| Summary: | 碩士 === 國立臺灣大學 === 電機工程學研究所 === 94 === Pressed by market globalization and concomitant competition, more and more manufacturers are relying on their suppliers to provide raw materials and component parts so as to focus on their core competence. Outsourcing becomes an increasing trend due to the competitiveness of the IT (Information Technology) industry.
In this study, we focus on the job assignment and scheduling problem between job provider and contract manufacturers. In the semiconductor supply chain, fabless design houses of integrated circuits generate various job orders and compete for the capacity of qualified foundry service providers. On the other hand, foundry fabs/companies compete to get the job orders by providing low cost and timely manufacturing services. In this not only competed but also cooperative environment, all the decision-makers (DMs), i.e., job owners and fabs all hope keep their private information such as ones’ own valuation of jobs, actual capacity and operational constraints. So, traditional centralized methods are not directly applicable in the problem.
In order to make DMs can assign jobs with keeping private information, we choose reverse auction among several kinds of auctions to develop our algorithm in solving the problem. A job order owner announces job requirements and payments for fabs to bid on while qualified fabs bid on a job by offering the discount to payment and processing schedule of the job. The auction is processed through iterations. In each round of bidding, the bidders send job “bids” to the auctioneer and the auctioneer then temporarily assigns each job to the bidder who offers the highest bid on the job. The highest bid on each job serves as the starting bid for the job in the next round of bidding. The auction repeats round by round till no new bids are offered and the final assignment is determined.
The auction is a non-cooperative game so we model auctioneer’s and bidder’s problems separately and consider their interactions. We formulate the auctioneer behavior and the assignment is an integer-programming assignment problem. For auctioneer, it only considers the expected profit from job assigned and the cost from job unassigned. The not or late delivering job compensation is all compensated by bidder.
For bidder, his problem is how to get the maximum profit by biding jobs. So, the objective of a fab is to maximize the payment it may receive from processing the jobs minus the earliness/tardiness penalty for each job not processed within the desired time window of the job and subject to local constraints such as capacity constraint and operation precedence constraint. We apply the Lagrangian Relaxation to decompose the problem into individual job scheduling problems, and updated Lagrange multipliers according to a sub-gradient method. Besides, in order to be applied in the real condition, we will consider a situation where there are uncertainties and the cycle time of each job is a random variable. We simulate the stochastic cycle time and get its mean and variance. A simple heuristics with job schedule evaluation by simulation are adopted in the bidder’s scheduling algorithm. By re-formulating our mathematic formulation, we can make the algorithm be closer to the real problem.
Experiment results show that the stochastic problem formulation performs better than the deterministic problem formulation when the cycle time is a random variable, i.e., the algorithm with consideration of uncertainties has a better performance than optimality of the mean value-based bidder scheduling algorithm. And the consideration of uncertainties in bidders’ decisions has a lot of impact on performance of both bidders and the auctioneer. Besides, we simulate the case where there are asymmetric logistic capability bidders in the auction and the experiment result that auctioneer should also has risk when a bidder winner delays the job delivery. So when auctioneer assign job, he should take the consideration of risk in his decision.
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