IJE TRANSACTIONS B: Applications Vol. 31, No. 5 (May 2018) 676-685    Article in Press

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H. Farughi, A. Amiri and F. Abdi
( Received: August 20, 2017 – Accepted: March 09, 2018 )

Abstract    Project success is assessed based on various criteria, every one of which enjoys a different level of importance for the beneficiaries and decision makers. Time and cost are the most important objectives and criteria for the project success. On the other hand, reducing the risk of finishing activities until the predetermined deadlines should be taken into account. Having formulated the problem as a multi-objective planning problem, the present study aims at minimizing the project completion time as well as maximizing the net present value and project flexibility by taking into account the resource constraints and precedence relations. Here the flexibility of project is calculated by considering a free float for each activity and maximizing the sum of these flotation times. Although most of the researches considered the resources as non-renewable resources, here the resources are considered as renewable ones. Moreover, performing each activity may be possible in various states of using resources (mode) which can change the project completion time and cost. Owing to the complexity of the problem, the Multi Objective Simulated Annealing Meta-heuristic Algorithm is used to solve the proposed model. In doing so, first a feasible answers is proposed and then, using the aforementioned algorithm, it was attempted to find Pareto answers. For accrediting the algorithm, four benchmark problems have been considered. Since the algorithm performed well in finding the optimal answers to the benchmark problems, it was used to find the optimal answer of large scale problems.


Keywords    Resource constrained project scheduling, Time-cost trade-off, Simulated Annealing meta-heuristic algorithm, Project flexibility, Multi-mode activities


چکیده    موفقیت پروژه بر اساس معیارهای مختلفی سنجیده می‌شود که هرکدام از این معیارها از نظر ذینفعان پروژه از اهمیت متفاوتی برخوردار است. زمان و هزینه از مهمترین اهداف و معیارهای موفقیت هر پروژه‌ای هستند. از طرف دیگر کاهش ریسک مربوط به عدم اتمام فعالیت‌های اجرایی تا زمان‌های از پیش تعیین شده به دلیل عوامل غیرقابل پیش‌بینی بایستی مورد توجه قرار گیرد. در تحقیق حاضر، پس از فرموله کردن مسأله در قالب یک مسأله برنامه­ریزی چند هدفه سعی در کمینه کردن زمان اتمام پروژه، بیشینه کردن ارزش فعلی خالص پروژه و انعطاف­پذیری پروژه با در نظر گرفتن محدودیت­های منابع و روابط پیش­نیازی، خواهیم داشت. انعطاف پذیری پروژه با در نظر گرفتن یک زمان شناوری برای فعالیتها و بیشینه کردن مجموع این زمانهای شناوری، درنظر گرفته شده است. علیرغم اینکه اکثر مسائل در نظر گرفته شده در این حوزه دارای منبع تجدیدناپذیر هستند در تحقیق پیشرو منابع موجود به صورت تجدیدپذیر درنظر گرفته شده‌اند. علاوه بر این، برای انجام هر فعالیت در یک پروژه حالت­های مختلفی از مصرف منابع در نظر گرفته شده است، که می‌تواند باعث تغییر در زمان و هزینه اجرای آن فعالیت گردد. با توجه به پیچیدگی مسأله از الگوریتم فراابتکاری شبیه­سازی تبرید چند هدفه برای حل مدل استفاده شده است. برای اعتبار دهی به الگوریتم مورد استفاده چهار مسأله محک مورد استفاده قرار گرفته است. با توجه به عملکرد خوب الگوریتم در یافتن جواب بهینه این مسائل محک، از این الگوریتم برای یافتن جواب بهینه در مسائل بزرگ استفاده شده است.

