This is actually a complex question to answer. In practice, we encounter a lot of problems where different components are hard to quantify in terms of costs. As per example, in many vehicle routing applications, you want to: (i) minimize total driving cost, (ii) maximize on-time arrival or delivery speed, (iii) minimize carbon emissions, (iv) maximize niceness of a route. A route could be considered 'nice' if drivers have pleasant working hours, sufficient breaks, and can be home by the end of the day.
Issue 1: many of these requirements are incomparable because they are expressed in different quantities
Issue 2: many of these requirements conflict. Maximizing delivery speed often drives up delivery cost and carbon (e.g. you would use an airplane to get somewhere fast but that takes more carbon than a slow freight train).
Solution 1: accept that the quantities are incomparable, create a Pareto curve and let the user/customer choose his/her preferred solution. Do you prefer solution A that costs \$100 and produces 5kg of carbon, or do you prefer solution B that costs \$120 but only produces 3.5kg of carbon? One difficulty here is that the Pareto curve often contains a lot of points, so you need to preselect a subset of points to limit the choice set presented to a human.
Solution 2: capture some objectives as a constraint instead of as an objective value. E.g. minimize the routing cost, subject to the constraint that no customer is visited more than X minutes late. Or express it as a chance constraint: Minimize cost, subject to the requirement that we have an on-time arrival rate of X%. The choice of X can be something sensible, or something that's market driven (e.g. if a competitor has a consistent 96% of-the-time on-time delivery, then you might want to meet or exceed this performance).
Solution 3: convert objectives into dollars. This is challenging and often subjective.
- For carbon, you could look at carbon pricing and use the cost of a carbon credit.
- You could use a survey/market experiment to figure out what value to attach. E.g. what it it worth to you if your parcel is delivered in 2 days instead of 5, or delivered to a nearby location instead of your home?
- You could use pricing mechanisms such as auctions to determine the value of a service, or the customer's willingness to pay.
- Use the cost-of-alternatives. A set of vehicle routes could cost \$2MM in driver fees and emit 1MMkg in carbon. An alternative set of vehicle routes could cost us \$2.5MM but only emit 0.75MMkg carbon. In essence, to reduce the amount of carbon by 0.25MMkg you would pay $0.5MM. As an alternative, you could take the same \$0.5MM and buy electrical vehicles, thereby saving 0.3MMkg of carbon. This fictional comparison allows you to evaluate your choices without knowing the true value of carbon.
From my experience, this is a tough subject though, in particular for many companies. Many managers have a hard time justifying more expensive solutions even though such a solution is more environmentally sustainable. As a manager, would you buy solution A that produces 2kg of carbon for 100$, or would you rather buy solution B for \$120 that produces 1.5kg carbon? How do you make this trade-off, especially if you need to justify this to shareholders... In practice the best solution is to associate a carbon price and show that solution A is actually more expensive than B if you factor in the cost of carbon...
