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# Minimizing shipping costs

The three blood banks in Franklin County are coordinated through a central office that facilitates blood delivery to four hospitals in the region. The cost to ship a standard container of blood from each bank to each hospital is shown in the table below. Also given are the biweekly number of containers available at each bank and the biweekly number of containers of blood needed at each hospital.

How many shipments should be made biweekly from each blood bank to each hospital so that total shipment costs are minimized?

_____________________ TO _______________________

FROM Hospital 1 Hospital 2 Hospital 3 Hospital 4 SUPPLY
Bank 1 \$8 \$9 \$11 \$16 50
Bank 2 \$12 \$7 \$5 \$8 80
Bank 3 \$14 \$10 \$6 \$7 120
DEMAND 90 70 40 50 250

#### Solution Preview

The three blood banks in Franklin County are coordinated through a central office that facilitates blood delivery to four hospitals in the region. The cost to ship a standard container of blood from each bank to each hospital is shown in the table below. Also given are the biweekly number of containers available at each bank and the biweekly number of containers of blood needed at each hospital.

How many shipments should be made biweekly from each blood bank to each hospital so that total shipment costs are minimized?

_____________________ TO _______________________

FROM Hospital 1 Hospital 2 Hospital 3 Hospital 4 SUPPLY
Bank 1 \$8 \$9 \$11 \$16 50
Bank 2 \$12 \$7 \$5 \$8 80
Bank 3 \$14 \$10 \$6 \$7 120
DEMAND 90 70 40 50 250

We will use Vogel's approximation method (VAM) to solve the problem. VAM tackles the problem of finding a good initial solution by taking into account the costs associated with each route alternative. To ...

#### Solution Summary

This solution is comprised of a detailed explanation to find how many shipments should be made biweekly from each blood bank to each hospital so that total shipment costs are minimized.

\$2.19