Applications of the Knapsack Problem

The Knapsack problem has several real-life applications. Some of them are mentioned here:

• One of the early applications of the Knapsack problem was in construction and scoring of exams in which the test takers have a choice as to which questions they answer.
• The subset sum problem is solved using the concept of the Knapsack problem.
• The multiple objective variations of the Knapsack problem is frequently used for transportation logistics optimization problems.
• The multiple knapsack problem is often used in many loading and scheduling algorithms in Operational Research.

The Knapsack problem is an example of the combinational optimization problem. This problem is also commonly known as the “Rucksack Problem“. The name of the problem is defined from the maximization problem as mentioned below:

Given a bag with maximum weight capacity of W and a set of items, each having a weight and a value associated with it. Decide the number of each item to take in a collection such that the total weight is less than the capacity and the total value is maximized.