Scientist Management
Scientist Management
Develop a linear preprogramming model that can be used to evaluate the performance of the Clarksville Ranch House restaurant.
To determine the weight that each restaurant will have in computing the outputs and inputs for the Ranch House. Inc. We use the following decision variable:
wb= weight applied to input and output for Bardstown
wc= weight applied to input and output for Clarksville
wj= weight applied to input and output for Jeffersonville
wn= weight applied to input and output for New Albany
ws= weight applied to input and output for St.Matthews
The DEA approach requires that the sum of these weights equal 1. Thus, the first constraint is:
wb+wc+wj+wn+ws=1
Relationship between the input measures for the five restaurant and the input measures for the Ranch House.
FIGURE 1.1
wb wc wj
Bardstown
Clarksville
Jeffersonville
Hours of Operation 96
FTE Staff 16
Supplies($) 850
Hours of Operation 110
FTE Staff 22
Supplies($) 1400
Hours of Operation 100
FTE Staff 18
Supplies($) 1200
wn ws
New Albany
St. matthewa
Hours of Operation 125
FTE Staff 25
Supplies($) 850
Hours of Operation 120
FTE Staff 24
Supplies($) 1600
Ranch House
Hours of Operation 96wb+110wc+100wj+125wn+120ws
FTE Staff 16wb+22wc+18wj+25wn+24ws
Supplies 850wb+1400wc+1200wj+1500wn+1600ws
Relationship between the output measures for the five restaurant and the output measures for the Ranch House.
Figure 1.2
wb wc wj
Bardstown
Clarksville
Jeffersonville
Weekly profit $3800
Market Share(%) 25
Growth Rate(%) 8.0
Weekly profit $4600
Market Share(%) 32
Growth Rate(%) 8.5
Weekly profit $4400
Market Share(%) 35
Growth Rate(%) 8.0
wn ws
New Albany
St.matthewa
Weekly profit $6500
Market Share(%) 30
Growth Rate(%) 10.0
Weekly profit $6000
Market Share(%) 28
Growth Rate(%) 9.0
Ranch House
Weekly Profit 3800wb+4600wc+4400wj+6500wn+6000ws
Market Share 25wb+32wc+35wj+30wn+28ws
Growth Rate 8.0wb+8.5wc+8.0wj+10.0wn+9.0ws
In general, every DEA liner programming model will include a constraint that requires the weight for the operating units to sum to 1.
As we know, for each output measure, the output for the composite restaurant is determined by computing a weighted average of the corresponding outputs for all five restaurants. The general form for the output constraints is as follows:
Weekly Profit for the Composite restaurant
=3800wb+4600wc+4400wj+6500wn+6000ws
For each of the four output measures, we need to