We consider the problem of bounding the expected value of a linear program (LP) containing random coe&cients, with applications to solving two-stage stochastic programs. An upper bound for minimizations is derived from a restriction of an equivalent, penalty-based formulation of the primal stochastic LP, and a lower bound is obtained from a restriction of a reformulation of the dual. Our “restr...

An e ective algorithm for solving stochastic resource allocation problems is to build piecewise linear, concave approximations of the recourse function based on sample gradient information. Algorithms based on this approach are proving useful in application areas such as the newsvendor problem, physical distribution and eet management. These algorithms require the adaptive estimation of the app...

We study an adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse. A partition-based formulation is a relaxation of the original stochastic program, and we study a finitely converging algorithm in which the partition is adaptively adjusted until it yields an optimal solution. A solution guided refinement strategy is developed to refine the partition by ...

This paper investigates the stability of optimal solution sets to stochastic programs with complete recourse, where the underlying probability measure is understood as a parameter varying in some space of probability measures.piro proved Lipschitz upper semicontinuity of the solution set mapping. Inspired by this result, we introduce a subgradient distance for probability distributions and esta...

Stochastic programming models are large-scale optimization problems that are used to facilitate decision-making under uncertainty. Optimization algorithms for such problems need to evaluate the expected future costs of current decisions, often referred to as the recourse function. In practice, this calculation is computationally difficult as it involves the evaluation of a multidimensional inte...

Recent advances in computer architecture has started to in uence the eld of numerical optimisation. Several methods to solve large mathematical programming problems which were tried and given up in the last three decades has gained renewed interest. stochastic optimisation is such area which has a huge potential of providing successful results due to its high parallel content. In most practical...

We consider shortest path problems defined on graphs with random arc costs. We assume that information on arc cost values is accumulated as the graph is being traversed. The objective is to devise a policy that leads from an origin to a destination node with minimal expected cost. We provide dynamic programming algorithms, estimates for their complexity, negative complexity results, and analysi...

In this paper, we introduce a class of stochastic programming problem with fixed charge recourse in which a fixed cost is imposed if the value of the continuous recourse variable is strictly positive. The algorithm of a branch-and-cut method to solve the problem is developed by using the property of the expected recourse function. Then, the problem is applied to a power generating system. The n...

 Inventory space requirements in remanufacturing facilities can vary significantly over time and by type of space needed due to variability in recaptured component quality, availability of refurbished components, remanufactured product demand, and returned product rates. Multi-period stochastic programming recourse models are developed to identify optimal adaptive schedules for internal, exter...