Rank the dmus based on cross efficiency

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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

Reference no: EM131163786

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