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Knapsack Problems

In: Introduction to Cutting and Packing Optimization

Author

Listed:
  • Guntram Scheithauer

    (TU Dresden)

Abstract

The Knapsack Problem is a linear integer programming problem with only one constraint which defines a relation between the variables. In this respect, it is the ‘simplest’ integer optimization problem. Since the knapsack problem already possesses essential difficulties of integer programming, it is subject of numerous investigations. It is well-known that the knapsack problem belongs to the class of NP-hard problems, i.e., with high probability there does not exist any algorithm for the knapsack problem which computes an optimal solution in polynomial time. Within this chapter we present basic techniques to solve the knapsack problem which often can be used in solution approaches for other cutting and packing problems.

Suggested Citation

  • Guntram Scheithauer, 2018. "Knapsack Problems," International Series in Operations Research & Management Science, in: Introduction to Cutting and Packing Optimization, chapter 0, pages 19-45, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-64403-5_2
    DOI: 10.1007/978-3-319-64403-5_2
    as

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