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The Fortnightly 100: Which Utility Ranks the Highest?

Fortnightly Magazine - September 1 1998

the coming decade. We believe that the measurement process itself leads to improvements. As Kenneth Galbraith once said, "Things that are measured tend to improve."

Janice Forrester is a Ph.D. student in system science at Portland State University and is the director of strategic and analytical services at Cytera Systems Inc. M. Sami Khawaja, Ph.D., is president of Quantec L.L.C., an energy economics consulting firm. Hossein Haeri, Ph.D., is director of energy information services at PG&E Energy Services. Michael Carter is an analyst with Financial Times Energy's Energy Insight.

Mathematical Appendix

Following is a brief summary of the mathematical programming model used. Readers interested in more detail may contact the authors at samik@quantecllc.com.

First stage Second stage

Min ui Max 1s + 1e

S.t. S.t.

1) Yl # y1 1) Yl - s1 = y1

2) Xl - ux1 # 0 2) Xl + e1 = u1x1

3) Sili = 1

Where Y represents outputs, X represents inputs, and u represents the inverse of the proportionate reduction in inputs required to become efficient, (if u = 0.8, then a 20-percent reduction of all inputs is required for technical efficiency). The second stage equations are used to determine the target values where the s and e represent additional reduction in individual inputs in order not only to seek the shortest path to the efficient frontier but to find the optimal position. Efficiency scores for all utilities are first computed under each of different assumptions regarding returns to scales, i.e., constant (CRS), decreasing (DRS) and variable (VRS). Three technical efficiency scores are calculated: (1) CRS using the above equations as is (no restrictions on the ls); (2) VRS using the above equations with the added the restriction Sil = 1; and (3) DRS using the above equations with added the restriction Sil < 1. Since most utilities appeared to be operating under DRS conditions, decreasing returns efficiency scores were used.

Malmquist productivity index (M) can be decomposed into two distinct pieces M=E*P:

(E) D efficiency = Efficiencyt,t/Efficiencyt+1,t+1

(P) D technology = [(Efficiencyt,t+1/Efficiencyt+1,t+1)*( Efficiencyt,t/Efficiencyt+1,t)]0.5

Therefore

Mit = [(Efficiencyt,t+1/Efficiencyt,t)*( Efficiencyt+1,t+1/Efficiencyt+1,t)]0.5

Where

Efficiencyt,t = input technical efficiency under CRS for a given utility in year t with respect to all other

utilities at year t.

Efficiencyt+1,t+1 = input technical efficiency under CRS for a given utility in year t+1 with respect to all

other utilities at year t+1.

Efficiencyt+1,t = input technical efficiency under CRS for a given utility in year t+1 with respect to all other

utilities at year t.

Efficiencyt,t+1 = input technical efficiency under CRS for a given utility in year t with respect to all other

utilities at year t+1.

Note: All systems of linear equations are solved using the commercial solver XA from Sunset Technologies Inc. that employs the Primal and Dual Simplex solving method.

1 We would have preferred to conduct the analysis at the utility level, and we set out to do so. However, as we conducted the analysis, it became apparent that the data, while accurate at the holding company level, were not very useful at the utility