Measuring performance in the presence of noisy data with targeted desirable levels: evidence from healthcare units
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Measuring performance in the presence of noisy data with targeted desirable levels: evidence from healthcare units Panagiotis Mitropoulos1
· Panagiotis D. Zervopoulos2 · Ioannis Mitropoulos1
© Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract Noise in data is not uncommon in real-world cases, although it is commonly omitted from performance measurement studies. In this paper, we develop a stochastic DEA-based methodology to measure performance when the endogenous (e.g. efficiency) and exogenous variables (e.g. perspectives of patients’ satisfaction), which are incorporated in the assessment, are inversely related. This methodology identifies benchmark units that are not only efficient but are also assigned scores for their exogenous variables, which are at least equal to userdefined critical values. We apply the performance measurement methodology to the 14 largest Cypriot health centers. The advantages of our methodology are pointed out through comparative analysis with alternative stochastic and non-stochastic DEA approaches. Keywords Data envelopment analysis · Stochastic DEA · Customer satisfaction · Performance measurement · Statistical noise
List of symbols (ηh )ad η* b* c*
B
Adjusted efficiency score of the hth disqualified unit (h ⊂ j) Cut-off level for the efficiency scores Cut-off level for the exogenous variables’ scores User-defined critical value (or threshold target level)
Panagiotis Mitropoulos [email protected] Panagiotis D. Zervopoulos [email protected] Ioannis Mitropoulos [email protected]
1
Department of Management Science and Technology, University of Patras, 1 M. Alexandrou St, 26334 Patras, Greece
2
Department of Management, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates
123
Annals of Operations Research
bkdo h
k o th undesirable exogenous variable of the hth unit that mostly deviates from c* (k ⊂ t, t 1, . . . , w, h ⊂ j) d b(kko )h kth k o th undesirable exogenous variable of the hth unit (ko ⊂ k ⊂ t, t 1, . . . , w, h ⊂ j) d ad (b(k ) kth k o th adjusted undesirable exogenous variable of the ko )h hth unit q blh lth desirable exogenous variable of the hth unit (l ⊂ t, t 1, . . . , w, h ⊂ j) q (blh )ad lth adjusted desirable exogenous variable of the hth unit (l ⊂ t, t 1, . . . , w, h ⊂ j) h Disqualified unit HB-HE Desirable exogenous variable (B ≥ c* )—desirable efficiency quadrant (η ≥ 1.0) LB-HE Undesirable exogenous variable (B < c* )—desirable efficiency quadrant (η ≥ 1.0) LB-LE Undesirable exogenous variable (B < c* )—undesirable efficiency quadrant (η < 1.0) HB-LE Desirable exogenous variable (B ≥ c* )—undesirable efficiency quadrant (η < 1.0) h(A,C); h(A,D); h(A,F) Facets of the hth unit in the plane defined by alternative coordinates h(A’,C’); h(A’,D’); h(A’,F’) Facets of the adjusted hth unit in the plane (1) A, C; (2) A, D; (3) A, F Start and end points of the hypotenuses of the triangles: (1) Ah(A,C)C where A(b* ,1.0), h(bkdo h ,1.0) and C(bkdo h , d η* ), (2) Ah(A,D)D where A(b* ,1.0), h(
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