In this paper, we consider a new formulation for stochastic mathematical programs with complementarity constraints and recourse. We show that the new formulation is equivalent to a smooth semi-infinite program that does no longer contain recourse variables. Optimality conditions for the problem are deduced and connections among the conditions are investigated. Then, we propose a combined Monte ...

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is containe...

We develop and test an integrated forecasting and stochastic programming approach to workforce management in call centers. We first demonstrate that parametric forecasts can be used to drive stochastic programs whose results are stable with relatively small numbers of scenarios. We then extend our approach to include forecast updates and two-stage stochastic programs with recourse and provide a...

n this paper the problem of capacity planning under risk from demand and price/cost uncertainty of the finished products is addressed. The deterministic model is extended into a two-stage stochastic model with fixed recourse by means of various expected levels of demand as random. A recourse penalty is also included in the objective for both shortage and surplus in the finished products. The mo...

Although stochastic programming problems were always believed to be computationally challenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Mathematical Programming A, 106(3):423–432, 2006). Amongst others, that paper argues that linear two-stage stochastic programs with fixed recourse are #P-hard even if the random problem da...

The vehicle routing problem with hard time windows and stochastic service times (VRPTWST) introduced by Errico et al. (2013) in the form of a chance-constrained model, mainly differs from other vehicle routing problems with stochastic service or travel times considered in literature by the presence of hard time windows. This makes the problem extremely challenging. In this paper, we model the V...

In this paper, we propose a new method to compute lower bounds on the optimal objective value of a stochastic program and show how this method can be used to construct separable approximations to the recourse functions. We show that our method yields tighter lower bounds than Jensen’s lower bound and it requires a reasonable amount of computational effort even for large problems. The fundamenta...

Stochastic programming is concerned with practical procedures for decision-making under uncertainty , by modelling uncertainties and risks associated with decisions in a form suitable for optimization. The eld is developing rapidly with contributions from many disciplines such as operations research, probability and statistics, and economics. A stochastic linear program with recourse can equiva...

The main focus of this paper is in a discussion of complexity of stochastic programming problems. We argue that two-stage (linear) stochastic programming problems with recourse can be solved with a reasonable accuracy by using Monte Carlo sampling techniques, while multi-stage stochastic programs, in general, are intractable. We also discuss complexity of chance constrained problems and multi-s...