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Discussion Paper No. 1436
Northwestern University, Kellogg School of Management, Center for Mathematical Studies in Economics and Management Science, Evanston, IL
We study how rework routing together with wage and piece rate compensation can strengthen incentives for quality. Traditionally, rework is assigned back to the agent who generates the defect (in a self routing scheme) or to another agent dedicated to rework (in a dedicated routing scheme). In contrast, a novel cross routing scheme allocates rework to a parallel agent performing both new jobs and rework. The agent who passes quality inspection or completes rework receives the piece rate paid per job. We compare the incentives of these rework allocation schemes in a principal-agent model with embedded quality control and routing in a multi-class queueing network. We show that conventional self routing of rework can never induce first-best effort. Dedicated routing and cross routing, however, strengthen incentives for quality by imposing an implicit punishment for quality failure. In addition, cross routing leads to workload allocation externalities and a prisoner’s dilemma, thereby creating highest incentives for quality. Firm profitability depends on capacity levels, revenues, and quality costs. With ample capacity, dedicated routing and cross routing both achieve first-best profit rate, while self routing does not. With limited capacity, cross routing generates the highest profit rate when appraisal, internal failure, or external failure costs are high, while self routing performs best when gross margins are high. When the number of agents increases, the incentive power of cross routing reduces monotonically and approaches that of dedicated routing.
queueing networks
Nash equilibrium
quality control
piece rate
epsilon equilibrium.
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Working Paper

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