On Scheduling Fees to Prevent Merging, Splitting, and Transferring of Jobs
Mathematics of Operations Research
Two dimensional optimal mechanism design for a sequencing problem
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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We study the design of optimal mechanisms in a setting where job-agents compete for being processed by a service provider that can handle one job at a time. Each job has a processing time and incurs a waiting cost. Jobs need to be compensated for waiting. We consider two models, one where only the waiting costs of jobs are private information (1-d), and another where both waiting costs and processing times are private (2-d). An optimal mechanism minimizes the total expected expenses to compensate all jobs, while it has to be Bayes-Nash incentive compatible. We derive closed formulae for the optimal mechanism in the 1-d case and show that it is efficient for symmetric jobs. For non-symmetric jobs, we show that efficient mechanisms perform arbitrarily bad. For the 2-d case, we prove that the optimal mechanism in general does not even satisfy IIA, the `independent of irrelevant alternatives' condition. We also show that the optimal mechanism is not even efficient for symmetric agents in the 2-d case.