In this paper, the problem of minimizing the total completion time on a single machine with the presence of release dates is studied. We introduce two different approaches leading to very large-scale neighborhoods in which the best improving neighbor can be determined in polynomial time. Furthermore, computational results are presented to get insight in the performance of the developed neighborhoods.
Very large-scale neighborhoods Local search Single machine
This is a preview of subscription content, log in to check access.
The authors are grateful to the anonymous referees for their helpful comments on an earlier draft of the paper.
Tobias Brueggemann is supported by the Netherlands Organization for Scientific Research (NWO) grant 613.000.225 (Local Search with Exponential Neighborhoods). Johann L. Hurink is supported by BSIK grant 03018 (BRICKS: Basic Research in Informatics for Creating the Knowledge Society).
Ahmadi RH, Bagchi U (1990) Lower bounds for single-machine scheduling problems. Nav Res Logist 37(6):967–979Google Scholar
Ahuja RK, Özlem E, Orlin JB, Punnen AP (2002) A survey of very large-scale neighborhood search techniques. Discrete Appl Math 123:75–102CrossRefGoogle Scholar
Baker KR (1974) Introduction to sequencing and scheduling. Wiley, New YorkGoogle Scholar
Chu C (1992) A branch-and-bound algorithm to minimize total flow time with unequal release dates. Nav Res Logist 39:859–875Google Scholar
Congram RK, Potts CN, van de Velde SL (2002) An iterated dynasearch algorithm for the single-machine total weighted tardiness scheduling problem. INFORMS J Comput 14(1):52–67CrossRefGoogle Scholar
Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 5:287–326CrossRefGoogle Scholar
Hurink J (1999) An exponential neighborhood for a one machine batching problem. OR Spectrum 21:461–476CrossRefGoogle Scholar
Lenstra JK, Rinnooy Kan AHG, Brucker P (1977) Complexity of machine scheduling problems. Ann Discrete Math 1:343–362Google Scholar
Potts CN, van de Velde SL (1995) Dynasearch-iterative local improvement by dynamic programming. Part 1. The traveling salesman problem. Technical Report, University of Twente, The NetherlandsGoogle Scholar
Rinnooy Kan AHG (1976) Machine scheduling problems: classification, complexity and computations. Martinus Nijhoff, The Hague, pp 79–88Google Scholar
Smith WE (1956) Various optimizers for single-stage production. Nav Res Logist Q 3:59–66CrossRefGoogle Scholar
Yanai S, Fujie T (2004) On a dominance test for the single machine scheduling problem with release dates to minimize total flow time. J Oper Res Soc Jpn 47(2):96–111Google Scholar