Approximation in Stochastic integer programming

The study of stochastic linear programming problems has resulted in an abundancy of literature, indicating on one hand the proceeds of the investigations and on the other the complexity of the problem type. In stochastic integer programming this complexity is multiplied by the inherent complexity of the general integer programming problem, established in the theory of computational complexity. This, together with the fact that very few researchers have thorough knowledge of both stochastic and integer programming, is the cause of the poor state of the art of the field.

[1]  Eitan Zemel,et al.  Probabilistic analysis of geometric location problems , 1984, Ann. Oper. Res..

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

[3]  Hiroaki Ishii,et al.  Stochastic spanning tree problem , 1981, Discret. Appl. Math..

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

[5]  R. Carraway,et al.  An algorithm for maximizing target achievement in the stochastic knapsack problem with normal returns , 1993 .

[6]  Gilbert Laporte,et al.  A Priori Optimization of the Probabilistic Traveling Salesman Problem , 1994, Oper. Res..

[7]  J. Steele Subadditive Euclidean Functionals and Nonlinear Growth in Geometric Probability , 1981 .

[8]  Hiroaki Ishii,et al.  Stochastic bottleneck spanning tree problem , 1983, Networks.

[9]  Gabriel R. Bitran,et al.  Hierarchical production planning , 1989 .

[10]  Alexander H. G. Rinnooy Kan,et al.  Bounds and Heuristics for Capacitated Routing Problems , 1985, Math. Oper. Res..

[11]  Giovanni Andreatta,et al.  Stochastic shortest paths with recourse , 1988, Networks.

[12]  Patrick Jaillet,et al.  A Priori Optimization , 1990, Oper. Res..

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

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

[15]  K. Jörnsten Sequencing offshore oil and gas fields under uncertainty , 1992 .

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

[17]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .