2-1
Scheduling Constraints
2-2
Outline
• Activities
• Temporal constraints
• Resources
• Resource constraints (mono-activity)
• Resource constraints (two activities)
2-3
Activities
• Interval (block) activities
• Splittable activities (with interruption cost?)
A
time
A
time
A A A
2-4
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
2-5
Resources
• Unary resources
• Discrete resources
• State resources
• Energetic resources
2-6
Unary resources
• Main resources in 4/10 problems
• Example: one individual machine or person
A B
C
time
2-7
Discrete resources
• Main resources in 5/10 problems
• Example: group of identical machines
A
B
Dtime
C
2-8
State resources
• Main resources in 1/20 problems
• Example: oven with different temperatures
D
time
A
B
C
2-9
Energetic resources
• Main resources in 1/20 problems
• Example: number of man-days per week
A B
timeC
2-10
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
2-11
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)
2-12
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
2-13
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
2-14
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
2-15
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
2-16
Optional or variable requirements
• Optional activities– Resource alternatives– Sub-contracts
2-17
Optional or variable requirements
• Time versus capacity tradeoffs
2 people during 3 days
or 3 people during 2 days
2-18
Optional or variable requirements
• Variable requirement over timeExample: 8 person-days with either 2 or 3 people at any time
2-19
Transition times
• Tool setup between two tasks on the same machine
• State change (oven temperature, color used in a painting shop)
• Cleaning
2-20
Resource constraints
• Two activities– Percentage constraints– Synchronization constraints
2-21
Percentage constraints
• % of activity A on resource RA must be done before (or after):– B starts– B ends
– % of activity B on resource RB are done
• Often complements variable requirements over time
2-22
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
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