Surrogate duality relaxation for job shop scheduling

Surrogate duality bounds for the job shop scheduling problem are obtained by replacing certain constraints by their weighted sum and strengthening the aggregate constraint by iterating over all possible weights. The constraints successively considered for this purpose are the capacity constraints on the machines and the precedence constraints determining the machine order for each job. The resulting relaxations are investigated from a theoretical and a computational point of view.

[1]  Marvin Minsky,et al.  Perceptrons: An Introduction to Computational Geometry , 1969 .

[2]  Michael Florian,et al.  An Implicit Enumeration Algorithm for the Machine Sequencing Problem , 1971 .

[3]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[4]  G. Nemhauser,et al.  Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms , 1977 .

[5]  I. Adiri,et al.  An Efficient Optimal Algorithm for the Two-Machines Unit-Time Jobshop Schedule-Length Problem , 1982, Math. Oper. Res..

[6]  N. Z. Shor The rate of convergence of the generalized gradient descent method , 1968 .

[7]  George L. Nemhauser,et al.  Note--On "Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms" , 1979 .

[8]  Jan Karel Lenstra,et al.  Complexity of machine scheduling problems , 1975 .

[9]  Wayne E. Smith Various optimizers for single‐stage production , 1956 .

[10]  W. D. Northup,et al.  USING DUALITY TO SOLVE DISCRETE OPTIMIZATION PROBLEMS: THEORY AND COMPUTATIONAL EXPERIENCE* , 1975 .

[11]  R. E. Marsten,et al.  The Boxstep Method for Large-Scale Optimization , 2011, Oper. Res..

[12]  Martin Dyer Calculating surrogate constraints , 1980, Math. Program..

[13]  B. J. Lageweg,et al.  Minimizing maximum lateness on one machine : Computational experience and some applications , 1976 .

[14]  Graham McMahon,et al.  On Scheduling with Ready Times and Due Dates to Minimize Maximum Lateness , 1975, Oper. Res..

[15]  John M. Charlton,et al.  A Method of Solution for General Machine-Scheduling Problems , 1970, Oper. Res..

[16]  J. K. Lenstra,et al.  Computational complexity of discrete optimization problems , 1977 .

[17]  J. Lenstra,et al.  Job-Shop Scheduling by Implicit Enumeration , 1977 .

[18]  Richard M. Soland,et al.  A branch and bound algorithm for the generalized assignment problem , 1975, Math. Program..

[19]  Alan S. Manne,et al.  On the Job-Shop Scheduling Problem , 1960 .

[20]  Linus Schrage,et al.  Solving Resource-Constrained Network Problems by Implicit Enumeration - Nonpreemptive Case , 1970, Oper. Res..

[21]  Fred Glover,et al.  Surrogate Constraint Duality in Mathematical Programming , 1975, Oper. Res..

[22]  Richard M. Karp,et al.  The traveling-salesman problem and minimum spanning trees: Part II , 1971, Math. Program..

[23]  James R. Jackson,et al.  An extension of Johnson's results on job IDT scheduling , 1956 .

[24]  Richard M. Karp,et al.  The Traveling-Salesman Problem and Minimum Spanning Trees , 1970, Oper. Res..

[25]  Eugene L. Lawler,et al.  Preemptive scheduling of uniform machines subject to release dates : (preprint) , 1979 .

[26]  Teofilo F. Gonzalez,et al.  Flowshop and Jobshop Schedules: Complexity and Approximation , 1978, Oper. Res..

[27]  Marshall L. Fisher,et al.  Optimal Solution of Scheduling Problems Using Lagrange Multipliers: Part I , 1973, Oper. Res..

[28]  Marshall L. Fisher,et al.  A dual algorithm for the one-machine scheduling problem , 1976, Math. Program..

[29]  M. Florian,et al.  On sequencing with earliest starts and due dates with application to computing bounds for the (n/m/G/Fmax) problem , 1973 .

[30]  Ravi Sethi,et al.  The Complexity of Flowshop and Jobshop Scheduling , 1976, Math. Oper. Res..