Abstract
We address the bicriteria problem of minimizing the number of tardy jobs and maximum earliness on a single machine where machine idle time is allowed. We show that the problem of minimizing the number of tardy jobs while maximum earliness is kept at its minimum value of zero is polynomially solvable. We present polynomial time algorithms for the maximum earliness problem subject to no tardy jobs and the maximum earliness problem for a given set of tardy jobs. Finally, we discuss the use of the latter algorithm in generating all efficient schedules.
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References
Lee CY and Vairaktarakis GL (1993). Complexity of single machine hierarchical scheduling: a survey. Complex Numer Optim 19: 269–298.
Hoogeveen JA (1992). Single machine bicriteria scheduling. PhD thesis. CWI, Amsterdam.
Garey MR, Tarjan RE and Wilfong GT (1988). One processor scheduling with symmetric earliness and tardiness penalties. Math Opl Res 13: 330–348.
Hoogeveen JA and van de Velde S (1997). A single machine scheduling model for coordinating logistics activities in simple supply chain. Management Report No 30(13), Rotterdam School of Management, Erasmus University.
Koksalan M, Azizoglu M and Kondakci S (1998). Minimizing flow time and maximum earliness on a single machine. IIE Trans 30: 192–200.
Azizoglu M, Kondakci S and Koksalan M (1997). Single machine scheduling with two criteria: maximum earliness and number tardy. Technical Report No: 97–02. Department of Industrial Engineering, METU, Ankara.
Moore JM (1968). An n job, one machine sequencing algorithm for minimizing the number of late jobs. Mngt Sci 15: 102–109.
Graham RL, Lawler EL, Lenstra JK and Rinnooy Kan AHG (1979). Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 5: 287–326.
Hall N, Posner M and Potts C (1998). Scheduling with finite capacity output buffers. Opns Res 46: 584–597.
Hoogeveen JA (1996). Minimizing maximum promptness and maximum lateness on a single machine. Math Opns Res 21: 100–114.
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Azizoglu, M., Koksalan, M. & Koksalan, S. Scheduling to minimize maximum earliness and number of tardy jobs where machine idle time is allowed. J Oper Res Soc 54, 661–664 (2003). https://doi.org/10.1057/palgrave.jors.2601478
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DOI: https://doi.org/10.1057/palgrave.jors.2601478