Auction Based

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Auction Based
Job Shop Scheduling problem

• Ming_Ming Hsieh

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Job Shop-Scheduling Problem(JSP)

• A set of job is to be completed
• Each job consists of a series of operations
• Each operation needs a certain machine for a
• processing time
• Constraints
• Non-preemption constraints
• Precedence constraints
• Single assignment constraint
• Capacity constraints

Objective minimize total weighted tardiness
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Why auction ?

• A decentralized scheduling problem has several
• different aspects
• Each individual decision-makers may has
• different objectives for their own profits .
• Decision-makers may have their own private
• information such as their valuations of the
  objects .
• There may have the authority problem of manage-
• ment and control .
• Decentralized system with the parallel
  processing
• power may speed up the calculation .

we identify the JSP as a decentralized
scheduling problem .
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• the auction market suits the situation with these
  properties
• The value of the merchandise is not obvious .
• The buyers have different objects for their own
  profits .
• Each buyer has his own private information such
  as valuation .

We propose an auction-based job shop scheduling
algorithm for marketing environment .
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Job(Bidder) operations
machines
Bid for the time slots of each machine
Fab(Auctioneer)
Resources allocation
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Flow Chart of the Auction Process or Ideas
InitializationThe auctioneer initializes the
machine-time slots prices0 and set iteration
counter0
Check if a stopping criterion is satisfied . If
yes , stop and get the best feasible schedule .
Each job solves the-job level utility
sub-problem then summit its optimal bid to the
auctioneer
Auctioneer computes the excess demand vector and
Updates time slots prices .
If not
Auctioneer combines all the bids and generate a
capacity infeasible shop-level schedule .
Auctioneer converts this capacity infeasible
schedule into a feasible one By resolving the
resource conflicts .
Auctioneer updates best feasible shop schedule .
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JSP
total weighted tardiness
the operation of in machine for
of processing time of of
job index( ) operation index(
) time slot index(
) machine index( ) tardiness
penalty of job due day of job
of has started by
otherwise
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s.t.
non-preemption constraints
precedence constraints
capacity constraints
integrality constraints
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Combinatorial Auction
operation bid
job bid
is a subset of
is a subset of
Non-preemption constraints
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job is overall bid
all allowed locally feasible bids
job js utility function
the best bid for job is one that
maximizes the utility function
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Operations job
machine(Bidder)
Bid for the operations of each job
Fab(Auctioneer)
Resources allocation
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• The shop-level objective is to minimize the
  tardiness
• and maximize the profit for the auctioneer
  (fab).
• Auctioneer must set the time slots and tardiness
• penalty for each operation
• No capacity constraint but single assignment
• constraint instead
• There may be some jobs uncompleted when auction
• finish .
• Jobs may have to loosen their deadlines or
  enhance
• their costs