DEA with Cross-Efficiencies Review Exercise 5.5. After looking at the analysis, your corporate client proposes yet another refinement to break ties in the efficiency ratings. The evaluation of the kth DMU produces a set of "optimal prices" that are as favorable as possible to unit k. Suppose we call these "set k prices." Now, to evaluate DMU k, compute the value of its efficiency (output value divided by input value) under each of the price sets (set 1 prices through set 5 prices, in this case). Then, average the five efficiency values. This average value is called the cross-efficiency.
(a) Rank the DMUs based on cross-efficiency.
(b) What are the advantages and disadvantages of using the cross-efficiency measure?
Exercise:
Evaluating Restaurant Efficiency Celia's Tacqueria is a chain of five Mexican restaurants in Florida. A DEA evaluation is being conducted to make comparisons of the different locations. Input measures for the restaurants include weekly hours of operation, fulltime equivalent staff, and weekly supply expenses. Output measures of performance include average weekly contribution to profit, market share, and annual growth rate. Data for the input and output measures are shown in Table 5.3.
(a) Perform a DEA evaluation for this set of units, listing the efficiency and the virtual outputs for each of restaurants.
(b) For each of the inefficient units, find the reference set and calculate the inputs and outputs for a corresponding HCU.
Table 5.3. Inputs and Outputs for Five Restaurants
|
Restaurant
|
|
Input measures
|
|
|
Hours of
operation
|
FIE
staff
|
Supplies
(S)
|
|
Jacksonville
|
96
|
16
|
850
|
|
Daytona
|
110
|
22
|
1400
|
|
Gainesville
|
100
|
18
|
1200
|
|
Ocala
|
125
|
25
|
1500
|
|
Orlando
|
120
|
24
|
1600
|
|
|
|
Output measures
|
|
|
|
Weekly
|
% Market
|
% Growth
|
|
Restaurant
|
profit (S)
|
share
|
rate
|
|
Jacksonville
|
3800
|
25
|
8.0
|
|
Daytona
|
4600
|
32
|
8.5
|
|
Gainesville
|
4400
|
35
|
8.0
|
|
Ocala
|
6500
|
30
|
10.0
|
|
Orlando
|
6000
|
28
|
9.0
|