[1] Combinatorial Optimisation, especially Scheduling & Sequencing and Polyhedral Combinatorics,
[2] Quality management
[3] Multivariate measurement methods,
[3] Optimisation in statistics
[4] Machine learning and
[5] Decision Making.

Summary Statement:

Combinatorial Optimisation, especially polyhedral combinatorics, quality management and multivariate measurement methods, optimisation in statistics and learning. The new formulation for the symmetric travelling salesman problem given by me was further studied and a student of mine could earn her PhD from that work. Another student of mine earned his PhD in software reliability. This work in part is based on the paradigm of oil exploration and software bug deduction. Dr.Genichi Taguchi’s use of Mahalanobis distance in his MTS (Mahalanobis Taguchi System/Strategy) attracted my interest due to its successful applications in industry and business. My research interests in MTS are from both the theoretical and applied perspectives. Currently stemming from my teaching Research Methods course, I am also interested in developing systems with natural language processing interfaces for learning specific topics in statistical inference.

Stochastic management

With Don Trietsch I have worked in the past two years discussing and refining concepts of interest in practical stochastic management. We have plans to bring out a book on Hierarchically Balanced Focusing. Recently we presented a paper on  this theme in the international conference on Industrial Engineering--Theory, Applications and Practice, held at Auckland.

Summer School in Mathematical Programming and Its Applications:

Indian Statistical Institute, Bangalore organised the above summer school between Jun 7 - July 7 2001. The participants were university lecturers and some research scholars. As part of the program, I was invited to deliver a course on new polyhedral approach to TSP. The participants were delighted by the presentation and lecture material provided.

Special session on Mahalanobis Taguchi Systems during IISA:

The organisers of IISA 2002 invited me to Chair and organise a special session on Mahalanobis Taguchi Systems (MTS) and their applications. Dr. Shin Taguchi (son of Dr. Genichi Taguchi), President, American Supplier Institute (ASI), a practitioner from Ford Motors and myself delivered talks. This session was well received and the discussions revealed the importance of the topic and the controversy surrounding ideas coming from Prof. Genichi Taguchi. One of the editors of the journal Tecchnometrics, who attended the session, requested me to be a discussant for a paper submitted to Technometrics on MTS. This opportunity later resulted in a full paper published in Statistical Methods.

1. Arthanari, T.S., On Pedigree Polytopes and Hamiltonian Cycles, Discrete Mathematics, 306, 1474-1492, 2006.
2. Arthanari, T.S., Making Decisions within the Space of Seven Breaths, In Sylnovie Merchant (ed.), Proceedings of 4th Global Conference on Business & Economics, Oxford, UK, June 26-28, 1-18, 2005.
3. Arthanari, T.S., Pedigree polytope is a Combinatorial Polytope, Chapter 1 in Operations Research with Economic and Industrial Applications: Emerging Trends, Eds. S.R. Mohan and S.K. Neogy, Anamaya Publishers, New Delhi, India, 2005.
4. Arthanari, T.S., A Game Theory Application in Robust Design, Quality Engineering, Vol. 17, 2, 291-300, 2005.
5. Arthanari, Tiru and Trietsch, Dan., A Graphical Method for the Pursuit of Optimal or Near Optimal Stochastic Balance, Proceedings of the 9th International Conference on Industrial Engineering--Theory, Applications and Practice, The University of Auckland, November 27-30, 260-266, 2004.
6. Arthanari, Tiru, Mahalanobis Distance in Multivariate Measurement Systems, Statistical Methods, Vol. 5, 2, 1-30, 2003.
7. Arthanari, T.S., Tolerancing – Approaches and Related Issues in Industry – A Chapter in Handbook of Statistics, Vol. 22, edited by C. R. Rao and R. Khattree, ISBN: 0-444-50614-4, North –Holland, 2003.
8. Arthanari, T.S., Is Learning an Optimisation Problem, Proceedings of the 53rd Session of the International Statistical Institute, Seoul, 2001.
9. Arthanari, T.S. and Usha, M., On the Equivalence of the Multistage - Insertion and Cycle - Shrink Formulations of the Symmetric Travelling salesman Problem, Operations Research Letters, 29, 3, 129-139, 2001.
10. Arthanari, T.S. and Kecman, V., Comparisons of QP and LP Based Learning from Empirical Data, (in Engineering of Intelligent Systems, L. Monostori, J. Váncza, M. Ali (eds.), Proceedings of 14th International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems, IEA/AIE 2001, Budapest, Hungary), Springer Verlag, LNAI 2070, pp. 326-332, 2001.
11. Arthanari, T.S., Kecman, V. and Hadzic, I., LP and QP Based Learning From Empirical Data, IEEE Proceedings of IJCNN 2001, Vol 4., pp., 2451-2455, Washington, DC, 2001.
12. Arthanari, T.S. and Usha, M., An Alternate Formulation of the Symmetric Travelling Salesman Problem and its Properties, Discrete Applied Mathematics, 98, 173-190, 2000.
13. Arthanari, T.S., Rajendra Prasad, V. and Manna, D.K, A Note on Lower Bound for Completion Time Variance in Single Machine Scheduling, Opsearch, 34, 4, 1997.
14. Arthanari, T.S. and Rao, C. R., Data Analysis and Statistical Thinking for Quality and Productivity Improvements, Keynote address, Proceedings of the International Conference on Quality and Productivity, Seoul, 1995.
15. Arthanari, T.S. and Chakraborty, A. K., Optimum Testing Time for Software under an Exploration Model, Opsearch, Vol. 31, 3, September 1994.
16. Arthanari, T.S. and Dodge, Y., Mathematical Programming in Statistics, Classics Library Series ,John Wiley and Sons, New York , 413 pages,1993.
17. Arthanari, T.S., Design and Analysis of Circuits and Networks – The Role of Mathematical Concepts - in Quality through Engineering Design, Edited by Kuo, W., Elsevier, Amsterdam, 1993.

