Research ArticleOpen AccessGoogle Scholar indexed
Interdependence of Software and Progress of Mathematics in OR: Some Illustrative Cases and Challenges
Department of Mathematical and Geospatial Sciences, School of Sciences, RMIT University, Melbourne, Australia
School of Economics and Decision Sciences, North West University, Mafikeng Campus, Mafikeng, South Africa
- 1 Department of Mathematical and Geospatial Sciences, School of Sciences, RMIT University, Melbourne, Australia
- 2 School of Economics and Decision Sciences, North West University, Mafikeng Campus, Mafikeng, South Africa
American Journal of Operations Research·Volume 11 (2021)·Pages 110–119·Published 8 March 2021·DOI10.4236/ajor.2021.112007
Copy link · social · email
Abstract
This paper points out that delayed or no supply of software can kill potential benefits associated with new mathematical ideas that have led to development of new mathematics in OR. It also points out that it is a self-created situation by the scientific community. This situation needs attention and should be resolved urgently. Many illustrative examples have been given to justify the claim .
KeywordsLinear and Integer ProgramsSoftware DevelopmentProtean SystemsAnalysis of Protean Systems
- Kirby, M.J.L. and Scobey, P.F. (1970) Production Scheduling of n Identical Machines. Journal of Canadian Operational Research Society, 8, 14-27.
- Kirby, M.J.L., Love, H.R. and Swarup, K. (1972) Extreme Point Mathematical Programming Problem. Management Science, 18, 540-549. https://doi.org/10.1287/mnsc.18.9.540
- Narula, S.C. and Nwosu, A.D. (1991) Two Level Resource Control Pre-Emptive Hierarchical Linear Programming Problem: A Review. In: Kumar, S., Ed., Recent Developments in Mathematical Programming, Gordon and Breach Science Publishers, Melbourne, 29-44.
- Kalyan, R. and Kumar, S. (1991) A Study of Protean Systems—Some Heuristics and Strategies for Redundancy Optimization. In: Kumar, S., Ed., Recent Developments in Mathematical Programming, Gordon and Breach Science Publishers, Melbourne, 181-198.
- Kumar, S. (1995) Optimization of Protean Systems: A Review. APORS’94, Fukuoka, 26-29 July 1994, 139-146.
- Kumar, S. and Arora, H. (1995) Shortest Paths and Connected Graphs in Protean Networks. In: Kapur, P.K. and Sehgal, V.K., Eds., Operations Research—Theory and Practice, Spaniel Publishers, New Delhi, 125-135.
- Kumar, S. and Bapoo, R. (1995) Shortest Routes in Protean Networks. In: Du, D.-Z., Zhang, X.-S. and Cheng, K., Eds., Operations Research and Its Applications, World Publishing Corporation, Beijing, 228-237.
- Kumar, S. and Wagner, D. (1979) Some Algorithms for Solving Extreme Point Mathematical Programming Problems. New Zealand Journal of OR, 7, 127-149.
- Kumar, S. (2005) Information Recycling Mathematical Methods for Protean Systems: A Pathway Approach. South African Journal of Industrial Engineering, 16, 82-101. https://doi.org/10.7166/16-2-168
- Treen, A. (2020) Knowledge Transfer Partnerships—An Introduction. Mathematics Today, 56, 192-193.
- Nyamugure, P., Munapo, E., Lesaoana, M. and Kumar, S. (2016) A Heuristic for a Mixed-Integer Program Using the Characteristic Equation Approach. International Journal of Mathematical, Engineering and Management Sciences, 2, 1-16. https://doi.org/10.33889/IJMEMS.2017.2.1-001
- Munapo, E. and Kumar, S. (2013) Solving Large-Scale Linear Optimization Problem with Non-Negative Coefficients by Transforming into a Two-Variable LP Problem. ASOR Bulletin, 32, 1-12.
- Munapo, E., Kumar, S., Lesaoana, M. and Nyamugure, P. (2014) Solving Large- Scale LP Model with Non-Negative Coefficients: An Hybrid Search over the Extreme Points and the Normal Direction of the Given Objective Function. ASOR Bulletin, 33, 11-23.