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Mixed-Integer Programming to Solve Distribution Problems

Year 2020, Volume: 9 Issue: 3, 38 - 50, 25.12.2020

Abstract

Mixed-integer linear and quadratic programming problems are considered to solve distribution problems in this paper. The first problem is the distribution of proctors with respect to the student placements to the class- rooms by mixed-integer linear programming whereas the second problem is the fair distribution of the workloads for teaching assistants in a department formulated by mixed-integer quadratic programming. Three approaches to find the solution for mixed-integer quadratic programming problem are proposed and a comparative example is given to measure the effects for the suggested criterion.

References

  • Adaköy, E., Mumcuoğlu, M., Şengül, S., Göksu, G., Oruçoğlu, K., 2017. Mixed Integer Quadratic Programming and an Application in Workload Assignment. Optimization 2017, pp. 86-87, September 06-08, Lisbon, Portugal.
  • Baykasoglu, A., Ozbakir, L. and Tapkan, P., 2009. The Bees Algorithm for Workload Balancing in Examination Job Assignment. European Journal of Industrial Engineering, 3(4): 424-435.
  • Bitzer, E.M., 2007. Attempting a Fair and Equitable Academic Workload Distribution in a Faculty of Education. South African Journal of Higher Education, 21(1): 23-37.
  • Bliek, C., Bonami, P., Lodi, A., 2014. Solving Mixed-Integer Quadratic Programming Problems with IBM-CPLEX: A Progress Report. 26th RAMP Symposium, pp. 16-17, October 16-17, Tokyo, Japan.
  • Gomory, R.E., 1960. Solving Linear Programming Problems in Integers. Combinatorial Analysis, 10: 211-215.
  • Karush W., 1939. Minima of Functions of Several Variables with Inequalities as Side Conditions. MSc. Thesis, Chicago University, USA.
  • Kelley, Jr, J.E., 1960. The Cutting-Plane Method for Solving Convex Programs. Journal of the Society for Industrial and Applied Mathematics, 8(4): 703-712.
  • Kenny, J., 2018. Re-Empowering Academics in a Corporate Culture: An Exploration of Workload and Performativity in a University. Higher Education, 75(2): 365-380.
  • Ku, W.Y., Pinheiro, T. and Beck, J.C., 2014. CIP and MIQP Models for the Load Balancing Nurse-to-Patient Assignment Problem. International Conference on Principles and Practice of Constraint Programming, pp. 424-439, September 8-12, Lyon, France.
  • Kuhn, H.W. and Tucker, A.W., 1951. Nonlinear Programming. Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481-492, July 31-August 12, University of California, Berkeley, USA.
  • Park, J. and Boyd, S., 2018. A Semidefinite Programming Method for Integer Convex Quadratic Minimization. Optimization Letters, 12(3): 499-518.
  • Parsons, P.G. and Slabbert, A.D., 2001. Performance Management and Academic Workload in Higher Education. South African Journal of Higher Education, 15(3): 74-81.
Year 2020, Volume: 9 Issue: 3, 38 - 50, 25.12.2020

