Abstract
This paper presents a multi-objective linear integer program that assigns student volunteers to present lectures at participating classes in local schools. A student’s class assignment is based upon his or her availability to teach at that time as well as several additional factors including student preferences regarding commuting and partners as well as the institution’s goal of creating diverse student groups. This case study shows that the proposed mathematical program dramatically improves the assignments of students to classes and provides increased flexibility for modeling other goals and factors in future years. In addition, this multi-phase model can be applied in other contexts, such as crew scheduling or the scheduling of parallel sessions of large conferences.
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Notes
Of course, the lower bound, 3, and the upper bound, 5, of this range could easily be made parameters that the Outreach Office can change from one semester to the next.
This is another parameter that the Outreach Office may possibly want to change or control itself.
References
Bao CP, Tsai MC, Tsai MI (2007) A new approach to study the multi-objective assignment problem. WHAMPOA-An Interdiscip J 53:123–132
Bayati M, Gleich D, Saber A, Wang Y (2013) Message passing algorithms for sparse network alignment. ACM Trans Knowl Discov Data 7(1), 3–31
Burkard R, Dell’Amico M, Martello S (2009) Assignment problems. SIAM, Philadelphia
Chavey DP, Campbell PJ, Straffin PD, Professor’s Commentary (1994) The politics of course time slots. UMAP J COMAP 15(2):123–136
Chen D-S, Batson RG, Dang Y (2010) Applied integer programming. Wiley, New York
Cook WJ (2012) In pursuit of the traveling salesman. Princeton University Press, Princeton, NJ
Emrah BE, Edis RS (2013) An integer programming model for the conference timetabling problem. C.B.U. J Sci 9(2):55–62
Franklin T, Jenkins E-W, Woodson K (1994) A case study in scheduling courses. UMAP J COMAP 15(2):115–122
Gale D, Shapely L (1962) College admissions and the stability of marriage. Am Math Mon 69:9–15
Glover F, Kuo C-C, Dhir KS (1998) Heuristic algorithms for the maximum diversity problem. J Inf Optim Sci 19(1):109–132
Gusfield D, Irving RW (1989) The stable marriage problem: structure and algorithms. MIT Press, Cambridge, MA
Gueret C, Prins C, Sevaux M, Heipcke S (2002) Applications of optimization with XpressMP. Dash Optimization Blisworth, UK
Kuo C-C, Glover F, Dhir KS (1993) Analyzing and modeling the maximum diversity problem by zero? One programming. Decis Sci 24(6):1171–1185
Langville AN, Pedings K, Yamamoto Y (2012) A minimum violations ranking method. Optim Eng 13(2), 349–370
Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim 26(6):369–395
Mart R, Gallego M, Duarte A (2010) A branch and bound algorithm for the maximum diversity problem. Eur J Oper Res 200(1):36–44
Nemhauser GL, Wolsey LA (1999) Integer and combinatorial optimization, 1st edn. Wiley-Interscience, New York
Potthoff RF, Brams SJ (2007) Scheduling of panels by integer programming: results for the 2005 and 2006 New Orleans meetings. Public Choice 131(3–4):465–8
Rardin RL (1997) Optimization in operations research. Prentice Hall, Englewood Cliffs, NJ
Roth A, Peranson E (1999) The redesign of the matching market for American physicians: some engineering aspects of economic design. Am Econ Rev 89(4):748–780
Roth A, Sotomayor M (1992) Two-sided matching: a study in game-theoretic modeling and analysis. Cambridge University Press, Cambridge, MA
Saaty TL (2008) Decision making for leaders: the analytic hierarchy process for decisions in a complex world. RWS Publications, Pittsburgh, PA
Sampson SE (2004) Practical implications of preference-based conference scheduling. Prod Opera Manag 13(3):205–15
Schniederjans MJ (1984) Linear goal programming. Petrocelli, Princeton, NJ
Silva GC et al (2007) New heuristics for the maximum diversity problem. J Heuristics 13(4):315–336
Taha HA (2006) Operations research, 8th edn. Prentice Hall, Englewood Cliffs, NJ
William HP (1999) Model building in mathematical programming, 4th edn. Wiley, New York
Wolsey LA (1998) Integer programming. Wiley, New York
Yu G, Arguello M, Song G, McCowan SM, White A (2003) A new era for crew recovery at continental airlines. Interfaces 33(1):5–22
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The authors are grateful to DASH Optimization for their Xpress-MP software, which was supplied through their generous Academic Partner Program.
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This research was supported in part by a research fellowship from the Alfred P. Sloan Foundation [T.C.P] and an NSF grant CISE-CCF-AF-1116963 [A.N.L].
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Chartier, T.P., Ellison, V. & Langville, A.N. A Davidson College multi-objective assignment problem: a case study. 4OR-Q J Oper Res 12, 379–401 (2014). https://doi.org/10.1007/s10288-014-0259-2
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DOI: https://doi.org/10.1007/s10288-014-0259-2