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Scheduling Constraints

Scheduling Constraints. Outline. Activities Temporal constraints Resources Resource constraints (mono-activity) Resource constraints (two activities). A. time. Activities. Interval (block) activities Splittable activities (with interruption cost?). A. A. A. A. time.

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Scheduling Constraints

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  1. Scheduling Constraints

  2. Outline • Activities • Temporal constraints • Resources • Resource constraints (mono-activity) • Resource constraints (two activities)

  3. A time Activities • Interval (block) activities • Splittable activities (with interruption cost?) A A A A time

  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

  5. Resources • Unary resources • Discrete resources • State resources • Energetic resources

  6. C Unary resources • Main resources in 4/10 problems • Example: one individual machine or person A B time

  7. Discrete resources • Main resources in 5/10 problems • Example: group of identical machines B A C time D

  8. B State resources • Main resources in 1/20 problems • Example: oven with different temperatures A C time D

  9. C Energetic resources • Main resources in 1/20 problems • Example: number of man-days per week A B time

  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

  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)

  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

  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

  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

  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

  16. Optional or variable requirements • Optional activities • Resource alternatives • Sub-contracts

  17. Optional or variable requirements • Time versus capacity tradeoffs 2 people during 3 days or 3 people during 2 days

  18. Optional or variable requirements • Variable requirement over time Example: 8 person-days with either 2 or 3 people at any time

  19. Transition times • Tool setup between two tasks on the same machine • State change (oven temperature, color used in a painting shop) • Cleaning

  20. Resource constraints • Two activities • Percentage constraints • Synchronization constraints

  21. 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

  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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