Consider the same data file as above.

Now assume the company has estimated the number of service calls from each city and wants to choose exactly four service center locations and assign each city to a service center. Once a city is assigned to a service center, all calls will be handled by an agent from that center.

Find the location and assignment that minimizes the total distance traveled based on the expected number of service calls.

N P N m n D M 1 Minneapolis Chicago Atlanta New York Boston Philadelphia 1,140 1,060 935 1,848 2,000 1,668 3 1,026 1,127 1,290 2,065 2,201 1,891 4 1,727 1,914 2,140 2,870 2,995 2,702 5 1,432 1,734 2,178 2,620 2,707 2,486 6 403 205 655 801 912 654 7 328 876 1,200 1,304 1,057 8 328 564 957 1,082 794 9 876 564 940 1,096 765 10 1,200 957 940 156 180 11 1,304 1,082 1,096 156 333 12 1,057 794 765 180 333 13 14 Minneapolis Chicago Atlanta New York Boston Philadelphia Total 15 16 0 0 0 0 0 17 0 0 0 0 0 18 0 0 0 0 0 19 0 0 0 0 0 0 20 1 1 1 0 1 21 1 0 0 0 22 1 1 1 0 0 0 23 0 1 1 0 0 0 24 0 0 0 1 1 1 25 0 0 0 1 1 1 26 0 0 0 1 1 1 27 28 N 2 1 >= O 1 O O O 1 >= 1 1 1 P 0 >= 0 >= 1 >= 1 >= 1 O O O 1 0 1 >= 1 1 >= 1 1 0 >= 0 >= 1 >= 1 1 Objective Cell (Min) Cell Name $M$15 Selection Total Final Value Original Value 5 2. Original Value 1 1 1 Variable Cells Cell Name $B$15 Selection San Antonio $C$15 Selection Phoenix $D$15 Selection Los Angeles $E$15 Selection Seattle $F$15 Selection Detroit $G$15 Selection Minneapolis $H$15 Selection Chicago $1$15 Selection Atlanta $J$15 Selection New York $K$15 Selection Boston $L$15 Selection Philadelphia 1 Final Value Integer 1 Contin Contin Contin Contin 1 Contin Contin Contin Contin Contin Contin Contin 1 Cell Value Constraints Cell Name $M$16 San Antonio Total $M$17 Phoenix Total $M$18 Los Angeles Total $M$19 Seattle Total $M$20 Detroit Total $M$21 Minneapolis Total $M$22 Chicago Total $M$23 Atlanta Total $M$24 New York Total $M$25 Boston Total $M$26 Philadelphia Total Formula Status Slack 1 $M$16>=$0$16 Binding 0 1 $M$17>=$0$17 Binding o 0 $M$18>=$0$18 Binding 0 0 $M$19>=$0$19 Binding 0 1 $M$20>=$0$20 Binding 0 1 $M$21>=$0$21 Binding 0 1 $M$22>=$0$22 Binding 0 1 $M$23>=$0$23 Binding o $M$24>=$0$24 Binding 0 o $M$25>=$0$25 Binding 1 $M$26>=$0$26 Binding 0 0 0 N P N m n D M 1 Minneapolis Chicago Atlanta New York Boston Philadelphia 1,140 1,060 935 1,848 2,000 1,668 3 1,026 1,127 1,290 2,065 2,201 1,891 4 1,727 1,914 2,140 2,870 2,995 2,702 5 1,432 1,734 2,178 2,620 2,707 2,486 6 403 205 655 801 912 654 7 328 876 1,200 1,304 1,057 8 328 564 957 1,082 794 9 876 564 940 1,096 765 10 1,200 957 940 156 180 11 1,304 1,082 1,096 156 333 12 1,057 794 765 180 333 13 14 Minneapolis Chicago Atlanta New York Boston Philadelphia Total 15 16 0 0 0 0 0 17 0 0 0 0 0 18 0 0 0 0 0 19 0 0 0 0 0 0 20 1 1 1 0 1 21 1 0 0 0 22 1 1 1 0 0 0 23 0 1 1 0 0 0 24 0 0 0 1 1 1 25 0 0 0 1 1 1 26 0 0 0 1 1 1 27 28 N 2 1 >= O 1 O O O 1 >= 1 1 1 P 0 >= 0 >= 1 >= 1 >= 1 O O O 1 0 1 >= 1 1 >= 1 1 0 >= 0 >= 1 >= 1 1 Objective Cell (Min) Cell Name $M$15 Selection Total Final Value Original Value 5 2. Original Value 1 1 1 Variable Cells Cell Name $B$15 Selection San Antonio $C$15 Selection Phoenix $D$15 Selection Los Angeles $E$15 Selection Seattle $F$15 Selection Detroit $G$15 Selection Minneapolis $H$15 Selection Chicago $1$15 Selection Atlanta $J$15 Selection New York $K$15 Selection Boston $L$15 Selection Philadelphia 1 Final Value Integer 1 Contin Contin Contin Contin 1 Contin Contin Contin Contin Contin Contin Contin 1 Cell Value Constraints Cell Name $M$16 San Antonio Total $M$17 Phoenix Total $M$18 Los Angeles Total $M$19 Seattle Total $M$20 Detroit Total $M$21 Minneapolis Total $M$22 Chicago Total $M$23 Atlanta Total $M$24 New York Total $M$25 Boston Total $M$26 Philadelphia Total Formula Status Slack 1 $M$16>=$0$16 Binding 0 1 $M$17>=$0$17 Binding o 0 $M$18>=$0$18 Binding 0 0 $M$19>=$0$19 Binding 0 1 $M$20>=$0$20 Binding 0 1 $M$21>=$0$21 Binding 0 1 $M$22>=$0$22 Binding 0 1 $M$23>=$0$23 Binding o $M$24>=$0$24 Binding 0 o $M$25>=$0$25 Binding 1 $M$26>=$0$26 Binding 0 0 0