After hurricane Sandy, county governments has been order to develop disaster pla
ID: 3436867 • Letter: A
Question
After hurricane Sandy, county governments has been order to develop disaster plans for assigning casualties to hospitals in the event of another serious weather event.
Hospital
(travel times—minutes)
Town
Point Pleasant
Atlantic
Estimated Casualties
Margate
10
15
250
Ventnor
20
5
350
Longport
15
20
200
Capacity
300
500
The estimated casualties from the three towns, their average travel times to the two hospitals and the capacity of each hospital is listed in the table above.
Formulate a linear program to assign casualties to the hospital so as to minimize travel time, take care of the estimated casualties given the capacity of the hospitals.
Solve this problem using Excel’s Solver. What is the optimal solution? Which constraints are binding? Non-binding?
Hospital
(travel times—minutes)
Town
Point Pleasant
Atlantic
Estimated Casualties
Margate
10
15
250
Ventnor
20
5
350
Longport
15
20
200
Capacity
300
500
Explanation / Answer
The total amount of time lost to transport will thus be
T = 10*x1+ 15 *y1 + 20*x2 +5*y2+ 15*x3 +20*y3
and we have to minimize it.
we know by capacity
x1+x2+x3 <=300
y1+y2+y3 <=500
and x1, x2, x3 , y1, y2, y3 are non negative.
x1 + y1 = 250
x2 +y2 =350
x3 + y3 =200
By solving it
Optimal solution
T= 8000;
x1= 100,
y1= 150,
x2= 0,
y2= 350,
x3= 200,
y3= 0
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