Page 66 - programme book

OR-008
Uncertain Negative Data in DEA: An Application of Banking in Malaysia

1,b
1,a
Rokhsaneh Yousef Zehi and Noor Saifurina Nana Khurizan
1 School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia

a) Corresponding author: yousefzehi.rokhsaneh@gmail.com
b) saifurina@usm.my

Abstract. DEA models and their applicability is heavily depended on the type of data that has been
used for efficiency assessment. Conventional DEA models assume the all the involved data in the
efficiency evaluation are non-negative which in many cases seems unrealistic specially when the profit
or the rate of growth are involved in the evaluation of organizations. Moreover, the perturbation in
data is unavoidable in real-world applications and negative data also might be affected by error. In this
paper, we propose a robust DEA model to handle uncertain negative data that guarantees the robustness
of solution against the uncertainty in data. The proposed robust DEA model is constructed under a
box-ellipsoidal uncertainty set and an application of banking in Malaysia is presented to validate the
applicability of proposed model and evaluate the effect of uncertainty in efficiency assessment and
ranking of 30 banks in Malaysia.

Keywords: Data envelopment analysis (DEA), Mathematical programming, Robust optimization,
Uncertainty, Negative data

OR-009
A Review on the Development of Interval Iterative Algorithms for
Polynomial Root Finding

Nur Raidah Salim 1, b) and Chen Chuei Yee 1, 2, a)

1 Institute for Mathematical Research, Universiti Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.
2 Department of Mathematics, Faculty of Science, Universiti Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.

a) Corresponding author: cychen@upm.edu.my
b) nurraidah@upm.edu.my

Abstract. Many mathematical problems concerning nonlinear equations can be well interpolated as
polynomials in most cases. Interval iterative algorithms are among the most efficient ways for
polynomial roots finding. Recent interest in the research and development of this method stems from
its capacity to overcome the theoretical limitations associated with point iterative methods in terms of
order of convergence and computational efficiency. This review article encompasses theoretical
findings as well as algorithmic considerations, with the aim of presenting an overview of effective
root-finding methods and the corresponding methodologies. Particular emphasis is dedicated to
iterative algorithms via interval arithmetic capable of approximating the zeros using fast and accurate
algorithms while minimizing and enclosing the inevitable rounding errors. Several classical results,
which substantially influenced the development of the subject, are also discussed in depth.

Keywords: polynomial; interval arithmetic; interval iterative algorithm; order of convergence, root-
finding method

64