Currently with Felicity Lamm, Department of MER, leading a project on unwanted fire alarms for New Zealand Fire Service and the total grant is $44, 390.  During 2004 received a TIG of $ 4500 for the teaching assistant ROBOT project.

In 1999, the Department of Engineering Science, University of Auckland, supported my research on polyhedral combinatorics- new polyhedral approaches to symmetric travelling salesman problem with a grant of $ 20,000 and a workshop organised to present my results. In 2000 the department of MSIS allotted a research grant of $3000 for my work on MTS.

As head of SQC & OR division of ISI, I launched the Quality Mission Project, which received massive financial support (equivalent to NZ$ 3 million) from the government of India, for its national importance. I was instrumental in producing ‘Quality – Our Own Heritage’, a video which documents for the first time the connections of the quality Gurus like Shewhart, Deming and Taguchi with the Indian Statistical Institute.

1. “Pedigree polytope is a Combinatorial Polytope”, -invited talk given at the international Conference ICOR 2004, Kolkata, January 2004.
2. “Mahalanobis Distance in Multivariate measurement systems”, - invited talk, international conference on Statistics in Industry and Business, at Cochin, India, January, 2003.
3. “On Pedigree polytopes and Hamiltonian Cycles”- invited paper presented at Bose Centenary Symposium, 20-23 December, 2002, Kolkata, India.
4. “On Mahalanobis Taguchi System and its Applications”- invited talk, IISA conference at DeKalb, USA. 2001.
5. “Is Learning an Optimisation Problem?” – invited paper presented at the 53^rd Session of International Statistical Institute, at Seoul, August, 2001.
6. "Recent Developments in Mathematical Programming Approaches in Classification"-invited paper read by the chairman of the session, at the Fifth Conference of the International Federation of Classification Societies, March 27-30, 1996, Kobe, Japan.
7. "Game Theory and Quality" - in International workshop on Co-operative Games held during 2-January 1996 as part of II international Conference on Game theory and its Economic Applications at Bangalore.
8. "Game Theory and Quality engineering" - invited paper for the International Game Theory Conference, SUNY, Stony Brook, 17-20, July 1995.
9. "On Some Problems in Construction of Designs" - invited talk presented at R.C. Bose memorial Conference held at Colorado State Univ., Fort Collins between 7-11 June, 1995.
10. "Optimal Design of Electrostatic Precipitators" - invited talk at the Conference on Environmental Statistics held at Calcutta as part of Prof. P.C. Mahalanobis Centenary 1994.
11. "On Taguchi's Minute Analysis"- invited talk given at the Conference on IS and QI held at Oakland University, Rochester, Michigan, August 1993.
12. "Design and Analysis of Circuits and Networks - Role of Mathematical Concepts" - paper presented at the Indo-US-Japan Conference on Quality through Engineering Design held during January 12-14. 1993, at Bangalore, India.
13. "An Approach for Parameter Design with Several Responses" - invited paper presented at International Conference on Game Theory and Economic Applications, during December 18-22,1990, New Delhi, India.
14. "Parameter Design and Global Optimisation" - invited paper presented at the First International Conference - Workshop On Optimal Design and Analysis of Experiments, held at Neuchatel, Switzerland from July 25-28, 1988.
15. "Optimisation in Statistics - Recent Trends" - invited paper presented in Compstat, IX Symposium held at Dubrovnik, Yugoslavia, 1990.