PSU CS410/510SS: Search and Scheduling
Lecture 5
Realistic Scheduling Problems

Administrative

• Homework 3: look at it now
• Project teams
• Syllabus change
• Reading for next week (online)
• Search Research?

Lecture 5

• Brucker: OR Scheduling Notation
  • Basics
    • Machines M
    • Jobs J
    • Operations O: sub-jobs
    • Machines for O; mu: resources used by O
    • Cost f: may be function of t
  • Job Characteristics: we care mostly about
    • no preemption
    • arbitrary precedence (DAG)
    • problems with and without release times
    • no special processing requirements
    • problems with and without deadlines
  • Machine Environment: we care mostly about
    • QMPM or less
    • 1 operation per job
    • Job-shop problems
  • Objectives
    • bottleneck/makespan
    • rarely sum
    • very common to hack objective together
    • Why regular (monotonic) objectives?
  • Active (left-most) and semi-active (left-shifted) schedules.

• Brucker: Common Manufacturing Scheduling Domains
  • Disjunctive Graphs
  • Various Shop Problems
    • Open Shop
      • Each job has m operations, m machines
      • Operation O_ij requires machine j
      • Polytime for O2 (w. proof)
    • Flow Shop
      • Open Shop restricted to O_ij in j order
      • Polytime for F2 (w. proof sketch)
      • Permutation Flow Shop = Flow Shop with every machine processing jobs in a given order
    • Job Shop
      • Flow Shop generalized to
        • Allow arbitrary number n of jobs
        • Require O_ij to be processed on some given machine mu_ij
      • WLOG mu_ij not equal to mu_i,j+1
      • Very extensively studied
      • Famous benchmark: Sadeh (Micro-BOSS) synthetics [Project?]
      • Heuristics

• Brucker: Techniques For NP-hard Scheduling
  • DFBnB on disjunctive graphs
    • Disjunctive graphs = precedence based
    • ``Critical path''
    • Branching scheme = variable ordering + value ordering + symmetry breaking
    • One possible branching scheme (Grabowski)
      • Construct a heuristic soln
      • Systematically search all possible improvements of that soln
      • Some improvements can be ruled out by ``candidates thm''
    • ``Heads and Tails''
      • Head of job i is lower bound on span preceding i
      • Tail of job i is lower bound on span following i
      • ``Pigeonhole'' refinement for heads and tails
    • Carlier and Pinson: cool work on improving this stuff
    • Note complexity of scheme: not necessarily worth it (i.e. switch search techniques)
  • Tabu Search
    • Neighborhood = search space
      • N1: Flip jobs processed on same machine in critical path (sound, opt-connected)
      • N4: Flip job inside block on critical path close as possible to beginning or to end of block
    • Tabu list: FIFO buffer of visited solns
      • Can catch more than one per entry
      • Can grow or shrink as needed
    • Aspiration: cancelling tabus

• Realistic Constraints In Shop Scheduling
  • Deadlines
  • Release times
  • Setups and forbidden setups
  • Fixed times and time relationships
  • Time and cost objectives