Bounds are given on the number of steps sufficient for convergence of simulation algorithms on domains of nonnegative integer constraint sets.

We study Graver test sets for families of linear multi-stage stochastic integer programs with varying number of scenarios. We show that these test sets can be decomposed into finitely many “building blocks”, independent of the number of scenarios, and we give an effective procedure to compute them. The paper includes an introduction to Nash-Williams’ theory of better-quasi-orderings, which is u...

We consider stochastic programming problems with probabilistic constraints in volving integer valued random variables The concept of p e cient points of a prob ability distribution is used to derive various equivalent problem formulations Next we modify the concept of r concave discrete probability distributions and analyse its relevance for problems under consideration These notions are used t...

We present an algorithm for solving stochastic integer programming problems with recourse, based on a dual decomposition scheme and La-grangian relaxation. The approach can be applied to multi-stage problems with mixed-integer variables in each time stage. Numerical experience is presented for some two-stage test problems.

This paper introduces a new cutting plane method for two-stage stochastic mixed-integer programming (SMIP) called Fenchel decomposition (FD). FD uses a class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from integer programming. First, we derive FD cuts based on both the first and second-stage variables, and devise an FD algorithm for SMIP and establi...

We consider a stochastic variant of the integer linear programming problem, which contains random variables in the objective vector. We are allowed to reveal each entry of the objective vector by conducting a query, and the task is to find a good solution by conducting a small number of queries. We propose adaptive and nonadaptive algorithms for this problem, and provide a general technique for...

A stochastic approximation method for optimizing a class of discrete functions is considered. The procedure is a version of the Simultaneous Perturbation Stochastic Approximation (SPSA) method that has been modified to obtain a stochastic optimization method for cost functions defined on a grid of points in Euclidean p-space having integer components. We discuss the algorithm and examine its co...

Stochastic capacitated lot sizing problem is considered in the presence of probabilistic processing times and demand in this paper. A two-step hierarchical methodology is developed. First, stochastic capacity requirements are determined with statistical analysis & Monte-Carlo simulation. Second, a stochastic nonlinear mixed integer mathematical model is developed to solve the problem.

We present a novel method for estimating tree-structured covariance matrices directly from observed continuous data. Specifically, we estimate a covariance matrix from observations of p continuous random variables encoding a stochastic process over a tree with p leaves. A representation of these classes of matrices as linear combinations of rank-one matrices indicating object partitions is used...

The US air fleet is tasked with the worldwide movement of cargo and personnel. Due to a unique mixture of operating circumstances, it faces a large scale and dynamic set of cargo movement demands with sudden changes almost being the norm. Airfleet management involves periodically allocating aircraft to its myriad operations, while judiciously accounting for this uncertainty to minimize operatin...