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2004/11/01 corolla 1 Auction Based Ming_Ming Hsieh Job Shop Scheduling problem

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2004/11/01corolla2 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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2004/11/01corolla3 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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2004/11/01corolla4 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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2004/11/01corolla5 Job(Bidder) operations Fab(Auctioneer) machines Bid for the time slots of each machine Resources allocation

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2004/11/01corolla6 Flow Chart of the Auction Process or Ideas Check if a stopping criterion is satisfied. If yes, stop and get the best feasible schedule. Initialization:The auctioneer initializes the machine-time slots prices=0 and set iteration counter=0 Each job solves the-job level utility sub-problem then summit its optimal bid to the auctioneer 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. Auctioneer computes the excess demand vector and Updates time slots prices. If not

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2004/11/01corolla7 JSP :job index( ) :operation index( ) :time slot index( ) :machine index( ) :tardiness penalty of job :due day of job :the operation of in :machine for of :processing time of of of has started by otherwise total weighted tardiness

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2004/11/01corolla8 s.t. non-preemption constraints precedence constraints capacity constraints integrality constraints

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2004/11/01corolla9 Combinatorial Auction : operation bid : job bid is a subset of Non-preemption constraints

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2004/11/01corolla10 job i`s overall bid : all allowed locally feasible bids job j`s utility function the best bid for job is one that maximizes the utility function

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2004/11/01corolla11 machine(Bidder) Fab(Auctioneer) Operations job Bid for the operations of each job Resources allocation

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2004/11/01corolla12 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

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