Minimum Moment Method for Resource Leveling Using Entropy Maximization
Publication: Journal of Construction Engineering and Management
Volume 136, Issue 5
Abstract
The minimum moment method for resource leveling is revisited and restated as an entropy-maximization problem. The minimum moment method assumes that the moment of the daily resource demands about the horizontal axis of a project’s resource histogram is a good measure of the resource utilization and that the optimal resource allocation exists when the total moment is at a minimum, thus when the resource histogram is of rectangular shape. The entropy-maximization method proposed in this paper makes use of the general theory of entropy and two of its principal properties (subadditivity and maximality) to revisit the minimum moment method for resource leveling. The entropy-maximization method presented allows for activity stretching and provides resource allocation solutions that show improvement over previous approaches. A case study is also presented that validates the results.
Get full access to this article
View all available purchase options and get full access to this article.
References
Aslani, P. (2007). “Dynamic resource-constrained scheduling.” Ph.D. thesis, Polytechnic Univ., Brooklyn, N.Y.
Brucker, P., and Knust, S. (2003). “Lower bounds for resource-constrained project scheduling problems.” Eur. J. Oper. Res., 149, 302–313.
Brucker, P., Knust, S., Schoo, A., and Thiele, O. (1998). “A branch and bound algorithm for the resource-constrained project scheduling problem.” Eur. J. Oper. Res., 107, 272–288.
Carruthers, J. A., and Battersby, A. (1966). “Advances in critical path methods.” Oper. Res., 17, 359–380.
Choi, J., and Russell, J. S. (2005). “Long-term entropy and profitability change of United States public construction firms.” J. Manage. Eng., 21(1), 17–26.
Christodoulou, S. (2005). “Ant colony optimization in construction scheduling.” Proc., ASCE Int. Conf. on Computing in Civil Engineering, ASCE, Reston, Va.
Christodoulou, S. (2007). “Resource-constrained scheduling using ant colony optimization.” Proc., 9th Int. Conf. on the Application of Artificial Intelligence to Civil, Structural and Environmental Engineering (AICC07), Civil-Comp Press, St. Julian’s, Malta.
Christodoulou, S. (2008). “A bid-unbalancing method for lowering a contractor’s financial risk.” Constr. Manage. Econom., 26(12), 1291–1302.
Christodoulou, S., Ellinas, G., and Aslani, P. (2009). “Disorder considerations in resource-constrained scheduling.” Constr. Manage. Econom., 27(3), 229–240.
Colak, S., Agarwal, A., and Erenguc, S. (2006). “Resource constrained project scheduling: A hybrid neural approach.” Perspectives in modern project scheduling, J. Józefowska, and J. Weglarz, eds., Springer, 297–318.
Crawford, J. (1996). “An approach to resource constrained project scheduling.” Proc., 1996 AI and Manufacturing Research Planning Workshop, Association for the Advancement of Artificial Intelligence (AAAI), Calif.
Demeulemeester, E., and Herroelen, W. (1992). “A branch-and-bound procedure for the multiple resource-constrained project scheduling problem.” Manage. Sci., 38, 1803–1818.
Demeulemeester, E. L., and Herroelen, W. S. (1997). “New benchmark results for the resource-constrained project scheduling problem.” Manage. Sci., 43, 1485–1492.
Garey, M. R., Graham, R. L., Johnson, D. S., and Yao, A. C. C. (1976). “Resource constrained scheduling as generalized bin packing.” J. Comb. Theory Ser. A, 21, 257–298.
Harris, R. B. (1978). Precedence and arrow networking techniques for construction, Wiley, New York.
Harris, R. B. (1990). “Packing method for resource leveling (pack).” J. Constr. Eng. Manage., 116(2), 331–350.
Hegazy, T. (1999). “Optimization of resource allocation and leveling using genetic algorithms.” J. Constr. Eng. Manage., 125(3), 167–175.
Hegazy, T. (2001). Computer-based construction project management, Prentice-Hall, Upper Saddle River, N.J.
Hiyassat, M. A. S. (2000). “Modification of minimum moment approach in resource leveling.” J. Constr. Eng. Manage., 126(4), 278–284.
Hiyassat, M. A. S. (2001). “Applying modified minimum moment method to multiple resource leveling.” J. Constr. Eng. Manage., 127(3), 192–198.
Landsberg, P. (1984). “Is equilibrium always an entropy maximum?” J. Stat. Phys., 35, 159–169.
Liu, Y., Zhao, S. -L., Du, X. -K., and Li, S. -Q. (2005). “Optimization of resource allocation in construction using genetic algorithms.” Proc., 2005 Int. Conf. on Machine Learning and Cybernetics, Vol. 6, IEEE, Guangzhou, China, 3428–3432.
Martinez, J., and Ioannou, P. (1993). “Resource leveling based on the modified minimum moment heuristic.” Computing in civil and building engineering, ASCE, New York, 287–294.
Martinez, J. C., and Ioannou, P. G. (1992). “CPMlevel, resource leveling using the generalized minimum moment algorithm.” User’s guide, Univ. of Michigan.
Microsoft project electronic manual, v2000 edition. (2000). Microsoft, Redmond, Wash.
Mingozzi, A., Maniezzo, V., Ricciardelli, S., and Bianco, L. (1998). “An exact algorithm for the resource-constrained project scheduling problem based on a new mathematical formulation.” Manage. Sci., 44, 714–729.
Patterson, J. H. (1984). “A comparison of exact approaches for solving the multiple constrained resource, project scheduling problem.” Manage. Sci., 30, 854–867.
Primavera Project Planner electronic manual; v3.1 edition. (2001). Primavera Systems Inc., Bala Cynwyd, Pa.
Sakellaropoulos, S., and Chassiakos, A. P. (2004). “Project time-cost analysis under generalised precedence relations.” Adv. Eng. Softw., 35, 715–724.
Senouci, A. B., and Eldin, N. N. (2004). “Use of genetic algorithms in resource scheduling of construction projects.” J. Constr. Eng. Manage., 130(6), 869–877.
Winston, W. L., and Venkataramanan, M. (2002). Introduction to mathematical programming, 4th Ed., Thomson-Brooks/Cole, Pacific Grove, Calif.
Information & Authors
Information
Published In
Copyright
© 2010 ASCE.
History
Received: Dec 1, 2008
Accepted: Sep 8, 2009
Published online: Sep 11, 2009
Published in print: May 2010
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.