The Ranch House, Inc., operates five fast-food restaurants. Input measures for t

Question

The Ranch House, Inc., operates five fast-food restaurants. Input measures for the restaurants include weekly hours of operation, full-time equivalent staff, and weekly supply expenses. Output measures of performance include average weekly contribution to market share, and annual growth rate. Data for the input and output measures are shown in the following tables:

a. Develop a linear programming model that can be used to evaluate the performance of the Clarksville Ranch House restaurant.
b. Solve the model.
c. Is the Clarksville Ranch House restaurant relatively inefficient? Discuss.
d. Where does the composite restaurant have more output than the Clarksville restaurant? How much less of each input resource does the composite restaurant require when compared to the Clarksville restaurant?
e. What other restaurants should be studied to find suggested ways for the Clarksville restaurant to improve itsefficiency?

Restaurant Bardstown Clarksville Jeffersonville New Albany St. Matthews Restaurant Bardstown Clarksville Jeffersonville New Albany St. Matthews Input Measures FTE Staff Hours of operation Supplies (S) 850 16 110 1400 18 1200 100 1500 125 120 24 1600 Output Measures Weekly Profit Market Share Growth Rate $3800 80 $4600 8.5 $4400 80 $6500 100 $6000 9.0

Explanation / Answer

a. Develop a linear programming model that can be used to evaluate the performance of the Clarksville Ranch House restaurant.

Answer:  

B tends to Bardstown

C tends to Clarksville

J tends to Jeffers On Ville

N tends to New Albany

S tends to St. Mathews

B+C+J+N+S=1

Inputs:

93B+110C+100J+125N+120S<=110E

16B+22C+18J+25N+24S<=22E

850B+1400C+1200J+1500N+1600S<=1400E

Outputs:

3800B+4600C+4400J+6500N+6000S>=4600

25B+32C+35J+30N+28S>=32

8B+8.5C+8J+10N+9S>=8.5

B,C,J,N,S>=0

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b. Solve the model.

Answers:

Minimize E:

E                            B             C             J              N (Restaurants)

0.9595454545 0.175 0              0.575      0.25

1                              0              0              0              0                             

Standard Technique: S.T:

E                             B             C             J              N

1 1              1              1

-110                        96           110         100         125

-22                          16           22           18           25

-1400                     850         1400       1200       1500

3800       4600       4400       6500

25           32           35           30

8              8.5          8              10

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c. Is the Clarksville Ranch House restaurant relatively inefficient? Discuss.

Answer:

The Clarksville restaurant is inefficient because it is not at 100%.

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d. Where does the composite restaurant have more output than the Clarksville restaurant? How much less of each input resource does the composite restaurant require when compared to the Clarksville restaurant?

Answer:

1) The other restaurants that seem efficient are Bardstown, Jeffersonville, and New Albany.

2) By Comparing the Growth Rate of the Restaurant we able to see the efficiency equal or less than to the Clarksville Restaurant.

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e. What other restaurants should be studied to find suggested ways for the Clarksville restaurant to improve its efficiency?

Answer:

It can be measured by using the Minimizing Technique as explained in the section (b) and taken an objective of E as 0.959545

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