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lecture9 - 1.224J/ESD.204J Transit Crew Scheduling Outline...

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11/26/03 1.224J/ESD.204J 1 Outline Crew Scheduling Work Rules and Policies Model Formulation Matching Problem Approximation approach for large problems Experience with Automated Crew Scheduling Systems 1.224J/ESD.204J Transit Crew Scheduling
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11/26/03 1.224J/ESD.204J 2 Input • A set of vehicle blocks each starting with a pull-out and ending with a pull-in at the depot • Crew work rule constraints and pay provisions Objective: • Define crew duties (aka runs, days, or shifts) covering all vehicle block time so as to: minimize crew costs Crew Scheduling Problem
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11/26/03 1.224J/ESD.204J 3 Constraints: • Work rules: hard constraints • Policies: preferences or soft constraints • Crews available: in short run the # of crews available are known Variations: • different crew types: full-time, part-time • mix restrictions: constraints on max # of part-timers Crew Scheduling Problem
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11/26/03 1.224J/ESD.204J 4 Three-stage sequential approach: 1. Cutting long vehicle blocks into pieces of work 2. Combining pieces to form runs 3. Selection of minimum cost set of runs Manual process includes only steps 1 and 2; optimization process also involves step 3 Typical Crew Scheduling Approach
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11/26/03 1.224J/ESD.204J 5 Cutting Blocks: each block consists of a sequence of vehicle revenue trips and non-revenue activities blocks can be cut only at relief points where one crew can replace another. relief points are typically at terminals which are accessible avoid cuts within peak period resulting pieces typically: have minimum and maximum lengths should be combinable to form legal runs Typical Crew Scheduling Approach
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11/26/03 1.224J/ESD.204J 6 Definition: a partition of a block is the selection of a set of cuts each representing a relief Key problems: -- very hard to evaluate a partition before forming runs -- many partitions are possible for any vehicle block Possible Approaches: -- generate only one partition for each vehicle block -- generate multiple partitions for each vehicle block -- generate all possible partitions for each vehicle block Vehicle Block Partitions
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11/26/03 1.224J/ESD.204J 7 A Vehicle Block on Route AB d i = departure time from terminal i a i = arrival time at terminal i 19:50 14:05 14:15 a B d B 17:50 17:55 a B d B 15:55 16:05 a B d B 19:30 a B a A d A 13:15 13:25 a A d A 15:00 15:10 a A d A 16:55 17:00 a A d A 18:40 18:50 d A 5:45 6:00 a A d A 7:40 7:50 a A d A 9:35 9:45 a A d A 11:25 11:35 6:40 7:00 a B d B 8:40 8:45 a B d B 10:30 10:40 a B d B 12:20 12:30 a B d B Deadhead from Depot Deadhead to Depot
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11/26/03 1.224J/ESD.204J 8 • Large number of feasible runs by combining pieces of work • Work rules are complex and constraining: maximum work hours: e.g. 8 hrs 15 min minimum paid hours - guarantee time: e.g. 8 hrs overtime constraints and pay premiums: e.g. 50% pay premium spread constraints and pay premiums: time between first report and last release for duty, e.g.
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lecture9 - 1.224J/ESD.204J Transit Crew Scheduling Outline...

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