Abstract
In this paper, we consider single machine bi-criteria scheduling problems where jobs are from multiple job classes and there are customer orders such that each customer order consists of at least one job from each of the job classes. A set-up time is needed whenever the machine is changed over from a job in one class to a job in another class. One objective is to minimize the makespan which is equivalent to minimizing the total set-up time. The other objective is to minimize total carrying costs of the customer orders. The carrying cost of a customer order is measured by the length of the time interval between the completion times of the first job and the last job in the customer order. We propose constructive polynomial time algorithms for the two hierarchical scheduling problems with these two objectives, i.e. the two scheduling problems in which one objective is to be optimized while holding the other objective fixed at its optimal value.
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References
B.H. Ahn and J.H. Hyun, Single facility multi-class job scheduling, Computers and Operations Research 17(1990)265–272.
D.D. Bedworth and J.E. Bailey, Integrated Production Control Systems: Management, Analysis, Design, 2nd ed., Wiley, 1987.
R.E. Burkard, V.G. Deineko, R. van Dal, J.A.A. van der Veen and G.J. Woeginger, Well-solvable special cases of the TSP: A survey, Nijenrode Research Paper Series No. 04, 1996.
V. Chvátal, Hamiltonian cycles, in: The Traveling Salesman Problem, E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys, eds., Wiley-Interscience, 1985, pp. 403–429.
V. Chvátal and P. Erdös, A note on Hamiltonian circuits, Discrete Mathematics 2(1972)111–113.
P. Dileepan and T. Sen, Bicriterion static scheduling research for a single machine, Omega 16 (1988)53–59.
T.D. Fry, R.D. Armstrong and H. Lewis, A framework for single machine multiple objective sequencing research, Omega 17(1989)595–607.
P.C. Gilmore, E.L. Lawler and D.B. Shmoys, Well-solved special cases, in: The Traveling Salesman Problem, E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys, eds., Wiley-Interscience, 1985, pp. 87–143.
J.N.D. Gupta, Optimal schedules for single facility with two job classes, Computers and Operations Research 11(1984)409–413.
J.N.D. Gupta, Single facility scheduling with multiple job classes, European Journal of Operational Research 8(1988)42–45.
C.-Y. Lee and G.L. Vairaktarakis, Complexity of single machine hierarchical scheduling: A survey, in: Complexity in Numerical Optimization, P.M. Pardalos, ed., World Scientific, NJ, 1993, pp. 269–298.
C.J. Liao, Tradeoff between setup times and carrying costs for finished items, Computers and Operations Research 20(1993)697–705.
A.J. Mason and E.J. Anderson, Minimizing flow times on a single machine with job classes and setup times, Naval Research Logistics 38(1991)333–350.
C.L. Monma and C.N. Potts, On the complexity of scheduling with batch setup times, Operations Research 37(1989)798–804.
C.N. Potts, Scheduling two job classes on a single machine, Computers and Operations Research 18(1991)411–415.
C.N. Potts and L.N. van Wassenhove, Integrating scheduling with batching and lot-sizing: A review of algorithms and complexity, Journal of the Operational Research Society 43(1992)395–406.
H.N. Psaraftis, A dynamic programming approach for sequencing groups of identical jobs, Operations Research 28(1980)1347–1359.
J.A.A. van der Veen and S. Zhang, Low-complexity algorithms for sequencing jobs with a fixed number of job-classes, Nijenrode Working Paper Series 1, 1995.
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Gupta, J.N., Ho, J.C. & van der Veen, J.A. Single machine hierarchical scheduling with customer orders and multiple job classes. Annals of Operations Research 70, 127–143 (1997). https://doi.org/10.1023/A:1018913902852
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DOI: https://doi.org/10.1023/A:1018913902852