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Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs. (English) Zbl 1100.68007
Summary: We consider the feasibility model of multi-agent scheduling on a single machine, where each agent’s objective function is to minimize the total weighted number of tardy jobs. We show that the problem is strongly NP-complete in general. When the number of agents is fixed, we first show that the problem can be solved in pseudo-polynomial time for integral weights, and can be solved in polynomial time for unit weights; then we present a fully polynomial-time approximation scheme for the problem.

##### MSC:
 68M20 Performance evaluation of computer systems; queueing; scheduling 90B35 Scheduling theory, deterministic
##### Keywords:
scheduling; multi-agent deterministic sequencing
Full Text:
##### References:
 [1] Agnetis, A.; Mirchandani, P. B.; Pacciarelli, D.; Pacifici, A.: Scheduling problems with two competing agents. Oper. res. 52, 229-242 (2004) · Zbl 1165.90446 [2] Baker, K. R.; Smith, J. C.: A multiple-criterion model for machine scheduling. J. scheduling 6, 7-16 (2003) · Zbl 1154.90406 [3] Curiel, I.; Pederzoli, G.; Tijs, S.: Sequencing games. European J. Oper. res. 40, 344-351 (1989) · Zbl 0674.90107 [4] Garey, M. R.; Johnson, D. S.: Computers and intractability: A guide to the theory of NP-completeness. (1979) · Zbl 0411.68039 [5] Hamers, H.; Borm, P.; Tijs, S.: On games corresponding to sequencing situations with ready times. Math. programming 70, 1-13 (1995) · Zbl 0844.90120 [6] K. Kim, B.C. Paulson, C.J. Petrie, V.R. Lesser, Compensatory negotiation for agent-based project schedule coordination, CIFE Working Paper No. 55, Stanford University, Stanford, CA, 1999. [7] Lawler, E. L.; Moore, J. M.: A functional equation and its application to resource allocation and sequencing problems. Management sci. 16, 77-84 (1969) · Zbl 0184.23303 [8] Moore, J. M.: An n job, one machine sequencing algorithm for minimizing the number of late jobs. Management sci. 15, 102-109 (1968) · Zbl 0164.20002 [9] Scharbrodt, M.; Steger, A.; Weisser, H.: Approximability of scheduling with fixed jobs. J. scheduling 2, 267-284 (1999) · Zbl 0953.90025 [10] D. Schultz, S.-H. Oh, C.F. Grecas, M. Albani, J. Sanchez, C. Arbib, V. Arvia, M. Servilio, F. Del Sorbo, A. Giralda, G. Lombardi, A QoS concept for packet oriented S-UMTS services, In: Proc. of the 1st Mobile Summit 2002, Thessaloniki, Greece. [11] Yuan, J. J.; Lin, Y. X.: Single machine preemptive scheduling with fixed jobs to minimize tardiness related criteria. European J. Oper. res. 164, 851-858 (2005) · Zbl 1057.90024