Abstract
This paper addresses the airport flight gate scheduling problem with multiple objectives. The objectives are to maximize the total flight gate preferences, to minimize the number of towing activities, and to minimize the absolute deviation of the new gate assignment from a so-called reference schedule. The problem examined is a multicriteria multi-mode resource-constrained project scheduling problem with generalized precedence constraints or time windows. While in previous approaches the problem has been simplified to a single objective counterpart, we tackle it directly by a multicriteria metaheuristic, namely Pareto Simulated Annealing, in order to get a representative approximation of the Pareto front. Possible uncertainty of input data is treated by means of fuzzy numbers.
Similar content being viewed by others
References
Aarts, E. H. L., & Korst, J. H. M. (1989). Simulated annealing and Boltzmann machines. New York: Wiley.
Bartusch, M., Möhring, R. H., & Radermacher, F. J. (1988). Scheduling project networks with resource constraints and time windows. Annals of Operations Research, 16, 201–240.
Błażewicz, J., Lenstra, J. K., & Rinnoy Kan, A. H. G. (1983). Scheduling projects subject to resource constraints: classification and complexity. Discrete Applied Mathematics, 5, 11–24.
Boctor, F. (1996). Resource-constrained project scheduling by simulated annealing. International Journal of Production Research, 34, 2335–2351.
Bouleimen, K., & Lecocq, H. (2003). A new efficient simulated annealing algorithm for the resource-constrained project scheduling problem and its multiple mode version. European Journal of Operations Research, 149, 268–281.
Brucker, P., Knust, S., Schoo, A., & Thiele, O. (1998). A branch-and-bound algorithm for resource-constrained project scheduling. European Journal of Operational Research, 112, 262–273.
Brucker, P., Drexl, A., Möhring, R., Neumann, K., & Pesch, E. (1999). Resource-constrained project scheduling: notation, classification, models and methods. European Journal of Operational Research, 112, 3–41.
Cho, J.-H., & Kim, Y.-D. (1997). A simulated annealing algorithm for resource constrained project scheduling problems. Journal of the Operational Research Society, 48, 736–744.
Christofides, N., Alwarez-Valdes, R., & Tamarit, J.-M. (1987). Project scheduling with resource constraints: a branch and bound approach. European Journal of Operations Research, 29, 262–273.
Czyzak, P., & Jaszkiewicz, A. (1997). Pareto simulated annealing. In G. Fandel & T. Gal (Eds.), Multiple criteria decision making. Proceedings of the XIIth international conference, Hagen (Germany) (pp. 297–307). Berlin–Heidelberg: Springer.
Czyzak, P., & Jaszkiewicz, A. (1998). Pareto simulated annealing—a metaheuristic technique for multiple-objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis, 7, 34–47.
Demeulemeester, E., & Herroelen, W. (1992). A branch-and-bound procedure for the multiple resource-constrained project scheduling problem. Management Science, 38, 1803–1818.
Ding, H., Lim, A., Rodrigues, B., & Zhu, Y. (2004a). New heuristics for the over-constrained airport gate assignment problem. Journal of the Operational Research Society, 55, 760–768.
Ding, H., Lim, A., Rodrigues, B., & Zhu, Y. (2004b). Aircraft and gate scheduling optimization at airports. In Proceedings of the 37th annual Hawaii international conference on system sciences, IEEE (pp. 74–81).
Ding, H., Lim, A., Rodrigues, B., & Zhu, Y. (2004c). The over-constrained airport gate assignment problem. Computers & Operations Research, 32, 1867–1868.
Dorndorf, U. (2002). Project scheduling with time windows: from theory to applications. Heidelberg: Physica-Verlag.
Dorndorf, U., Pesch, E., & Phan Huy, T. (2000a). A time-oriented branch-and-bound algorithm for the resource-constrained project scheduling problem with generalised precedence constraints. Management Science, 46, 1365–1384.
Dorndorf, U., Pesch, E., & Phan Huy, T. (2000b). A branch-and-bound algorithm for the resource-constrained project scheduling problem. Mathematical Methods of Operations Research, 52, 413–439.
Dorndorf, U., Drexl, A., Nikulin, Y., & Pesch, E. (2006). Flight gate scheduling: state-of-the-art and recent developments. Omega, 35, 326–334.
Dorndorf, U., Jaehn, F., Lin, C., Ma, H., & Pesch, E. (2007). Disruption management in flight gate scheduling. Statistica Neerlandica, 61, 92–114.
Dorndorf, U., Jaehn, F., & Pesch, E. (2008). Modelling robust flight gate scheduling as a clique partitioning problem. Transportation Science, 42, 292–301.
Drexl, A., & Nikulin, Y. (2008). Multicriteria airport gate assignment and Pareto simulated annealing. IIE Transactions, 40, 385–397.
Ehrgott, M. (2005). Multicriteria optimization. Berlin: Springer.
Garey, M., & Johnson, D. (1979). Computers and intractability: a guide to the theory of NP-completeness. New York: Freeman.
Geoffrion, A. (1968). Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and Applications, 22, 618–630.
Hapke, M., Jaszkiewicz, A., & Słowiński, R. (1998a). Interactive analysis of multiple-criteria project scheduling problems. European Journal of Operational Research, 107, 315–324.
