Stochastic resource-constrained project scheduling

PREFACE After having received my diploma from the Technische Universität Berlin in 1996, Rolf Möhring, the supervisor of my diploma thesis, offered me a research position in his group. At that time I was employed at a Berlin software company the head of which, Gert Scheschonk, strongly encouraged me to accept the offer. I accepted and in 1997 I began to work within a research initiative funded by the Deutsche Forschungsgemeinschaft DFG. The members engaged in this initiative belong to five research groups in Germany which are located at universities in Bonn, Karlsruhe, Kiel, Osnabrück, and Berlin. In Berlin, the scope of the project was to develop algorithms and theory for stochastic resource-constrained project scheduling problems which is the main topic of this thesis. I am thankful to Rolf Möhring for his support, his encouragement, and the supervision of my thesis. In particular, I greatly benefited from his guidance during my work on AND/OR precedence constraints and scheduling policies. My special thanks go to my colleagues Martin Skutella and Marc Uetz. Martin greatly helped to establish, generalize, and improve many of my original considerations on AND/OR precedence constraints which finally led to the results presented in Chapters 2 and 3. The continuous fruitful discussion with Marc led to new insights in the field of deterministic resource-constrained project scheduling. The results presented in Chapter 4 on different representations of resource constraints are one example of this productive collaboration. I am also very grateful to my colleagues Andreas Schulz and Matthias Müller-Hannemann. I gained a lot from Andreas' expertise and his co-authorship in papers on deterministic project scheduling (which are not part of this thesis). My former roommate Matthias was always willing to interrupt his work in order to discuss the questions I raised. I would also like to mention the fruitful collaboration with the other members of the DFG research initiative on resource-constrained project scheduling. In particular , I thank Peter Brucker for the willingness to serve as a member of my thesis committee. Some parts of this thesis rely on software implementations that would not have reached the current quality without the support of Ewgenij Gawrilow. I thank him for introducing me to the concept of generic programming; he had a great share in establishing the basis of our programming environment, a collection of fundamental scheduling algorithms and data structures. for their careful proofreading of different parts of the manuscript. …

[1]  R. E. Cooke-Yarborough Critical Path Planning and Scheduling: An Introduction and Example , 1964 .

[2]  W. Trotter,et al.  Combinatorics and Partially Ordered Sets: Dimension Theory , 1992 .

[3]  Rolf H. Möhring,et al.  Resource-constrained project scheduling: Notation, classification, models, and methods , 1999, Eur. J. Oper. Res..

[4]  Giorgio Ausiello,et al.  Graph Algorithms for Functional Dependency Manipulation , 1983, JACM.

[5]  Vidyadhar G. Kulkarni,et al.  A classified bibliography of research on stochastic PERT networks: 1966-1987 , 1989 .

[6]  V. Tanaev,et al.  Stability Radius of an Optimal Schedule: A Survey and Recent Developments , 1998 .

[7]  M. Dessouky,et al.  Solving the Project Time/Cost Tradeoff Problem Using the Minimal Cut Concept , 1977 .

[8]  Rolf H. Möhring,et al.  Scheduling under Uncertainty: Bounding the Makespan Distribution , 2001, Computational Discrete Mathematics.

[9]  Van Slyke,et al.  MONTE CARLO METHODS AND THE PERT PROBLEM , 1963 .

[10]  P. Hammer,et al.  Aggregation of inequalities in integer programming. , 1975 .

[11]  Yechezkel Zalcstein,et al.  A Graph-Theoretic Characterization of the PV_chunk Class of Synchronizing Primitives , 1977, SIAM J. Comput..

[12]  Paul Bratley,et al.  A guide to simulation (2nd ed.) , 1986 .

[13]  Robert L. Armacost,et al.  The role of the nonanticipativity constraint in commercial software for stochastic project scheduling , 1996 .

[14]  Laureano F. Escudero,et al.  Production planning via scenario modelling , 1993, Ann. Oper. Res..

[15]  M. F.,et al.  Bibliography , 1985, Experimental Gerontology.

[16]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[17]  Rainer Kolisch,et al.  PSPLIB - a project scheduling problem library , 1996 .

[18]  Uwe Schwiegelshohn,et al.  Dynamic Min-Max Problems , 1999, Discret. Event Dyn. Syst..

[19]  Alexander Shapiro,et al.  The Sample Average Approximation Method for Stochastic Discrete Optimization , 2002, SIAM J. Optim..

[20]  Peter Brucker,et al.  A branch and bound algorithm for the resource-constrained project scheduling problem , 1998, Eur. J. Oper. Res..

[21]  Giorgio Ausiello,et al.  Structure Preserving Reductions among Convex Optimization Problems , 1980, J. Comput. Syst. Sci..

[22]  Egon Balas,et al.  PROJECT SCHEDULING WITH RESOURCE CONSTRAINTS. , 1968 .

[23]  J. M. Tamarit,et al.  Project scheduling with resource constraints: A branch and bound approach , 1987 .

