Abstract
Given a digraphG=(V, A), a weight for each node inV and a weight for each arc inA, the Sequential Ordering Problem (SOP) consists of finding a Hamiltonian path, such that a release date and a deadline for each node and precedence relationships among nodes are satisfied and a linear function is minimized. In our case, the objective function is the maximum cumulated potential of the nodes (also, the so-called makespan). The SOP has a broad range of applications, mainly in production planning and manufacturing systems. Nodes represent jobs (to be processed on a single machine), arcs represent sequencing of the jobs, the nodes' weights are the processing time for the jobs, the arcs' weights are the setup times for two consecutive jobs, and the cumulated potential of a node is the completion time of a job. The goal is to produce a feasible scheduling of the jobs so that the makespan is minimized. We present an approximate algorithm for improving feasible solutions to the SOP. The algorithm is based on two local searchκ-opt procedures to reduce the makespan while satisfying the time window (i.e. release date and deadline) and precedence constraints, forκ=3 and 4. The complexity of the algorithm isO(bn 4), wheren denotes the number of nodes andb is the average number of precedences per node. Extensive computational experience and implementation aspects are reported for very large-scale instances up to 3000 nodes and 9000 precedences. Experience with real-life cases is also reported.
Similar content being viewed by others
References
B.H. Ahn and J.H. Hyun, Single facility multiclass job scheduling, Comp. Oper. Res. 17(1990)265–272.
N. Ascheuer, L.F. Escudero, M. Groetschel and M. Stoer, A cutting plane approach to the sequential ordering problem, SIAM J., to be published.
K.R. Baker,Introduction to Sequencing and Scheduling (Wiley, New York, 1974).
K.R. Baker and G.D. Scudder, Sequencing and earliness and tardiness penalties: A review, Oper. Res. 38(1990)22–36.
E. Balas and W.R. Pulleyblank, Precedence constrained routing, Seminar given at the University of Waterloo, Ontario (1989), as credited by M.T.F. Timlin, in: Precedence constrained routing and helicopter scheduling, Ms. Thesis, University of Waterloo (1989).
J. Bruno and P. Downey, Complexity of task sequencing with deadlines, setup times and changeover costs, SIAM J. Comput. 7(1978)393–404.
R.W. Convay, W.L. Maxwell and L.W. Miller,Theory of Scheduling (Addison-Wesley, Reading, MA, 1967).
L.F. Escudero, An inexact algorithm for the sequential ordering problem, Eur. J. Oper. Res. 37(1988)236–253.
L.F. Escudero, M. Guignard, K. Malik and A. Sciomachen, On Lagrangian-based lower bounds for the sequential ordering problem with time windows and precedence relationships,14th Mathematical Programming Symp., Amsterdam (1991).
L.F. Escudero and A. Sciomachen, An approximate algorithm for the sequential ordering problem with time windows and precedence relationships, RC-16820, IBM Research, T.J. Watson Research Center, Yorktown Heights, NY (1990).
L.F. Escudero and A. Sciomachen, AnO(n 3) implementation of an approximate algorithm for finding a feasible solution for the sequential ordering problem, Autofaber Research Report R.R. 8/90 (1990).
L.F. Escudero and A. Sciomachen, Job sequencing ordering problem on a card assembly line, in:Optimization in Industrial Environments, ed. T.A. Ciriani and R.C. Leachman (Wiley, London, 1992).
S. French,Sequencing and Scheduling. An Introduction to the Mathematics of the Job Shop (Wiley, New York, 1982).
P.C. Kanellakis and C.C. Papadimitriou, Local search for the asymmetric travelling salesman problem, Oper. Res. 28(1980)1086–1098.
J.K. Lenstra and A.H.G. Rinnooy Kan, Complexity scheduling under precedence constraints, Oper. Res. 26(1978)22–35.
E.L. Lawler, J.K. Lenstra, A.H. Rinnooy Kan and D.B. Shmoys, Sequencing and scheduling algorithms and complexity, in:Logistics of Production and Inventory, ed. S.C. Graves, A.H. Rinnooy Kan and P. Zipkin (North-Holland, Amsterdam, 1990).
H.N. Psaraftis, A dynamic programming approach for sequencing groups of identical jobs, Oper. Res. 28(1980)1337–1352.
M. Queyranne and Y. Wang, Single machine scheduling polyhedra with precedence constraints, Math. Oper. Res. 16(1991)1–20.
D.L. Woodruff and M.L. Spearman, Sequencing and batching for two classes of jobs with deadlines and setup times, Prod. Oper. Manag. 1(1992)87–102.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Escudero, L.F., Sciomachen, A. Local search procedures for improving feasible solutions to the sequential ordering problem. Ann Oper Res 43, 397–416 (1993). https://doi.org/10.1007/BF02024937
Issue Date:
DOI: https://doi.org/10.1007/BF02024937