Abstract

References

  • Adaköy, E., Mumcuoğlu, M., Şengül, S., Göksu, G., Oruçoğlu, K., 2017. Mixed Integer Quadratic Programming and an Application in Workload Assignment. Optimization 2017, pp. 86-87, September 06-08, Lisbon, Portugal.
  • Baykasoglu, A., Ozbakir, L. and Tapkan, P., 2009. The Bees Algorithm for Workload Balancing in Examination Job Assignment. European Journal of Industrial Engineering, 3(4): 424-435.
  • Bitzer, E.M., 2007. Attempting a Fair and Equitable Academic Workload Distribution in a Faculty of Education. South African Journal of Higher Education, 21(1): 23-37.
  • Bliek, C., Bonami, P., Lodi, A., 2014. Solving Mixed-Integer Quadratic Programming Problems with IBM-CPLEX: A Progress Report. 26th RAMP Symposium, pp. 16-17, October 16-17, Tokyo, Japan.
  • Gomory, R.E., 1960. Solving Linear Programming Problems in Integers. Combinatorial Analysis, 10: 211-215.
  • Karush W., 1939. Minima of Functions of Several Variables with Inequalities as Side Conditions. MSc. Thesis, Chicago University, USA.
  • Kelley, Jr, J.E., 1960. The Cutting-Plane Method for Solving Convex Programs. Journal of the Society for Industrial and Applied Mathematics, 8(4): 703-712.
  • Kenny, J., 2018. Re-Empowering Academics in a Corporate Culture: An Exploration of Workload and Performativity in a University. Higher Education, 75(2): 365-380.
  • Ku, W.Y., Pinheiro, T. and Beck, J.C., 2014. CIP and MIQP Models for the Load Balancing Nurse-to-Patient Assignment Problem. International Conference on Principles and Practice of Constraint Programming, pp. 424-439, September 8-12, Lyon, France.
  • Kuhn, H.W. and Tucker, A.W., 1951. Nonlinear Programming. Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481-492, July 31-August 12, University of California, Berkeley, USA.
  • Park, J. and Boyd, S., 2018. A Semidefinite Programming Method for Integer Convex Quadratic Minimization. Optimization Letters, 12(3): 499-518.
  • Parsons, P.G. and Slabbert, A.D., 2001. Performance Management and Academic Workload in Higher Education. South African Journal of Higher Education, 15(3): 74-81.
There are 12 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Gökhan Göksu 0000-0001-8442-9637

Elif Adaköy This is me

Melis Mumcuoğlu This is me

Seray Şengül This is me

Kamil Oruçoğlu 0000-0002-8848-0058

Publication Date December 25, 2020
Published in Issue Year 2020 Volume: 9 Issue: 3

Cite

APA Göksu, G., Adaköy, E., Mumcuoğlu, M., Şengül, S., et al. (2020). Mixed-Integer Programming to Solve Distribution Problems. Journal of New Results in Science, 9(3), 38-50.
AMA Göksu G, Adaköy E, Mumcuoğlu M, Şengül S, Oruçoğlu K. Mixed-Integer Programming to Solve Distribution Problems. JNRS. December 2020;9(3):38-50.
Chicago Göksu, Gökhan, Elif Adaköy, Melis Mumcuoğlu, Seray Şengül, and Kamil Oruçoğlu. “Mixed-Integer Programming to Solve Distribution Problems”. Journal of New Results in Science 9, no. 3 (December 2020): 38-50.
EndNote Göksu G, Adaköy E, Mumcuoğlu M, Şengül S, Oruçoğlu K (December 1, 2020) Mixed-Integer Programming to Solve Distribution Problems. Journal of New Results in Science 9 3 38–50.
IEEE G. Göksu, E. Adaköy, M. Mumcuoğlu, S. Şengül, and K. Oruçoğlu, “Mixed-Integer Programming to Solve Distribution Problems”, JNRS, vol. 9, no. 3, pp. 38–50, 2020.
ISNAD Göksu, Gökhan et al. “Mixed-Integer Programming to Solve Distribution Problems”. Journal of New Results in Science 9/3 (December 2020), 38-50.
JAMA Göksu G, Adaköy E, Mumcuoğlu M, Şengül S, Oruçoğlu K. Mixed-Integer Programming to Solve Distribution Problems. JNRS. 2020;9:38–50.
MLA Göksu, Gökhan et al. “Mixed-Integer Programming to Solve Distribution Problems”. Journal of New Results in Science, vol. 9, no. 3, 2020, pp. 38-50.
Vancouver Göksu G, Adaköy E, Mumcuoğlu M, Şengül S, Oruçoğlu K. Mixed-Integer Programming to Solve Distribution Problems. JNRS. 2020;9(3):38-50.


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