You need a new car. To meet your needs it must be a midsized four-door family car with a petrol engine delivering at least 150 horsepower—enough to tow your sailboat. Given all of these requirements, you want the car to cost as little to own and run as possible (see Figure 8.1, left side). There are three constraints here, but they are not all of the same type:
■ The requirements of four-door family car and petrol power are simple constraints—a car must have these to be a candidate.
■ The requirement of at least 150hp places a lower limit but no upper one on power; it is a limit constraint—any car with 150 hp or more is acceptable.
The wish for minimum cost of ownership is an objective, a criterion of excellence. The most desirable cars from among those that meet the constraints are those that minimize this objective.
To proceed, you need information about available cars (Figure 8.1, right side). Carmakers ‘ Websites, dealers, car magazines, and advertisements in the national press list such information, including car type and size, number of doors, fuel type, engine power, and price. Car magazines go further and estimate the cost of ownership (meaning the sum of running costs, tax, insurance, servicing and depreciation), listing it as $/mile or €/km.
Now it’s decision time (Figure 8.1, central box). The selection engine (you, in this example) uses the constraints to screen out, from all the available cars, those that are not four-door gasoline-powered family vehicles with 150 hp. Many cars meet these constraints; the list is still long. You need a way to order it so that the best choices are at the top. That is what the objective is for: it allows you to rank the surviving candidates by cost of ownership—those with the lowest values are ranked most highly. Rather
Selecting a car. The requirements are expressed as constraints and objectives (objectives in blue). Records containing data for cars are screened using the constraints and ranked by the objectives to find the most attractive candidates. These are then explored further by examining documentation.
than simply choosing the one at the top, it is better to keep the top three or four and seek further documentation, exploring their other features in depth (delivery time, size of trunk, comfort of seats, security, and so on) and weighing the small differences in cost against the desirability of these features.
But we have overlooked a second objective, listed in blue on the left of Figure 8.1. You are an environmentally responsible person; you want to minimize the CO2 rating as well as the cost of ownership. The choice to meet two objectives is more complicated than that to meet just one. The problem is that the car that best satisfies one objective—minimizing cost, for example—might not be the one that minimizes the other (CO2), and vice versa, so it is not possible to minimize both at the same time. A compromise has to be reached, and that needs tradeoff methods.
Figure 8.2 shows such a method. Its axes are the two objectives: cost of ownership and CO2 rating. Suppose a friend has recommended a particular car, shown as a red dot at the center of the diagram. Your research has revealed cars with combinations of cost and carbon, shown by the other dots. Several—the purple ones in the upper right—have higher values of both; they lie in the "unacceptable" quadrant. Several—the blue ones—either have lower cost or lower carbon, but not both. One—the green one—is both cheaper and produces less carbon; it ranks more highly by both objectives. Thus it is the obvious choice.
Or is it? That depends on the value you attach to low carbon footprint. If you think it is a good idea as long as you don’t have to pay, the car marked "Choice if cost matters most" is the best. If instead you are ready to pay whatever it takes to minimize CO2 emissions, the car marked "Choice if carbon matters most" is the one to go for.
All three choices lie, with several others that are compromises between them, on the boundary of the occupied region of the figure. The envelope of these—the broken line—is called the tradeoff line. Cars that lie on or near this line have the best compromise combination of cost and carbon. So even if we can’t reach a single definitive choice (at least without knowing exactly what you think a low carbon footprint is worth), we have made progress. The viable candidates are those on or close to the tradeoff line. All others are definitely less good.
Methods like this are used as tools for decision making in many fields; in deciding between design options for new products, in optimizing the operating methods for a new plant, in guiding the siting of a new town— and in selecting materials. We turn to that topic next.