Auction Algorithms on Job Shop Scheduling Problem

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Auction Algorithms on Job Shop Scheduling Problem

• Ming-Ming Hsieh

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Job Shop Scheduling Problem

• A set of job is to be completed and each job
  requires a set of machines for a certain period
  of time for processing .
• Each job consists of a series of operations that
  represent the production steps of the job .
• Each operation needs a certain machine for a
  certain time period called processing time .

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Constraints

• Non-preemption constraints
• Precedence constraints
• Capacity constraints
• Scheduling Objective
• To minimize total weighted tardiness

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Job(Bidder) operations
machines
Bid for the time slots of each machine
Broker(Auctioneer)
Resources allocation
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JSP
s.t.
non-preemption constraints
precedence constraints
capacity constraints
integrality constraints
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Combinational Auction
is a subset of
is a subset of
Non-preemption constraints
job is overall bid
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job js utility function is defined as follows
the best bid for job is one that
maximizes the utility function
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A strategy is to have the auctioneer raise the
prices in proportion to the excess demand as
follows
standard Walrasian tatonnement
Adaptive Tatonnement