Scheduling and Design Problems

Abstract

In addition to location problems, a truly amazing variety of scheduling and design problems has been formulated by numerous professionals in industrial engineering, management science, computer science and the social sciences as Boolean quadratic problems with special ordered set constraints (BQPSs). These include notorious problems such as the traveling salesman problem and seemingly innocuous, but NP-hard optimization problems such as the unconstrained quadratic zero-one optimization problem. In this chapter we collect a representative number of these problems with the aim of classifying them into a schema that will permit us to detect commonalities and differences for further in-depth study of the essential problem classes. Right from the outset, we wish, however, to make clear that we do not advocate the exclusive treatment of every zero-one optimization problem that fits into our framework within the classes of BQPSs that we consider. Additional structural properties of a combinatorial optimization problem — if present — must be exploited fully in order to achieve numerical success and while we subscribe to the often heard maxim “...as global as possible, as local as necessary ...”, we do it with the right amount of caution.