ILOG CPLEX 11.0 User's Manual

Describing the ProblemThe problem is to plan the blending of five kinds of oil, organized in two categories (twokinds of vegetable oils and three kinds of non vegetable oils) into batches of blendedproducts over six months.Some of the oil is already available in storage. There is an initial stock of oil of 500 tons ofeach raw type when planning begins. An equal stock should exist in storage at the end of theplan. Up to 1000 tons of each type of raw oil can be stored each month for later use. Theprice for storage of raw oils is 5 monetary units per ton. Refined oil cannot be stored. Theblended product cannot be stored either.The rest of the oil (that is, any not available in storage) must be bought in quantities to meetthe blending requirements. The price of each kind of oil varies over the six-month period.The two categories of oil cannot be refined on the same production line. There is a limit onhow much oil of each category (vegetable or non vegetable) can be refined in a given month:●Not more than 200 tons of vegetable oil can be refined per month.● Not more than 250 tons of non vegetable oil can be refined per month.There are constraints on the blending of oils:●●The product cannot blend more than three oils.When a given type of oil is blended into the product, at least 20 tons of that type mustbe used.● If either vegetable oil 1 (v1) or vegetable oil 2 (v2) is blended in the product, thennon vegetable oil 3 (o3) must also be blended in that product.The final product (refined and blended) sells for a known price: 150 monetary units per ton.The aim of the six-month plan is to minimize production and storage costs whilemaximizing profit.Representing the DataTo represent the problem accurately, there are several questions to consider:◆ What Is Known? on page 361◆ What Is Unknown? on page 361◆ What Are the Constraints? on page 362◆ What Is the Objective? on page 363360 ILOG CPLEX 11.0 — USER’ S MANUAL