Minimizing Transportation Costs From Generation
Sites to Final Destinations

Generic Situation:

Many small businesses must transport their products from various "generation" sites to multiple locations. In such a case the owner must decide which items, and in what quantities, to ship to which location in order to minimize transportation costs.

Example:

Beaumont Apple Orchards has orchards in three different locations, each with different production numbers - Finley (275,000 bushels), Claremont Hills (400,000 bushels), and Westlake (300,000 bushels). Beaumont's processing plants are in Toler City, Cambridge, and Utica with processing capacities of 200,000, 600,000, and 225,000 respectively. The owner contracts with a local trucking company to transport the apples from orchard to plant. The trucking company charges a flat rate for every mile that each bushel is transported. Beaumont management wants to determine how many bushels to ship from each orchard to each processing plant in order to minimize the total number of miles the apples must be shipped.

OrchardToler CityCambridgeUtica
Finley215040
Claremont Hills353022
Westlake552025
DISTANCE BETWEEN ORCHARDS AND PLANTS
Profit Maximizing Solution:

The following table shows that shipping setup that guarantees the absolute minimum shipping costs.

OrchardToler CityCambridgeUtica
Finley200,000075,000
Claremont Hills0250,000150,000
Westlake0300,0000
NUMBER OF BUSHELS SHIPPED FROM ORCHARDS TO CITIES