Worst-Case Analysis

Abstract

Since most complicated logistics problems, for example, the bin-packing problem and the traveling salesman problem, are (Formula Presented)-Hard, it is unlikely that polynomial-time algorithms will be developed for their optimal solutions. Consequently, a great deal of work has been devoted to the development and analyses of heuristics. In this chapter, we demonstrate one important tool, referred to as worst-case performance analysis, which establishes the maximum deviation from optimality that can occur for a given heuristic algorithm. We will characterize the worst-case performance of a variety of algorithms for the bin-packing problem and the traveling salesman problem. The results obtained here serve as important building blocks in the analysis of algorithms for vehicle routing problems.