53 research outputs found
The stratified p-center problem
This work presents an extension of the p-center problem. In this new model,
called Stratified p-Center Problem (SpCP), the demand is concentrated in a set
of sites and the population of these sites is divided into different strata
depending on the kind of service that they require. The aim is to locate p
centers to cover the different types of services demanded minimizing the
weighted average of the largest distances associated with each of the different
strata. In addition, it is considered that more than one stratum can be present
at each site. Different formulations, valid inequalities and preprocessings are
developed and compared for this problem. An application of this model is
presented in order to implement a heuristic approach based on the Sample
Average Approximation method (SAA) for solving the probabilistic p-center
problem in an efficient way.Comment: 32 pages, 1 pictur
Sample-path solutions for simulation optimization problems and stochastic variational inequalities
inequality;simulation;optimization
Simulation-Based Solution of Stochastic Mathematical Programs with Complementarity Constraints: Sample-Path Analysis
We consider a class of stochastic mathematical programs with complementarity constraints, in which both the objective and the constraints involve limit functions or expectations that need to be estimated or approximated.Such programs can be used for modeling average or steady-state behavior of complex stochastic systems.Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models.Here we broaden the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints.The convergence analysis of sample-path methods rely heavily on stability conditions.We first review necessary sensitivity results, then describe the method, and provide sufficient conditions for its almost-sure convergence.Alongside we provide a complementary sensitivity result for the corresponding deterministic problems.In addition, we also provide a unifying discussion on alternative set of sufficient conditions, derive a complementary result regarding the analysis of stochastic variational inequalities, and prove the equivalence of two different regularity conditions.stochastic processes;mathematics;stability;simulation;regulations;general equilibrium
Simulation-based solution of stochastic mathematical programs with complementarity constraints: Sample-path analysis
We consider a class of stochastic mathematical programs with complementarity constraints, in which both the objective and the constraints involve limit functions or expectations that need to be estimated or approximated. Such programs can be used for modeling \\average" or steady-state behavior of complex stochastic systems. Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models. Here we broaden the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints. The convergence analysis of sample-path methods rely heavily on stability conditions. We first review necessary sensitivity results, then describe the method, and provide sufficient conditions for its almost-sure convergence. Alongside we provide a complementary sensitivity result for the corresponding deterministic problems. In addition, we also provide a unifying discussion on alternative set of sufficient conditions, derive a complementary result regarding the analysis of stochastic variational inequalities, and prove the equivalence of two different regularity conditions.simulation;mathematical programs with equilibrium constraints;stability;regularity conditions;sample-path methods;stochastic mathematical programs with complementarity constraints
Sample-Path Optimization in Simulation
This paper summarizes information about a method, called sample-path optimization, for optimizing performance functions in certain stochastic systems that can be modeled by simulation. We explain the method, give conditions under which it converges, and display some sample calculations that indicate how it performs. We also describe briefly some more extensive numerical experiments on large systems (PERT networks with up to 110 stochastic arcs, and tandem production lines with up to 50 machines). Details of these experiments are reported elsewhere; we give references to this and other related work. We conclude with some currently unanswered questions
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