[24]  B. Arnold Bounds on the expected maximum , 1988 .

[25]  George B. Kleindorfer,et al.  Bounding Distributions for a Stochastic Acyclic Network , 1971, Oper. Res..

[26]  Martin Skutella,et al.  Scheduling precedence-constrained jobs with stochastic processing times on parallel machines , 2001, SODA '01.

[27]  Ran Raz,et al.  A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP , 1997, STOC '97.

[28]  Walter Ludwig,et al.  A Subexponential Randomized Algorithm for the Simple Stochastic Game Problem , 1995, Inf. Comput..

[29]  Jane W.-S. Liu,et al.  Scheduling tasks with AND/OR precedence constraints , 1990, Proceedings of the Second IEEE Symposium on Parallel and Distributed Processing 1990.

[30]  Rolf H. Möhring,et al.  Solving Project Scheduling Problems by Minimum Cut Computations , 2002, Manag. Sci..

[31]  J. H. Patterson,et al.  An Algorithm for a general class of precedence and resource constrained scheduling problems , 1989 .

[32]  Donald E. Knuth,et al.  A Generalization of Dijkstra's Algorithm , 1977, Inf. Process. Lett..

[33]  Arno Sprecher,et al.  Scheduling Resource-Constrained Projects Competitively at Modest Memory Requirements , 2000 .

[34]  R. Möhring Algorithmic Aspects of Comparability Graphs and Interval Graphs , 1985 .

[35]  Rainer Kolisch Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation , 1994 .

[36]  Giorgio Ausiello,et al.  Minimal Representation of Directed Hypergraphs , 1986, SIAM J. Comput..

[37]  Rolf H. Möhring,et al.  Forcing relations for AND/OR precedence constraints , 2000, SODA '00.

[38]  Armin Scholl,et al.  Computing lower bounds by destructive improvement: An application to resource-constrained project scheduling , 1999, Eur. J. Oper. Res..

[39]  Robert J. Vanderbei,et al.  Robust Optimization of Large-Scale Systems , 1995, Oper. Res..

[40]  Rolf H. Möhring,et al.  Scheduling under uncertainty: Optimizing against a randomizing adversary , 2000, APPROX.

[41]  Roger J.-B. Wets,et al.  The aggregation principle in scenario analysis stochastic optimization , 1989 .

[42]  Jean-Marie Proth,et al.  The PERT Problem with Alternatives: Modelisation and Optimisation , 1999 .

[43]  Jan Węglarz,et al.  Project scheduling : recent models, algorithms, and applications , 1999 .

[44]  Greg N. Frederickson,et al.  Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan , 1981, JACM.

[45]  U. Dorndorf,et al.  A Time-Oriented Branch-and-Bound Algorithm for Resource-Constrained Project Scheduling with Generalised Precedence Constraints , 2000 .

[46]  Rajeev Motwani,et al.  Complexity Measures for Assembly Sequences , 1999, Int. J. Comput. Geom. Appl..

[47]  Thomas Kämpke Optimalitätsaussagen für spezielle stochastische Schedulingprobleme , 1985 .

[48]  Luc Devroye Inequalities for the Completion Times of Stochastic PERT Networks , 1979, Math. Oper. Res..

[49]  Marcin Jurdzinski,et al.  A Discrete Strategy Improvement Algorithm for Solving Parity Games , 2000, CAV.

[50]  A. Ehrenfeucht,et al.  Positional strategies for mean payoff games , 1979 .

[51]  E. W. Davis,et al.  Multiple Resource–Constrained Scheduling Using Branch and Bound , 1978 .

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

[53]  Rolf H. Möhring,et al.  Introduction to Stochastic Scheduling Problems , 1985 .

[54]  Uriel Feige,et al.  Zero Knowledge and the Chromatic Number , 1998, J. Comput. Syst. Sci..

[55]  Gideon Weiss,et al.  Stochastic scheduling problems II-set strategies- , 1985, Z. Oper. Research.

[56]  Douglas D. Gemmill,et al.  Using tabu search to schedule activities of stochastic resource-constrained projects , 1998, Eur. J. Oper. Res..

[57]  Mark M. Klein,et al.  Scheduling project networks , 1967, CACM.

[58]  R. Tyrrell Rockafellar,et al.  Scenarios and Policy Aggregation in Optimization Under Uncertainty , 1991, Math. Oper. Res..

[59]  Franz Josef Radermacher,et al.  Preselective strategies for the optimization of stochastic project networks under resource constraints , 1983, Networks.

[60]  Eugene Levner,et al.  On Project Scheduling with Alternatives , 2000 .

[61]  R. Kolisch,et al.  Heuristic algorithms for the resource-constrained project scheduling problem: classification and computational analysis , 1999 .

[62]  Giorgio Gallo,et al.  Directed Hypergraphs and Applications , 1993, Discret. Appl. Math..

[63]  R. Möhring Algorithmic graph theory and perfect graphs , 1986 .

