论文信息 - Stochastic integer programming by dynamic programming

Stochastic integer programming by dynamic programming

Stochastic integer programming is a suitable tool for modeling hierarchical decision situations with combinatorial features. In continuation of our work on the design and analysis of heuristics for such problems, we now try to find optimal solutions. Dynamic programming techniques can be used to exploit the structure of two-stage scheduling, bin packing and multiknapsack problems. Numerical results for small instances of these problems are presented.

[1] Jan Karel Lenstra,et al. A framework for the probabilistic analysis of hierarchical planning systems , 1984, Ann. Oper. Res..

[2] R. Bellman. Dynamic programming. , 1957, Science.

[3] Charles E. Blair,et al. The value function of an integer program , 1982, Math. Program..

[4] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[5] B. J. Lageweg,et al. Analytical Evaluation of Hierarchical Planning Systems , 1981, Oper. Res..

[6] Alexander H. G. Rinnooy Kan,et al. Hierarchical vehicle routing problems , 1984, Networks.

[7] B. J. Lageweg,et al. Analysis of Heuristics for Stochastic Programming: Results for Hierarchical Scheduling Problems , 1983, Math. Oper. Res..

[8] J. B. G. Frenk,et al. A hierarchical scheduling problem with a well-solvable second stage , 1984, Ann. Oper. Res..

[9] E.L. Lawler,et al. Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[10] Leen Stougie. Design and analysis of algorithms for stochastic integer programming , 1987 .

[11] M. Held,et al. Assembly-Line Balancing---Dynamic Programming with Precedence Constraints , 1963 .

[12] Roger J.-B. Wets,et al. Stochastic Programming: Solution Techniques and Approximation Schemes , 1982, ISMP.