Discrete optimization

This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas

TABU SEARCH FOR A CLASS OF SCHEDULING PROBLEMS (Preprint)

Scheduling problems are often modeled as resource constrained problems in which critical resource assignments to tasks are known and the best assignment of resource time must be made subject to these constraints. Generalization to resource scheduling, where resource assignments are chosen concurrently with times results in a problem which is much more di±cult. A simpli¯ed model of the general resource scheduling model is possible, however, in which tasks must be assigned a single primary resource, subject to constraints resulting from preassignment of secondary, or auxiliary, resources. This paper describes extensions and enhancements of Tabu Search for the special case of the resource scheduling problem described above. The class of problems is further restricted to those where it is reasonable to enumerate both feasible time and primary resource assignments. Potential applications include shift oriented production and manpower scheduling problems as well as course scheduling where classrooms (instructors) are primary and instructors (rooms) and students are secondary resources. The underlying model is a type of quadratic multiple choice problem which we call multiple choice quadratic vertex packing (MCQVP). Results for strategic oscillation and biased candidate sampling strategies are shown for reasonably sized real and randomly generated, synthetic, problem instances. These strategies are compared with other variations using consistent measures of solution time and quality developed for this study.

TABU SEARCH FOR A CLASS OF SCHEDULING PROBLEMS (Preprint)

Scheduling problems are often modeled as resource constrained problems in which critical resource assignments to tasks are known and the best assignment of resource time must be made subject to these constraints. Generalization to resource scheduling, where resource assignments are chosen concurrently with times results in a problem which is much more difficult. A simplified model of the general resource scheduling model is possible, however, in which tasks must be assigned a single primary resource, subject to constraints resulting from preassignment of secondary, or auxiliary, resources. This paper describes extensions and enhancements of Tabu Search for the special case of the resource scheduling problem described above. The class of problems is further restricted to those where it is reasonable to enumerate both feasible time and primary resource assignments. Potential applications include shift oriented production and manpower scheduling problems as well as course scheduling where..

Large Scale Classroom Scheduling

Classroom scheduling is an important part of course scheduling at Purdue University. The objective is to choose meeting rooms and times for each class that maximize student and instructor preferences without creating student, room or instructor schedule conflicts. An approach for solving classroom scheduling problems of practical size has been developed and implemented in CHRONOS, a scheduling support system developed at Purdue and described in this paper. Requirements for CHRONOS derive from the course scheduling process at Purdue and are specified in a mathematical model of the classroom scheduling problem. Database, preprocessing, and search components provide computerized support to decision makers. Results obtained from preliminary tests and ongoing use scheduling 500 course sections in a set of 31 large lecture rooms are positive. Work is currently under way to implement the system in a client-server environment and improve the qualitative aspects of generated schedules. 1 Intr..