Machine Scheduling to Minimize Weighted Completion Times

This work reviews the most important results regarding the use of the a-point in Scheduling Theory. It provides a number of different LP-relaxations for scheduling problems and seeks to explain their polyhedral consequences. It also explains the concept of the a-point and how the conversion algorithm works, pointing out the relations to the sum of the weighted completion times. Lastly, the book explores the latest techniques used for many scheduling problems with different constraints, such as release dates, precedences, and parallel machines. This reference book is intended for advanced undergraduate and postgraduate students who are interested in scheduling theory. It is also inspiring for researchers wanting to learn about sophisticated techniques and open problems of the field.

Auteur

Nicoló Gusmeroli completed his Master's degree at the ELTE University of Budapest in 2017, and is currently working on the project High-Performance Solver for Binary Quadratic Problems at the Alpen-Adria University of Klagenfurt as a PhD student. His main research interests are in combinatorial optimization, semidefinite optimization, and scheduling theory. He completed his Bachelor's studies at the University of Verona prior to spending an exchange semester at the University of Primorska (Slovenia), where he wrote his Bachelor's thesis.

Résumé

This work reviews the most important results regarding the use of the -point in Scheduling Theory. It provides a number of different LP-relaxations for scheduling problems and seeks to explain their polyhedral consequences. It also explains the concept of the -point and how the conversion algorithm works, pointing out the relations to the sum of the weighted completion times. Lastly, the book explores the latest techniques used for many scheduling problems with different constraints, such as release dates, precedences, and parallel machines. This reference book is intended for advanced undergraduate and postgraduate students who are interested in scheduling theory. It is also inspiring for researchers wanting to learn about sophisticated techniques and open problems of the field.

Contenu
1 Introduction.- 2 List of Main Results.- 3 LP Relaxations for the Release Dates Case.- 4 Conversion Algorithm.- 5 Approximations for 1| rj | w**jCj.- 6 Approximations for 1| rj | Cj.- 7 Approximation for 1| rj, prec | w**j C**j.- 8 Approximation for P | *r j | *C**j.- 9 Approximation for P | d**ij | w**j C**j.- 10 Conclusions.