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We consider a multi-agent scheduling problem such that each agent tries to maximize the weighted number of just-in-time jobs. Two objectives are considered: the first is to find the optimal solution for one agent with constraints on the other agents' weight functions, and the second is to find the largest set of efficient schedules of which corresponding objective vectors are different for the case with identical weights. We show that when the number of agents is fixed, the single machine case with the first objective is NP-hard in the ordinary sense, and present the polynomial-time algorithm for the two-machine flow shop case with the second objective and identical weights.