Interval Scheduling, Reservations, and Timetabling

Abstract

This chapter considers two types of timetabling problems. The first type of timetabling problem assumes that all operators are identical, i.e., the operators constitute a single homogeneous workforce. The total number of operators available is W and in order to do activity j on one of the resources W j operators have to be present. If the sum of the people required by activities j and k is larger than W (i.e., W j + W k > W), then activities j and k may not overlap in time. This type of timetabling is in what follows referred to as timetabling with workforce or personnel constraints. In this chapter we often make a distinction between the feasibility version of a problem and its optimization version. In the feasibility version we need to determine whether or not a feasible schedule exists; in the optimization version an objective has to be minimized. If no efficient algorithm exists for the feasibility version, then no efficient algorithm exists for the optimization version either. Throughout this chapter we assume that all data are integer and that preemptions are not allowed.