European Journal of Operational Research 37 (1988) 303-317 303 North-Holland Invited Review New trends in machine scheduling J. BLAZEWICZ Instytut Automatyki, Politechnika Poznanska, Poznan, Poland G. FINKE Department of Applied Mathematics, Technical University of Nova Scotia, Halifax, Canada R. HAUPT Universitiit zu Kgln, Krln, Germany, Fed. Rep. G. SCHMIDT F.B. Informatik, Technische Universitiit Berlin, West Berlin, German)', Fed. Rep. Abstract: This review is concerned with new directions in deterministic machine scheduling theory. We study: resource constrained scheduling, scheduling tasks that require more than one machine at a time, scheduling with nonlinear speed-resource allotted functions, and scheduling in flexible manufacturing systems. The two features that distinguish the above problems are the use of resources in addition to the machines and new models for the processing of tasks. The study of these models was primarily motivated by their practical importance. In each case, we overview the existing results and present solution strategies for particularly chosen problems. Keywords: Scheduling, parallel and dedicated machine systems, resource constraints, FMS 1. Introduction In the classical deterministic machine schedul- ing theory a set of tasks is to be processed on a set of machines (processors) in order to minimize (maximize) a certain performance measure. All the task and processor parameters are assumed to be known in advance. Such a model has been suc- cessfully developed and studied over the past thirty years, and has been applied to many problems in industrial, economical as well as computer en- vironments. On the other hand, studies carried out within the scheduling theory framework stimu- lated also progress in such areas as complexity theory, worst case and probabilistic analysis of approximation algorithms that have been neces- sary for the proper analysis of the problems in question. Numerous papers have been devoted to study- ing various aspects of machine scheduling (we recommend [2,12,41,16,20,32,31,5] as surveys). In the present review we would like to discuss new directions in machine scheduling theory which have been recently studied, primarily because of their practical importance. Among them are: scheduling problems where tasks need additional resources, scheduling tasks that require more than one machine at a time (scheduling in micro- processor systems), scheduling models with speed-resource functions and scheduling in flexi- ble manufacturing systems. The two new features for these scheduling problems are related to ad- 0377-2217/88/$3.50 © 1988, Elsevier Science Publishers B.V. (North-Holland)