Have you ever faced the challenge of packing for a trip, trying to fit all your essentials into a limited space? These kinds of scenarios are actually a fascinating mathematical conundrum known as the “knapsack problem.” In this article, we’ll explore what knapsack problems are, how they relate to our everyday lives, and the benefits that arise from their application.
At its core, a knapsack problem is a mathematical puzzle. It involves finding the most valuable combination of items to fit into a constrained container, often referred to as a knapsack.
The challenge lies in selecting items with the highest total value while ensuring that their combined size or weight does not exceed the knapsack’s capacity.
Although the concept sounds simplistic, knapsack problems have real-world applications that can make a big impact. For example:
By applying knapsack problem solutions, we unlock several advantages in various domains:
The Defence Science and Technology Laboratory (Dstl), an executive agency of the United Kingdom’s Ministry of Defence, was facing a challenge. In the middle of complex operating environments, packers need to put materials and equipment into the right transport vehicles to ensure that the right items go to the right place at the right time—in the most efficient way possible.
Using a Gurobi-powered solution, created by Gurobi partner Decision Lab, Dstl was able to increase packing efficiency by 20% and provide logisticians with a solution in tens of seconds. The solution guides packers through the process in real-time, taking out the guesswork.
Read the Dstl case study to learn more about this real-world knapsack problem.
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