An Algorithm for Project (Job) Sequencing with Resource Constraints

This paper treats the problem of project (or machine) scheduling with resource constraints to achieve minimum total duration time as a disjunctive graph. The prospective advantage of this approach is the elimination of the need to consider individual time periods over the program horizon; a feasibility check determines whether the resource constraints can be met by any particular network representation of the project. The paper gives an algorithm that uses partial enumeration for what is essentially a mixed integer program. The algorithm employs a maximum-flow computation as a check for feasibility with respect to available resources.

[1]  S. M. Johnson,et al.  Optimal two- and three-stage production schedules with setup times included , 1954 .

[2]  Z. A. Lomnicki.  A “Branch-and-Bound” Algorithm for the Exact Solution of the Three-Machine Scheduling Problem , 1965 .

[3]  G. B. McMahon,et al.  Flow-Shop Scheduling with the Branch-and-Bound Method , 1967, Oper. Res..

[4]  Kurt Spielberg,et al.  Direct Search Algorithms for Zero-One and Mixed-Integer Programming , 1967, Oper. Res..

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

[6]  J. F. Benders.  Partitioning procedures for solving mixed-variables programming problems , 1962 .

[7]  James E. Kelley,et al.  Critical-Path Planning and Scheduling: Mathematical Basis , 1961 .

[8]  E. Ignall,et al.  Application of the Branch and Bound Technique to Some Flow-Shop Scheduling Problems , 1965 .

[9]  Harvey M. Wagner,et al.  An integer linear‐programming model for machine scheduling , 1959 .

[10]  Harold H. Greenberg,et al.  A Branch-Bound Solution to the General Scheduling Problem , 1968, Oper. Res..

[11]  J.-F. Raimond.  Minimaximal paths in disjunctive graphs by direct search , 1969 .

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

[13]  D. R. Fulkerson.  A Network Flow Computation for Project Cost Curves , 1961 .

[14]  E. H. Bowman.  THE SCHEDULE-SEQUENCING PROBLEM* , 1959 .

[15]  D. S. Palmer.  Sequencing Jobs Through a Multi-Stage Process in the Minimum Total Time—A Quick Method of Obtaining a Near Optimum , 1965 .

[16]  Kurt Spielberg,et al.  Algorithms for the Simple Plant-Location Problem with Some Side Conditions , 1969, Oper. Res..

[17]  Monique Guignard-Spielberg,et al.  Search techniques with adaptive features for certain integer and mixed integer programming problems , 1968, IFIP Congress.