Data Envelopment Analysis from simulation on the Lattice QCD using CCR model

Subject Areas : Data Envelopment Analysis

محمد حسین  درویش متولی ¹ (گروه مدیریت صنعتی دانشگاه آزاد اسلامی واحد فیروزکوه)

Received: 2016-07-17 Accepted : 2017-05-27 Published : 2017-06-01

Keywords: Data envelopment analysis, Ranking model, CCR model, Lattice QCD, Continuum limit,

Abstract :

One of the most serious principles in production theory in economic is the principle of "efficiency". Simply put, efficiency can be defined as the demand that the desired goals (outputs) are achieved with the minimum use of the available resources (inputs). In order to, distinguish the relative efficiency of organizational units with multiple inputs to produce multiple outputs, "Data Envelopment Analysis" (DEA) method was introduced by Charnes, Cooper and Rhodes. In fact, DEA is a linear mathematical programming which calculates the efficiency of an organization within a group relative to observed best practice within that group. Unlike common statistical analysis which are based on central tendencies, it is a methodology directed at the frontier. Recently, DEA has become one of the most favorite fields in operations research. The background was a motivation for us to in this paper, via running the CCR model in "DEA-Solver Software", present data envelopment analysis from simulation on the lattice QCD with temporal extent N_τ=4,6, respectively. Astonishingly, results are derived for both cases, indicating the fact that efficient data set belong to the areas of high temperature (deconfinement phase). It is very interesting to highlight that even an efficient data has not reported at low temperature (confinement phase). Note that the data obtained at the critical temperature is also efficient. As expected from practical lattice QCD, the DEA-CCR model presented in this paper also confirms the fact which the best data set arises from simulation in continuum limit a→0. Indeed, by taking the limit of vanishing lattice spacing, the efficiency of algorithms can be further.

References:

Anderson, P., & Petersen, N. C. (1933). A Procedure for Ranking Effi-cient in Data Envelopment Analysis. Management Sci-ence, 39(10), 1261-1264.

Aoki, Y., Fodor, Z., Katz, S. D., & Szabó, K. K. (2006). The equation of state in lattice QCD: with physical quark masses towards the continuum limit. Journal of High Energy Physics, 2006(01), 089.

Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9), 1078-1092.

Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge university press.

Charnes, A., & Cooper, W. W. (1962). Programming with linear fractional functionals. Naval Research Logistics (NRL), 9(3‐4), 181-186.

Charnes, A., & Cooper, W. W. (1973). An explicit general solution in linear fractional programming. Naval Research Logistics Quarterly, 20(3), 449-467.

Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444.

Cheng, M., Christ, N. H., Datta, S., Van der Heide, J., Jung, C., Karsch, F., ... & Petreczky, P. (2008). QCD equation of state with almost physical quark masses. Physical Review D, 77(1), 014511.

Cheng, M., Christ, N. H., Datta, S., Van der Heide, J., Jung, C., Karsch, F., ... & Petreczky, P. (2006). Transition temperature in QCD. Physical Review D, 74(5), 054507.

Cooper, W. W., Seiford, L. M., & Tone, K. (2006). Introduction to data envelopment analysis and its uses: with DEA-solver software and references. Springer Science & Business Media.

Creutz, M. (2011). Confinement, chiral symmetry, and the lattice. arXiv preprint arXiv:1103.3304.

Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society. Series A (General), 120(3), 253-290.

Fodor, Z., & Hoelbling, C. (2012). Light hadron masses from lattice QCD. Reviews of Modern Physics, 84(2), 449.

 Ginsparg, P. H., & Wilson, K. G. (1982). A remnant of chiral symmetry on the lattice. Physical Review D, 25(10), 2649.

 Gupta, R. (1998). Introduction to lattice QCD. arXiv preprint hep-lat/9807028.

Huovinen, P., & Petreczky, P. (2010). QCD equation of state and hadron resonance gas. Nuclear Physics A, 837(1-2), 26-53.

 Khezrimotlagh, D., Salleh, S., & Mohsenpour, Z. (2012). A new method in data envelopment analysis to find efficient decision making units and rank both technical efficient and inefficient DMUs together. Applied Mathematical Sciences, 6(93), 4609-4615.

 Khodadi, M., & Sepangi, H. R. (2014). Cosmological QCD phase transition in steady non-equilibrium dissipative Hořava–Lifshitz early universe. Annals of Physics, 346, 129-153.

 Mandl, F., & Shaw, G. (2010). Quantum field theory. John Wiley & Sons.

Peskin, M. E., Schroeder, D. V., & Martinec, E. (1996). An introduction to quantum field theory.

 Richards, D. G. (2001). LATTICE GAUGE THEORY-QCD FROM QUARKS TO. Hadronic Structure: 14th Annual HUGS at CEBAF, Newport News, Virginia, 1-18 June 1999, 105.

 Shifman, M. (Ed.). (2001). At the Frontier of Particle Physics: Handbook of QCD (In 3 Volumes). World Scientific.

Shokouhi, A. H., Hatami-Marbini, A., Tavana, M., & Saati, S. (2010). A robust optimization approach for imprecise data envelopment analysis. Computers & Industrial Engineering, 59(3), 387-397.