psop: using search to find better resource-leveled schedules matt ginsberg

PSOP: Using Search to Find Better Resource-Leveled

SchedulesMatt Ginsberg


Scheduling to an Academic

• Use small examples to: Understand why scheduling is hard Develop possible solutions

• Eventually, evaluate candidate approaches based on performance on real problems



Why Scheduling is Like Tetris


Scheduling and Tetris

• The idea is to squish a lot of stuff into a small space

• It helps to know what’s coming

• I am terrible at both


• Fact: Computer scientists tend to work on problems at which they are personally lousy.

• Consequence: Beware of people who say that they are working on “general intelligence.”


Summary

• The idea is to squish a lot of stuff into a small space

• It helps to know what’s coming

• I am terrible at both• … but Tetris is much more

forgiving than scheduling is


A Scheduling Problem

• The capacity of the red resource is one.

• The capacity of the blue resource is infinite.

• The capacity of the purple resource is two.


How Scheduling Algorithms Work

1. Select the highest-priority unscheduled task whose predecessors have all been scheduled.

2. Schedule it at its current early start.

3. Repeat.


Order Matters

1. Select the highest-priority unscheduled task whose predecessors have all been scheduled.

2. Schedule it at its current early start.

3. Repeat.


Order Matters

• The purple resource has capacity two.

• The bottom task should not be scheduled last.


Schedule the Longest Task First?

1

2

3


Schedule the Least Float Task First

2

3

1


No Obvious Order Works

longest, least float


The Example in Primavera

• Use a silly order• Prioritize by hand

longest, least float


No Order Works


Least Float First

least float


Most Float First?

least float


The Order That Works

• Prioritize by hand?least float


Prioritization by Hand


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Prioritization by Hand

• Unlikely to work in practice• What can you do?• Being good at Tetris will not save you


Outline

• If you want a good schedule, prioritization matters• Not obvious how to prioritize automatically• Prioritization by hand is impractical• Schedule packing• Squeaky wheel optimization

How it works Strengths, weaknesses Access


Schedule Packing

WARNING: Contents may have settled

during shipping


Schedule Packing

1. Slide tasks as far to right as possible

2. Reschedule using start time as priority

1 2

3

4


Outline

• If you want a good schedule, prioritization matters• Not obvious how to prioritize automatically• Prioritization by hand is impractical• Schedule packing• Squeaky wheel optimization

How it works Strengths, weaknesses Access


Squeaky Wheel Optimization

• Too many priority orders to figure out the best one

• Use search


think search

• Primavera• schedule packing

• squeaky wheel

P=NP?


Solving Problems Using Search

• The key is to control the search


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Solving Problems Using Search

• The key is to control the search• A machine can look at many candidate

schedules, but it still needs to focus on schedules that are likely to be good

• Squeaky wheel: Analyze the current schedule before generating the next one



• C-A-P loop Construct Analyze Prioritize



• C-A-P loop Construct a schedule from current priorities Analyze Prioritize



• C-A-P loop Construct a schedule from current priorities Analyze to evaluate performance by task Prioritize



• C-A-P loop Construct a schedule from current priorities Analyze to evaluate performance by task Prioritize so that poorly scheduled tasks

become more important• The squeaky wheel gets the grease!


Squeaky Wheel Where no Order Worked

1

2

3

1

2

3


3

Squeaky Wheel Where no Order Worked

• Search improves your ability to find good solutions, even if you guess wrong initially

1

2


Schedule Packing on This Problem


Squeaky Wheel


Enough Already with the Toy Problems!• Turnaround data from existing Primavera customer• 12,248 tasks, analyzed in 4.5 minutes

Primavera length

PSOP length

Primavera overload

PSOP overload

Primavera leveled

47 days 40 days 43 hours 11 hours

Leveled within total float

30 days 30 days 10,561 hours 2,653 hours


Pros and Cons

Schedule Packing• Simple• Fast (because no search)• Patented by Boeing

Squeaky Wheel• Not so simple• Potentially slower because of search• Better coverage• Patented by U Oregon• Available as an addon for Primavera 5.0


PSOP Demo


One Last Example

sand and prepare

mix and paint

-1


One Last Example

• No predecessor-based algorithms works!• Squeaky wheel need not follow “network” order• Schedule packing does

sand and prepare

mix and paint

-1


Pros and Cons

Schedule Packing• Simple• Fast (because no search)• Patented by Boeing• Add search?

Squeaky Wheel• Not so simple• Potentially slower because of search• Still• Patented by U Oregon• Available as an addon for Primavera 5.0

Better coverage


Questions?

psop: using search to find better resource-leveled schedules matt ginsberg

Documents

time systems

float slide

tetris slide

hand slide

float task

longest task

purple resource

order matters