Scheduling Constraints
2-1
Outline
• Activities
• Temporal constraints
• Resources
• Resource constraints (mono-activity)
• Resource constraints (two activities)
2-2
Activities
• Interval (block) activities
A
time
• Splittable activities (with interruption cost?)
A
A
A
A
time
2-3
Temporal constraints
•
•
•
•
•
•
Earliest and latest start and end times
Fixed or variable durations
Precedence constraints
Precedence constraints with minimal delays
Precedence constraints with fixed delays
Maximal delays
2-4
Resources
•
•
•
•
Unary resources
Discrete resources
State resources
Energetic resources
2-5
Unary resources
• Main resources in 4/10 problems
• Example: one individual machine or person
A
B
time
C
2-6
Discrete resources
• Main resources in 5/10 problems
• Example: group of identical machines
B
A
C
time
D
2-7
State resources
• Main resources in 1/20 problems
• Example: oven with different temperatures
B
A
C
time
D
2-8
Energetic resources
• Main resources in 1/20 problems
• Example: number of man-days per week
A
B
time
C
2-9
Resource constraints
• Mono-activity
–
–
–
–
Resource requirement
Resource provision
Resource consumption/production
Periods during which a resource is not (or not
fully) available
– Optional or variable requirements
– Transition times
2-10
Resource requirement
• Unary resource: A requires R
• Discrete resource: A requires c units of R
• State resource: A requires R ...
–
–
–
–
in a given state s
in any of a given set of states {s1 ... sn}
not in a given state s
not in any of a given set of states {s1 ... sn}
• Energetic resource: A requires w units of R per
time period (e.g., 4 man-months per month)
2-11
Resource provision
• Similar to resource requirement when part
of the problem is to make the resources
available for the requiring activities
• The required capacity can never exceed the
provided capacity
2-12
Resource consumption
• Unary resource: A consumes R
• Discrete resource: A consumes c units of R
• The consumed capacity is no longer available for
any other activity
• The resource is required from the start time of the
activity up to the end of the schedule
2-13
Resource production
• Unary resource: A produces R
• Discrete resource: A produces c units of R
• The produced capacity becomes available when
the activity ends
• The resource is provided from the end time of the
activity up to the end of the schedule
2-14
Capacity constraints
• Periods during which a resource is not fully
available
– Maintenance periods
– Vacations
– Forbidden states (at night)
• Periods during which some minimal amount
must be required or provided
2-15
Optional or variable requirements
• Optional activities
– Resource alternatives
– Sub-contracts
2-16
Optional or variable requirements
• Time versus capacity tradeoffs
2 people during 3 days
or 3 people during 2 days
2-17
Optional or variable requirements
• Variable requirement over time
Example: 8 person-days with either 2 or 3
people at any time
2-18
Transition times
• Tool setup between two tasks on the same
machine
• State change (oven temperature, color used
in a painting shop)
• Cleaning
2-19
Resource constraints
• Two activities
– Percentage constraints
– Synchronization constraints
2-20
Percentage constraints
• a% of activity A on resource RA must be
done before (or after):
– B starts
– B ends
– b% of activity B on resource RB are done
• Often complements variable requirements
over time
2-21
Synchronization constraints
• When A executes, B requires (at least, at
most) c1 units of resource R
• When A does not execute, B requires (at
least, at most) c2 units of resource R
2-22