Scientist Management

A. 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