References    [1] Brucker, P., Drexl, A., Mohring, R., Neumann, K., & Pesch, E., “Resource constrained project scheduling: notation, classification, models and methods”, European Journal of Operational Research, (1999), 3-41. [2] Weglarz, J., Jozefowska, J., Mika , M., & Waligora, G., “Project scheduling with finite or infinite number of activity processing modes – A survey”, European Journal of Operational Research, (2011), 177–205. [3] Pritsker, A. A., Waters , L. J., & Wolfe, P. M., “Multiproject scheduling with limited resources: a zero-one programming approach”,  Management Science, (1969), 93-107. [4] Blazewicz, J., Lenstra , J., & Rinnooy Kan, A., “Scheduling subject to resource constraints: classification and complexity”, Discrete Applied Mathematics, (1983), 11-24. [5] Russell, A., “Cash flows in networks”,  Management Science, (1970), 357–373. [6] Zhengwen, H., Rengina , L., & Tao, J., “Metaheuristics for multi-mode capital-constrained project payment scheduling”,  European Journal of Operational Research, (2012), 605-613. [7] Najafi A. A., Niaki S. T. A.,  “Resource Investment Problem With Discounted Cash Flows”, International Journal of Engineering, Vol. 18, No. 1 (2005), 53-64  [8] Seifi M. and Tavakkoli-Moghaddam R., “A New Bi-Objective Model For A Multi-Mode Resource-Constrained Project Scheduling Problem With Discounted Cash Flows And Four Payment Models”,  International Journal of Engineering Transactions A: Basics, Vol. 21, No. 4 (2008) 347-360 [9] Leymana, P., & Vanhoucke, M., “Payment models and net present value optimization for resource-constrained project scheduling”, Computers & Industrial Engineering, (2016), 139–153. [10] Huang, X., & Zhao, T., “Project selection and scheduling with uncertain net income and investment cost”,  Applied Mathematics and Computation, (2014), 61–71. [11] Wiesemann, W., Kuhn, D., & Rustem, B., “Maximizing the net present value of a project under uncertainty”,  European Journal of Operational Research, (2010), 356–367. [12] Al-Fawzan, M. A., & Haouari, M., “A bi-objective model for robust resource-constrained project scheduling”, Int. J. Production Economics, (2005), 175-187. [13] Kea, H., Wangb, L., & Huangc, H., “An uncertain model for RCPSP with solution robustness focusing on logistics project schedule”, International Journal of e-Navigation and Maritime Economy, (2015), 71–83. [14] Peng, W., & Wang, C., “A multi-mode resource-constrained discrete time-cost trade-off problem and its genetic algorithm based solution”,  International Journal of Project Management, (2008), 600-609. [15] Akkan, C., Drexl, A., & Kimms, A., “Network decomposition-based benchmark results for the discrete time-cost trade-off problem”,  European Journal of Operational Research, (2005),339–358. [16] Patterson, J. H., Slowinski, R., Talbot, F. B., & Weglarz, J., “An algorithm for a general class of precedence and resource constrained scheduling problems”, Advances in Project Scheduling, (1989), 3-28. [17] Talbot, F., “Resource-constrained project scheduling with time-resource trade-offs: the nonpreemptive case”, Management Science, (1982), 1197-1210. [18] Hartmann, S., “Project scheduling with multiple modes: a genetic algorithm”,  Annals of Operations Research, (2001), 111–135. [19] jozefoska, J., Mika, M., Rozycki, R., Waligora, G., & Weglarz, J., “Simulated annealing for multi-mode resource-constrained project scheduling”, Annals of Operations Research, (2001), 137–155. [20] Fahmy, A., Hassan, T. M., & Bassioni, H., “Improving RCPSP solutions quality with Stacking Justification – Application with particle swarm optimization”, Expert Systems with Applications, Vol. 41(13) (2014), 5870–5881. [21] Xiao, J., “Integration of electromagnetism with multi-objective evolutionary algorithms for RCPSP”, European Journal of Operational Research, Vol. 251(1) (2016), 22–35. [22] Kadri, R. L., & Boctor, F. F., “An efficient genetic algorithm to solve the resource-constrained project scheduling problem with transfer times: The single mode case”, European Journal of Operational Research, In Press. [23] Chakrabortty, R. K., Sarker , R. A., & Essam, D. L., “Multi-mode resource constrained project scheduling under resource disruptions”, Computers & Chemical Engineering, (2016), 13-29. [24] Ning, M., He, Z., Jia , T., & Wang, N., “Metaheuristics for multi-mode cash flow balanced project scheduling with stochastic duration of activities”,  Automation in Construction, (2017), 224-233. [25] Kirkpatrick, S., Gellat, C. D., & Vecchi, M. P., “Optimization by simulated annealing”, Scienc, (1983), 671-680. [26] Cerny, V., “A thermodinamical approach to the traveling salesman problem:An efficient simulatin algorithm”, Optimization Theory and Applications, (1985), 41-51. [27] Suppapitnarm, A., Clarkson, P. J., Seffen, K. A., & Parks, G. T., “Simulated annealing: an alternative approach to true multiobjective optimization”, Engin Optim, (2000), 33-59. [28] Suman1, B., & Kumar, P., “A survey of simulated annealing as a tool for single and multiobjective optimization”, Journal of the Operational Research Society, (2006), 1143–1160.

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