Question

An oil and gas company has M oil fields and N processing plants. Let i = 1, ..., M be the indices for oil the fields and j = 1, ..., N be the indices for processing plants. Crude oil is extracted from oil field i at a cost of ci dollars per barrel and its percentage of sulfur is ai , e.g. in every 10 barrels of oil, we have 10ai barrels of sulfur. All extracted oil is transported to the processing plants. At each processing plant, crude from various oil fields are blended together. The cost of transporting from oil field i to processing plant j is fij dollars per barrel.

Formulate an LP to determine the optimal production plan (how much oil to transport from field i to plant j) to minimize extraction and transportation cost, subject to the following constraints:

• the percentage of sulfur in the final product after blending in processing plant j cannot exceed uj ;

• the total crude transported to processing plant j has to be at least dj barrels;

• the total crude extracted at field i cannot exceed mi barrels.

Answer 1