Case Problem

The Metropolitan Police Patrol

Optimal patrol area for police cars to minimize average time to respond calls

Sergent Joe Davis solicited help from analyst Angela Maris

Assume Dimensions of sector are x in horizontal direction and y in vertical direction

Travel in horizontal direction must be accompanied by travel in vertical direction

The Case :

Total distance traveled is sum of horizontal and vertical distance

Average distance traveled by patrol cars in either direction is one third of dimensions of sector

Average time = Average Distance Travelled/Average Travel speed

The Case continued….

Limitations:

Perimeter of patrol sector should not be less than 5miles or exceed 12miles

Distance in vertical direction must be at least 50% more than distance in horizontal direction

Average speed in vertical direction is 15 miles per hour

Average speed in horizontal direction is 20 miles per hour

Model Formulation Steps :

1) Clearly Define The decision variables

2) Construct the Objective Function

3) Formulate the constraints

The Decision variables are :

x1 = Distance in horizontal direction in miles

x2 = Distance in vertical direction in miles

Linear Programming Model :

S.T.

Objective Function & Constraints:

5 ≥ 2x1 + 2x2 ≤ 12

x2 ≥ 1.5x1

x1,x2 ≥ 0

Z = x1/3(20) + x2/3(15)

MIN Z = x1/60 + x2/45

Thank You …