیار سنجش معینی ازجمله زمان انجام پروژه، هزینه انجام فعالیت‌ها، تعداد فعالیت‌های تأخیردار و غیره بهینه شوند. با توسعه این مسئله در طی سالیان اخیر، یک فعالیت می‌تواند از چندین راه یا حالت انجام پذیرد (برای مثال هر فعالیت می‌تواند در زمانی خاص و با مقداری خاص از منبع تجدیدپذیر یا تجدیدناپذیر انجام پذیرد). این مفهوم جدید سبب توسعه یکی از عمومی‌ترین حالت‌های مسائل زمان‌بندی، با عنوان زمان‌بندی پروژه با منابع محدود چندحالته شده است. از طرفی انسان امروزه در حالی به هزاره سوم گام می‌نهد که هرروز دچار مسائل زیست‌محیطی و پیرامونی زیادی می‌شود و آثار آلودگی زیست‌محیطی و تخریب منابع طبیعی، هرلحظه بیش‌ازپیش حیات طبیعی را مورد تهدید قرار می‌دهد. ازاین‌رو مقابله با آثار مخرب فعالیت‌های نامتوازن اقتصادی و صنعتی بر پیکره محیط‌زیست، رفع و ترمیم آن، از دغدغه‌های مهم حیات کنونی است. هدف از این مقاله، با توجه به اهمیت امروزه معیارهای سبز، مدل‌سازی ریاضی و بهینه‌سازی مسئله زمان-بندی پروژه با منابع محدود چندحالته با در نظر گرفتن انتشار گاز می‌باشد. پس از مدل‌سازی مسئله در قالب یک مسئله برنامه‌ریزی عدد صحیح مختلط، خروجی‌ها تحلیل و ارزیابی شدند.

تازه های تحقیق

یک مدل بهینه‌سازی برای مسئله زمان‌بندی پروژه پیشنهاد شده است.
منابع چندحالته گنجانده شده است.
معیارهای محیطی پیشنهادی برای مسئله زمان‌بندی پروژه پیشنهاد شد.

کلیدواژه‌ها

زمان‌بندی پروژه با منابع محدود

زمان‌بندی پروژه با منابع محدود چندحالته

معیارهای سبز

مدل‌سازی ریاضی

بهینه‌سازی

موضوعات

سیستم‌های تصمیم‌گیری

عنوان مقاله English

Mathematical Programming Model for Multi-Mode Resource Constrained Project Scheduling Problem with Environmental Criteria

نویسندگان English

Farhad Hamidzadeh ¹

Hadi Mokhtari ²

¹ B.Sc., Department of Industrial Engineering, Faculty of Engineering, University of Kashan, Kashan, Iran

² Corresponding author: Associate Professor, Department of Industrial Engineering, Faculty of Engineering, University of Kashan, Kashan, Iran

چکیده English

The resource-constrained project scheduling problem seeks to find an appropriate sequence for performing the activities of a project such that precedence constraints in the project network and various types of resource limitations are satisfied simultaneously, while specific performance criteria—such as project completion time, activity execution costs, the number of delayed activities, and so on—are optimized. With the development of this problem in recent years, an activity can be performed in several possible modes (for example, each activity can be executed within a specific duration and with a certain amount of renewable or non-renewable resources). This new concept has led to the development of one of the most general forms of scheduling problems, known as the multi-mode resource-constrained project scheduling problem. On the other hand, as humanity steps into the third millennium, it faces numerous environmental and ecological issues every day. The effects of environmental pollution and the destruction of natural resources threaten natural life more than ever. Therefore, preventing the destructive impact of unbalanced economic and industrial activities on the environment, as well as restoring and repairing it, have become major concerns in modern life. Given the current importance of green criteria, the aim of this paper is to mathematically model and optimize the multi-mode resource-constrained project scheduling problem while considering gas emissions. After modeling the problem as a mixed-integer programming formulation, the results were analyzed and evaluated.

کلیدواژه‌ها English

Resource-Constrained Project Scheduling

Multi-Mode Resource-Constrained Project Scheduling

Green Criteria

Mathematical Modelling

Optimization

Copyright © Farhad Hamidzadeh, Hadi Mokhtari

License

This article is released under the Creative Commons Attribution (CC BY 4.0) license. Anyone is free to copy, share, translate, and adapt this article for any purpose, whether commercial or non-commercial, as long as proper citation is given to the authors and original publication.

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