The Knapsack Problem and Straightforward Optimization Methods

In the previous chapter we gave some examples for optimization problems in the application area of production and logistics. Recall the cargo-loading problem we described at last which consists in choosing an optimal subset of available products for shipping. In the theory of optimization this task is categorized under a special class of problems, called packing problems. Precisely speaking, we are facing a subclass of packing problems, called knapsack problems. The basic idea of optimally packing items into a single object, i.e. a knapsack in the simplest case, serves as an abstract model for a broad spectrum of packing, loading, cutting, capital budgeting or even scheduling problems. In order to provide a general basis for the subsequent chapters, we will first introduce an example knapsack optimization problem and then discuss various different approaches to solve it.