This paper studies a hierarchical optimization problem on an unbounded parallel-batching machine, in which two objective functions are maximum lateness induced by two sets of due dates, representing different purposes of two decision-makers. By a hierarchical optimization problem, we mean the problem of optimizing the secondary criterion under the constraint that the primary criterion is optimized. A parallel-batching machine is a machine that can handle several jobs in a batch in which all jobs start and complete respectively at the same time. We present an \(O(n\log P)\)-time algorithm and an \(O(n^3)\)-time algorithm for this hierarchical scheduling problem, where P is the total processing time of all jobs.
Hierarchical optimization Batching machine Double due dates Maximum lateness
Mathematics Subject Classification
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Agnetis A, Mirchani PB, Pacciarelli D, Pacifici A (2004) Scheduling problems with two competing agents. Oper Res 52:229–242CrossRefGoogle Scholar
Baker KR, Smith JC (2003) A multiple-criterion model for machine scheduling. J Sched 6:7–16CrossRefGoogle Scholar
Brucker P, Gladky A, Hoogeveen H, Kovalyov MY, Potts CN, Tautenhahn T, Van De Velde SL (1998) Scheduling a batching machine. J Sched 1:31–54CrossRefGoogle Scholar
Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discret Math 5:287–326CrossRefGoogle Scholar
He C, Lin YX, Yuan JJ (2007) Bicriteria scheduling on a batching machine to minimize maximum lateness and makespan. Theoret Comput Sci 381:234–240CrossRefGoogle Scholar
He C, Lin YX, Yuan JJ (2010) Some improved algorithms on the single machine hierarchical scheduling with total tardiness as the primary criterion. Asia Pacific J Oper Res 27(5):577–585CrossRefGoogle Scholar
He C, Lin YX, Yuan JJ (2010) A note on the single machine scheduling to minimize the number of tardy jobs with deadline. Eur J Oper Res 201:966–970CrossRefGoogle Scholar
Hoogeveen JA (1996) Single-machine scheduling to minimize a function of two or three maximum cost criteria. J Algorithms 21:415–433CrossRefGoogle Scholar