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Unformatted text preview: MGMT 306 — Quiz 3, Fall 2010 — SOLUTION Name: ID: Formulation Problem (6 points) The county commission is trying to determine where to station ambulances throughout the county. The
map above shows the townships in the county. A township is considered to be provided with
ambulance service if there is an ambulance in that township or in an adjacent township. For example, if
an ambulance was stationed in Township 2, it could serve Townships 1, 2, 3, and 4. Formulate a linear
program to ensure that service is provided to all townships with the fewest number of ambulances. Decision Variables
Let Xi = 1 if an ambulance is stationed in Township i, 0 otherwise. i: 1, 2, 3,, 9. Objective Function: Min: Total Ambulance Stations = X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9
Constraints: Township 1: X1 + X2 + X4 3 1
Township 2: X1 + X2 + X3 + X4 _>_ 1
Township 3: X2 + X; + X5 _>_ 1
Township 4: X1 + X2 + X4 + X5 + X; 2 1
Township 5: X3 + X4 + X5 + X7 3 1
Township 6: X4 + X6 + X7 + X8 + X9 3 1
Township 7: X5 + X6 + X7 + X9 3 1
Township 8: X6 + X8 + X9 3 1
Township 9: X6 + X7 + X8 + X9 _>_ 1
Binary: Xi is binary. ‘ True or False Please circle the best answer for each. (1 point each) T rue 1. The optimal value for an integer linear program(|LP) can never be larger than the optimal value for its relaxed linear program.
The optimal value for an lLP can be larger than the optimal value for its relaxed LP when the objective function is minimize. . Let A be a binary variable with a value of 1 if event A occurs and a 0 otherwise. Let B be a binary variable with a value of 1 if event B occurs and a 0 otherwise. Let C be a binary
variable with a value of 1 if event C occurs and a 0 otherwise.
The constraint: A + B + C 3 1 can be used to represent the logical condition: if A does not happen and B does not happen,then C must happen. . When formulating an lLP to assign sales people to territories, if the number'of sales people is larger than the number of territories, the constraints for each person will use a
5 sign and the constraints for each territory will use an = sign. . When using Solver with an integer linear program spreadsheet model, we set the tolerance in Solver Options to 0 so the computer will converge to a solution faster.
A Tolerance of 0 does not make the program converge faster but it does ensure that we
reach the optimal solution. (See slide 12 in notes or page 145 in book.) i
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