Hapke, M., Jaszkiewicz, A., & Słowiński, R. (1998b). Fuzzy multi-mode resource-constrained project scheduling with multiple objectives. In J. Węglarz (Ed.), Recent advances in project scheduling (pp. 355–382). Norwell: Kluwer Academic.
Hartmann, S. (2001). Project scheduling with multiple modes: A genetic algorithm. Annals of Operations Research, 102, 111–135.
Hartmann, S., & Drexl, A. (1998). Project scheduling with multiple modes: a comparison of exact algorithms. Networks, 32, 283–297.
Hartmann, S., & Kolisch, R. (2000). Experimental evaluation of state-of-the-art heuristics for the resource-constrained project scheduling problem. European Journal of Operational Research, 127, 394–407.
Jaszkiewicz, A. (2001). Multiple objective metaheuristic algorithms for combinatorial optimization. Habilitation thesis, Poznan University of Technology.
Józefowska, J., Mika, M., Rózycki, R., Waligóra, G., & Węglarz, J. (2001). Simulated annealing for multi-mode resource-constrained project scheduling. Annals of Operations Research, 102, 137–155.
Kirkpatrick, S. (1984). Optimization by simulated annealing—quantitative studies. Journal of Statistical Physics, 34, 975–986.
Kirkpatrick, S., Gelatt, C., & Vecchi, M. (1983). Optimization by simulated annealing. Science, 220, 671–680.
Kolisch, R., & Drexl, A. (1997). Local search for nonpreemptive multi-mode resource-constrained project scheduling. IIE Transactions, 29, 987–999.
Landelma, R., Miettinen, K., & Salminen, P. (2005). Reference point approach for multiple decision makers. European Journal of Operational Research, 162, 785–791.
Lee, J. K., & Kim, Y. D. (1996). Search heuristics for resource-constrained project scheduling. Journal of the Operational Research Society, 47, 678–689.
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., & Teller, E. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087–1092.
Mika, M., Waligóra, G., & Węglarz, J. (2005). Simulated annealing and tabu search for multi-mode resource-constrained project scheduling with positive discounted cash flows and different payment models. European Journal of Operational Research, 162, 639–668.
Neumann, K., Schwindt, C., & Zimmermann, J. (2003). Project scheduling with time windows and scarce resources (2nd ed). Berlin: Springer.
Panwalkar, S., Dudek, R., & Smith, M. (1973). Sequencing research and the industrial scheduling problem. In S. E. Elmaghraby (Ed.), Symposium on the theory of scheduling and its applications. New York: Springer.
Patterson, J. H., Słowiński, R., Talbot, F. B., & Węglarz, J. (1990). Computational experience with a backtracking algorithm for solving a general class of precedence and resource constrained project scheduling problem. European Journal of Operational Research, 49, 68–79.
Rommelfanger, H. (1990). An interactive method for solving multiobjective fuzzy linear programming problems. In R. Slowinski & J. Teghem (Eds.), Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty (pp. 279–299). Dordrecht: Kluwer Academic.
Serafini, P. (1992). Simulated annealing for multiple objective optimization problems. In: Proceedings of the 10th international conference on multiple criteria decision making, Taipei (pp. 87–96).
Serafini, P. (1994). Simulated annealing for multiple objective optimization problems. In G. H. Tzeng, H. F. Wang, V. P. Wen, & P. L. Yu (Eds.), Multiple criteria decision making (pp. 283–292). Berlin: Springer.
Słowiński, R., Soniewicki, B., & Węglarz, J. (1994). DSS for multiobjective project scheduling. European Journal of Operational Research, 79, 220–229.
Sprecher, A., & Drexl, A. (1998). Multi-mode resource-constrained project scheduling by a simple, general and powerful sequencing algorithm. European Journal of Operational Research, 107, 431–450.
Steuer, R. (1986). Multiple criteria optimization—theory, computation and applications. New York: Wiley.
Stinson, J. P., Davis, E. W., & Khumawala, B. M. (1978). Multiple resource-constrained scheduling using branch and bound. AIIE Transactions, 10, 252–259.
T’Kindt, V., & Billaut, J.-C. (2002). Multicriteria scheduling: theory, models and algorithms. Berlin–New York: Springer.
Xu, J., & Bailey, G. (2001). The airport gate assignment problem: mathematical model and a tabu search algorithm. In Proceedings of the 34th annual Hawaii international conference on system sciences, IEEE.
Yan, S., & Huo, C. (2001). Optimization of multiple objective gate assignments. Transportation Research, 35A, 413–432.
Yan, S., & Tang, C. H. (2007). A heuristic approach for airport gate assignment for stochastic flight delays. European Journal of Operational Research, 180, 547–567.
Zadeh, L. (1978). Fuzzy sets as a basic for a theory of possibility. Fuzzy Sets and Systems, 1, 3–28.
Zimmermann, H.-J. (2001). Fuzzy set theory and its applications. Norwell: Kluwer Academic.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work has been supported by the German Science Foundation (DFG) through the grant “Planung der Bodenabfertigung an Flughäfen” (Dr 170/9-1, 9-2 and Pe 514/10-2).
Rights and permissions
About this article
Cite this article
Nikulin, Y., Drexl, A. Theoretical aspects of multicriteria flight gate scheduling: deterministic and fuzzy models. J Sched 13, 261–280 (2010). https://doi.org/10.1007/s10951-009-0112-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-009-0112-1