For the oil blending example (Example 4.4 in Chapter 4), discuss where you think the assumptions of a linear model are most likely to break down. How might an NLP model look in this situation?
EXAMPLE 4.4 BLENDING AT CHANDLER OIL
Chandler Oil has 5000 barrels of crude oil 1 and 10,000 barrels of crude oil 2 available. Chandler sells gasoline and heating oil. These products are produced by blending the two crude oils together. Each barrel of crude oil 1 has a “quality level” of 10 and each barrel of crude oil 2 has a quality level of 5.6 Gasoline must have an average quality level of at least 8, whereas heating oil must have an average quality level of at least 6. Gasoline sells for $75 per barrel, and heating oil sells for $60 per barrel. We assume that demand for heating oil and gasoline is unlimited, so that all of Chandler’s production can be sold. Chandler wants to maximize its revenue from selling gasoline and heating oil.
Objective To develop an LP spreadsheet model for finding the revenue-maximizing plan that meets quality constraints and stays within limits on crude oil availabilities.
WHERE DO THE NUMBERS COME FROM? Most of the inputs for this problem should be easy to obtain.
■ The selling prices for outputs are dictated by market pressures.
■ The availabilities of inputs are based on crude supplies from the suppliers.
■ The quality levels of crude oils are known from chemical analysis, whereas the required quality levels for outputs are specified by Chandler, probably in response to competitive or regulatory pressures.