Aggregation bounds in stochastic linear programming

R.W. Ashford, “A stochastic programming algorithm for production planning,” Technical Report, Scicon Computer Services Limited (Milton Keynes, 1982).

E.M.L. Beale, “On minimizing a convex function subject to linear inequalities”,J. Royal Stat. Soc. 17 (1955) 173–184.

E.M.L. Beale, J.J.H. Forrest, and C. Taylor, “Multi-time period stochastic programming”, in: M.A.H. Dempster, ed,Stochastic programming (Academic Press, New York, 1980) pp. 387–402.

J.R. Birge, “Decomposition and partitioning methods for multi-stage stochastic linear programs”, Technical Report 82-6, Department of Industrial and Operations Engineering, The University of Michigan, (Ann Arbor, MI, 1982).

J.R. Birge and R.J.-B. Wets, “Approximations and error bounds in stochastic programming”, in: Y.L. Tong, ed.,Proceedings of the symposium on inequalities in statistics and probability, to appear.

G.B. Dantzig, “Linear programming under uncertainty”,Management Science 1 (1955) 197–206.

M.A.H. Dempster, “Introduction to stochastic programming”, in: M.A.H. Dempster, ed.,Stochastic programming (Academic Press, New York, 1980) pp. 3–59.

M.J. Eisner and P. Olsen, “Duality for stochastic programming, interpreted as L.P. in Lp-space”,SIAM Journal Applied Math. 28 (1975) 779–792.

R.C. Grinold, “Time horizons in energy planning models”, in: W.T. Ziemba and S.L. Schwartz, eds.,Energy policy modeling, vol. II (Martinus Nijhoff, Boston, 1980) pp. 216–237.

C. Huang, W. Ziemba, and A. Ben-Tal, “Bounds on the expectation of a convex function of a random variable with applications to stochastic programming”,Operations Research 25 (1974) 315–325.

P. Kall, “Approximations to stochastic programming with complete fixed recourse”,Num. Math. 22 (1974) 333–339.

A. Madansky, “Inequalities for stochastic linear programming problems”,Management Science 6 (1960) 197–204.

R. Mendelssohn, “Improved bounds for aggregated linear programs,”Operations Research 28 (1980) 1450–1453.

M. Queyranne and E.P.C. Kao, “Aggregation in a two-stage stochastic program for manpower planning in the service sector”, Technical Report, University of Houston (Houston, TX, 1981).

R.T. Rockafellar and R.J.-B. Wets, “Nonanticipativity andL 1-martingales in stochastic optimization problem”,Mathematical Programming Study 6 (1976) 170–187.

R.J.-B. Wets, “Stochastic programming: solution techniques and approximation schemes”, in: A. Bachem, M. Grötschel and B. Korte, eds.,Mathematical programming: State-of-the-art 1982 (Springer-Verlag, Berlin, 1983) pp. 506–603.

P. Zipkin, “Bounds on the effect of aggregating variables in linear programming”,Operations Research 28 (1980) 403–418.

P. Zipkin, “Bounds for row-aggregation in linear programming”,Operations Research 28 (1980) 903–916.