Syllabus (Tentative)

1. Introduction (Handout of Chapter 1 and 2 from (Pinedo 95))
   1. Models
   2. Notation
   3. Applications
   4. NP-completeness, Approximation, Linear Programming
2. Minimizing Schedule Length
   1. Solving P|pmtn|C_max (McNaughton59) and lower bounds (KSW 2.3.2)
   2. P||C_max
      1. List scheduling (2-approximation)
      2. LPT (4/3-approximation)
      3. Polynomial Approximation Scheme (Hochbaum Shmoys 87, KSW 3.3, 6.2)
   3. P|prec|C_max (KSW 2.3.4)
      1. NP-hardness of P|prec,p_j=1|C_max
      2. Algorithms for P2|p_j=1|C_max (Gabow 82)
      3. List Scheduling for P|prec|C_max (2-approximation)
   4. R|pmtn|C_max (LawlerL78) -- introducing Linear programs in scheduling (KSW 4.1)
   5. R||C_max (Shmoys Tardos 93) -- using linear program relaxations to get approximation algorithms (KSW 5.1)
3. Scheduling with Deadlines on One Machine
   1. 1||L_max - EDD (KSW 2.1.2)
   2. 1|r_j,pmtn| L_max - preemptive EDD (introducing release dates) (KSW 2.1.3)
   3. 1|prec|f_max - Least Cost Last (KSW 3.1.1)
   4. 1|pmtn,r_j,prec|f_max (Baker et al 83)
   5. Approx. algorithms for 1|r_j,prec|L_max and 1|r_j|L_max (Hall Shmoys 89,Hall97) (KSW 6.3.2)
   6. 1||∑w_jU_j - Dynamic programming solution, weak NP-completeness (KSW 3.2,6.1)
4. Scheduling to Minimize weighted completion time
   1. 1||∑w_jC_j - Smith's rule (KSW 2.1.1)
   2. Exact solutions to R||{∑C_j via linear programming and matching, specializations to P||∑C_j (KSW 4.1)
   3. Solving P|pmtn|∑C_j (McNaughton 59)
   4. Dealing with release dates and precedence constraints
   5. Solving 1|r_j,pmtn|C_j via SRPT (KSW 2.1.3)
   6. Approximations for 1|r_j|∑C_j and P|r_j|∑C_j (Phillips Stein Wein 98) -- using relaxations (KSW 5.2)
   7. Improvements through randomization for 1|r_j|∑C_j (Chekuri et. al. 97)
   8. Other LPs and roundings P|r_j|∑w_jC_j ( Hall et al 97)
   9. A PTAS (Afrati et al 99)
5. Minimizing Flow Time
   1. 1|r_j|∑F_j is NP-hard (Kellerer et al 1995)
   2. Resource augmentation (Kalyanasundaram and Pruhs 95, Phillip et al 97, Cho et al 2007)
6. On-line Scheduling
7. Power-Aware Scheduling
8. Mechanism Design for Scheduling
9. Shop Scheduling Models