Examen

Example 2: Transportation Problem. Minimize the costs of shipping goods from production plants to warehouses near metropolitan demand centers, while not exceeding the supply available from each plant and meeting the demand from each metropolitan area. Plants: Monterrey Guadalajara Mexico Puebla

Total 15000 6000 14000 11000

Totals:

Number to ship from plant x to warehouse y (at intersection): Tijuana Leon Mazatlan La Paz 0 0 6000 9000 0 0 6000 0 0 11000 3000 0 10000 1000 0 0 --------10000 12000 15000 9000

Color Coding

Demands by Whse --> 10000 12000 15000 9000 Plants: Supply Shipping costs from plant x to warehouse y (at intersection): Monterrey 15000 71 103 88 98 Guadalajara 6000 85 80 90 90 Mexico 14000 80 97 78 90 Puebla 11000 84 79 90 99 Shipping:

$3,630,000

$840,000

$1,146,000

$762,000

$882,000

The problem presented in this model involves the shipment of goods from three plants to five regional warehouses. Goods can be shipped from any plant to any warehouse, but it obviously costs more to ship goods over long distances than over short distances. The problem is to determine the amounts to ship from each plant to each warehouse at minimum shipping cost in order to meet the regional demand, while not exceeding the plant supplies. Problem Specifications Target cell

B20

Goal is to minimize total shipping cost.

Changing cells

C8:G10

Amount to ship from each plant to each warehouse.

Constraints

B8:B10<=B16:B18

Total shipped must be less than or equal to supply at plant.

C12:G12>=C14:G14

Totals shipped to warehouses must be greater than or equal to demand at warehouses.

C8:G10>=0

Number to ship must be greater than or equal to 0.

You can solve this problem faster by selecting the Assume linear model check box in the Solver Options dialog box before clicking Solve. A problem of this type has an optimum solution at which amounts to ship are integers, if all of the supply and demand constraints are integers.

Page

Target cell

Changing cells Constraints

Example 2: Transportation Problem. Minimize the costs of shipping goods from production plants to warehouses near metropolitan demand centers, while not exceeding the supply available from each plant and meeting the demand from each metropolitan area. Plants: Decatur Minneapolis Carbondale St. Louis

Total 300 200 150 150

Totals:

Number to ship from plant x to warehouse y (at intersection): Color Coding Blue Earth Ciro Desmoines 150 0 150 Target cell 0 0 200 0 150 0 100 50 0 Changing cells ------250 200 350 Constraints

Demands by Whse --> 250 200 350 Plants: Supply Shipping costs from plant x to warehouse y (at intersection): Decatur 300 20 25 23 Minneapolis 200 15 21 25 Carbondale 150 21 20 22 St. Louis 150 27 28 31 Shipping:

$13,550

$5,700

$4,400

$3,450

The problem presented in this model involves the shipment of goods from three plants to five regional warehouses. Goods can be shipped from any plant to any warehouse, but it obviously costs more to ship goods over long distances than over short distances. The problem is to determine the amounts to ship from each plant to each warehouse at minimum shipping cost in order to meet the regional demand, while not exceeding the plant supplies. Problem Specifications Target cell

B20

Goal is to minimize total shipping cost.

Changing cells

C8:G10

Amount to ship from each plant to each warehouse.

Constraints

B8:B10<=B16:B18

Total shipped must be less than or equal to supply at plant.

C12:G12>=C14:G14

Totals shipped to warehouses must be greater than or equal to demand at warehouses.

C8:G10>=0

Number to ship must be greater than or equal to 0.

You can solve this problem faster by selecting the Assume linear model check box in the Solver Options dialog box before clicking Solve. A problem of this type has an optimum solution at which amounts to ship are integers, if all of the supply and demand constraints are integers.

Page