Abstract
We study a scheduling problem, in which jobs of two agents are performed in agent specific batches on the same serial unbounded batching machine. On this machine, jobs of the same batch complete simultaneously, and the batch processing time is equal to the total processing time of its jobs plus a setup time. Each agent aims at minimizing a function which depends only on the completion times of its jobs. The problem is to find a schedule that minimizes the objective function of one agent, subject to the objective function of the other agent does not exceed a given threshold. The problem appears in optimizing product consolidation operations of a cross-docking distribution center. Polynomial and pseudo-polynomial dynamic programming algorithms are derived for settings with various combinations of the objective functions.
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