[64]  Hannah Bast Dynamic scheduling with incomplete information , 1998, SPAA '98.

[65]  Bajis M. Dodin,et al.  Bounding the Project Completion Time Distribution in PERT Networks , 1985, Oper. Res..

[66]  D. Atkin OR scheduling algorithms. , 2000, Anesthesiology.

[67]  Jerome D. Wiest Some Properties of Schedules for Large Projects with Limited Resources , 1964 .

[68]  Sacramento Quintanilla,et al.  Project Scheduling with Stochastic Activity Interruptions , 1999 .

[69]  Uri Zwick,et al.  The Complexity of Mean Payoff Games , 1995, COCOON.

[70]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[71]  Ramón Alvarez-Valdés Olaguíbel,et al.  The project scheduling polyhedron: Dimension, facets and lifting theorems , 1993 .

[72]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

[73]  J. Carlier The one-machine sequencing problem , 1982 .

[74]  David L. Dill,et al.  Algorithms for interface timing verification , 1992, Proceedings 1992 IEEE International Conference on Computer Design: VLSI in Computers & Processors.

[75]  Erik Demeulemeester,et al.  New Benchmark Results for the Resource-Constrained Project Scheduling Problem , 1997 .

[76]  Robert L. Armacost,et al.  Understanding Simulation Solutions to Resource Constrained Project Scheduling Problems with Stochastic Task Durations , 1998 .

[77]  Rolf H. Möhring,et al.  Scheduling project networks with resource constraints and time windows , 1988 .

[78]  Franz Josef Radermacher,et al.  Algorithmic approaches to preselective strategies for stochastic scheduling problems , 1983, Networks.

[79]  J. D. Uiiman Principles of database systems , 1982 .

[80]  Eugene Levner,et al.  Multiple-choice project scheduling , 1999 .

[81]  John R. Birge,et al.  Stochastic programming approaches to stochastic scheduling , 1996, J. Glob. Optim..

[82]  Uri Zwick,et al.  The Complexity of Mean Payoff Games on Graphs , 1996, Theor. Comput. Sci..

[83]  Gideon Weiss,et al.  Stochastic scheduling problems I — General strategies , 1984, Z. Oper. Research.

[84]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[85]  Rolf H. Möhring,et al.  Linear preselective policies for stochastic project scheduling , 2000, Math. Methods Oper. Res..

[86]  Sönke Hartmann,et al.  Self-adapting genetic algorithms with an application to project scheduling , 1999 .

[87]  Dimitri Golenko-Ginzburg,et al.  Stochastic network project scheduling with non-consumable limited resources , 1997 .

[88]  James H. Patterson,et al.  A Comparison of Exact Approaches for Solving the Multiple Constrained Resource, Project Scheduling Problem , 1984 .

[89]  William J. Cook,et al.  Combinatorial optimization , 1997 .

[90]  Marcin Jurdziński,et al.  Deciding the Winner in Parity Games is in UP \cap co-Up , 1998, Inf. Process. Lett..

[91]  Claudio Gentile,et al.  Max Horn SAT and the minimum cut problem in directed hypergraphs , 1998, Math. Program..

[92]  Jane N. Hagstrom,et al.  Computational complexity of PERT problems , 1988, Networks.

[93]  J. J. Martin Distribution of the Time Through a Directed, Acyclic Network , 1965 .

[94]  A. Brandstädt,et al.  Graph Classes: A Survey , 1987 .

[95]  Erik Demeulemeester,et al.  A branch-and-bound procedure for the multiple resource-constrained project scheduling problem , 1992 .

[96]  Donald William Gillies,et al.  Algorithms to Schedule Tasks With And/or Precedence Constraints , 1993 .

[97]  M. Yannakakis The Complexity of the Partial Order Dimension Problem , 1982 .

[98]  Paul Bratley,et al.  A guide to simulation , 1983 .

[99]  E. A. Dinic The Fastest Algorithm for the Pert Problem with AND-and OR-Nodes (The New-Product-New-Technology Problem) , 1990, IPCO.

[100]  K. Bouleimen,et al.  A new efficient simulated annealing algorithm for the resource-constrained project scheduling problem and its multiple mode version , 2003, Eur. J. Oper. Res..

[101]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[102]  Martin Bartusch,et al.  Optimierung von Netzplänen mit Anordnungsbeziehungen bei knappen Betriebsmitteln , 1983 .

[103]  Jean H. Gallier,et al.  Linear-Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae , 1984, J. Log. Program..

[104]  D. Malcolm,et al.  Application of a Technique for Research and Development Program Evaluation , 1959 .

[105]  Rolf H. Möhring,et al.  Approximation in stochastic scheduling: the power of LP-based priority policies , 1999, JACM.

[106]  Peter Brucker,et al.  A linear programming and constraint propagation-based lower bound for the RCPSP , 2000, Eur. J. Oper. Res..

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

[108]  E. Balas,et al.  Facets of the Knapsack Polytope From Minimal Covers , 1978 .