Machine Scheduling to Minimize Weighted Completion Times The Use of the α-point /

• Κύριος συγγραφέας: Gusmeroli, Nicoló (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: SpringerBriefs in Mathematics,
• Θέματα: Operations research.; Management science.; Mathematical optimization.; Applied mathematics.; Engineering mathematics.; Algorithms.; Polytopes.; Discrete mathematics.; Operations Research, Management Science.; Discrete Optimization.; Applications of Mathematics.; Discrete Mathematics.

 This work reviews the most important results regarding the use of the α-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 α-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. 

 1 Introduction -- 2 List of Main Results -- 3 LP Relaxations for the Release Dates Case -- 4 Conversion Algorithm -- 5 Approximations for 1| rj | ∑ wjCj -- 6 Approximations for 1| rj | ∑ Cj -- 7 Approximation for 1| rj, prec | ∑ wj Cj -- 8 Approximation for P | r j | ∑ Cj -- 9 Approximation for P | dij | ∑ wj Cj -- 10 Conclusions.