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 AAA

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 AB C time

2-7 Discrete resources Main resources in 5/10 problems Example: group of identical machines A B D time 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 AB time C

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 {s 1... s n } –not in a given state s –not in any of a given set of states {s 1... s n } 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 time Example: 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 R A must be done before (or after): – B starts – B ends –  % of activity B on resource R B are done Often complements variable requirements over time

2-22 Synchronization constraints When A executes, B requires (at least, at most) c 1 units of resource R When A does not execute, B requires (at least, at most) c 2 units of resource R