Auction Based Job Shop Scheduling problem MingMing Hsieh

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

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 2004/11/01 corolla 2

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 management and control. • Decentralized system with the parallel processing power may speed up the calculation. we identify the JSP as a decentralized scheduling problem. 2004/11/01 corolla 3

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. 2004/11/01 corolla 4

Job(Bidder) operations machines Bid for the time slots of each machine Fab(Auctioneer) Resources allocation 2004/11/01 corolla 5

Flow Chart of the Auction Process or Ideas 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 Check if a stopping criterion is satisfied. If yes , stop and get the best feasible schedule. 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. 2004/11/01 corolla Auctioneer computes the excess demand vector and Updates time slots prices. Auctioneer updates best feasible shop schedule. 6

JSP total weighted tardiness : job index( : the operation of ) : operation index( ) : time slot index( ) : machine for of : processing time of of : tardiness penalty of job in of has started by otherwise : due day of job 2004/11/01 corolla 7

s. t. non-preemption constraints precedence constraints capacity constraints integrality constraints 2004/11/01 corolla 8

Combinatorial Auction : operation bid : job bid is a subset of Non-preemption constraints 2004/11/01 corolla 9

job i`s overall bid : allowed locally feasible bids job j`s utility function the best bid for job utility function 2004/11/01 is one that maximizes the corolla 10

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

• 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 2004/11/01 corolla 12