Mixed-Integer Programming to Solve Distribution Problems

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

Gökhan Göksu Elif Adaköy Melis Mumcuoğlu Seray Şengül Kamil Oruçoğlu

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.

Keywords

Integer programming, Linear programming, Quadratic programming, Distribution problems

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.