The science of operations research (OR) is intended to be an alternative with enormous potential for solving complex problems. Traditionally, different types of problems are presented using playful contexts, for instance:
Contextualizing such problems is efficient to understand their concepts and challenges; however, for many students, this contextualization distances itself from the reality of a problem in the market.
In order to appreciate these classic problems, we will show how the Knapsack Problem can serve as a basis for more complex problems.
As previously described, the problem involves maximizing the value of a knapsack in such a way that the quantity of items loaded in it does not exceed its weight limit. To make the decision that maximizes the value of the knapsack, it is necessary to know:
From them, we can define for each item if it is part of the knapsack or not, being that:
This problem, at first, appears to be directly applicable only to a seller who needs to travel by plane and comply with the hand luggage limit. How could it assist an industry?
In its classic format, the Knapsack Problem is already capable of supporting the board's decision in investment planning. For that, we only need to (re)contextualize our concepts:
From this perspective, it is clear how an optimization model like the Knapsack Problem would help. It can show the ideal set of projects to be authorized to increase the return to the company. This is a problem of resource allocation!
Another context it could be applied to is the definition of customer supply. Imagine that a company has to rent a fleet of vehicles to distribute its products. For the company, it is important to define how to load the vehicles (intended for different customers) in order to maximize its profit. In this case:
In this scenario, it is important to note that it is essential to define:
Note that the weight of the product does not vary by vehicle or by customer.
The most common in industries would be to find Context 2 with additional restrictions. For example, teams can load the fleet with different rates and this should be considered when planning customer supply.
As much as the operational character of the load is emphasized, the core of the problem remains the Knapsack Problem! Operational restrictions will only exclude some of the Product-Vehicle-Customer combinations that would have previously been considered possible solutions in the model.
Discernment about the classification of a real problem into a classic problem by experience, however, is of great value in speeding up its resolution. Such problems already have a great theoretical basis and different technological possibilities to find the best solution.
For operations research enthusiasts, a tip: invest your time in understanding the classics to generate value in the future!
Co-author: Fabio Silva - Senior Manager at Cassotis Consulting