In the past, maximizing profit has been the focus for most companies and decision making models that support businesses with their decision. However, the decisions produced by these models can be very harmful to the environment. Sometimes, the cheapest option is also the most sustainable. For instance, the shortest route for a truck to deliver goods is probably also the route with the fewest emissions. Nevertheless, that is not always the case. Take the location of a new factory as an example. It might be that the operational costs are so much lower in a country that is further away from your customers that even with extra transportation costs the relocation of your factory is more profitable. Obviously, the extra shipment of goods will result in more emissions.
The good news is that with some adjustments the current algorithms could also help to make more sustainable decisions. In this blog, we will show you three different methods to find the most sustainable solution. We will use a simple example to illustrate all options. Let us consider a company that has the four alternatives in the table below. We will use profit and emission as objectives, but different indicators can be used in the same way.
| Alternative | Profit | Emission |
| 1 | 100 | 5 |
| 2 | 110 | 10 |
| 3 | 150 | 25 |
| 4 | 200 | 20 |
Restricted emission
The first option is to restrict the total emission. A cap can be imposed by a government or by a company itself. The advantage is that the total level of emissions will certainly not exceed this cap. However, the disadvantage is that the optimal solution is likely to come as close as possible to the maximum level of emission.
Assume that the maximum emission is set to 10 in our example. In that case, alternatives 3 and 4 are not allowed because their emissions are too high. From the other two alternatives, alternative 2 will be chosen as it results in more profit than alternative 1. However, alternative 1 would for many people be preferable: it is only about 10% less profitable while the total emissions halve.
True pricing
Another option is to include a price for every unit of emission. This price could be a tax imposed by the government but it could also reflect the social and environmental costs of the emission. If one adds these factors to the market price one gets the so-called true price. Let us consider two different prices for emissions: 5 and 10. In the table below, we see that with a price of 5, alternative 4 is the most profitable option. However, that alternative comes with a rather large amount of emission. When the price of emission is increased to 10, that alternative is no longer profitable. With this price, it is best to choose alternative 1 as the emissions of this alternative are the lowest.
| Alternative | Profit with price of emission = 5 | Profit with price of emission = 10 |
| 1 | 75 | 50 |
| 2 | 60 | 10 |
| 3 | 25 | -100 |
| 4 | 100 | 0 |
With a true price, an alternative that is slightly less profitable but comes with much fewer emissions will be chosen. Hence, the shortcoming of the restricted emission option is overcome. However, the true price option also has a disadvantage: what is the right value for the true price? In our example, we see that the value of the true price influences the decision that is made.
Pareto optimal
A third option is to calculate all Pareto optimal solutions to a problem. A Pareto optimal solution is a solution that cannot be improved in all objectives. In our example, the objectives are maximizing profit and minimizing emissions. Hence, alternative 2 is a Pareto optimal solution because alternative 1 is the only alternative with less emission but that option results in less profit. The only alternative that is not Pareto optimal is alternative 3 because alternative 4 is both more profitable and more sustainable. In other words, there is no good reason to prefer alternative 3 over alternative 4.
The Pareto technique has the advantage that multiple solutions are produced and that the user can decide on the best decision. However, this is also a disadvantage. If the number of Pareto optimal solutions is large it could be still difficult to choose the best alternative.
As you see, there are quite some options to include sustainability in your decision-making process. The best option depends on the business context, the available data, and the problem itself. We are happy to find the best method for your specific business. If you wish to contact us, do not hesitate to send an email to info@doingthemath.nl