Functional properties of throughput in tandem lines with unreliable servers and finite buffers

optimization;queueing theory;production

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

Sample-Path Optimization of Buffer Allocations in a Tandem Queue - Part I:Theoretical Issues

This is the first of two papers dealing with the optimal bu er allocation problem in tandem manufacturing lines with unreliable machines.We address the theoretical issues that arise when using sample-path optimization, a simulation-based optimization method, to solve this problem.Sample-path optimization is a recent method to optimize performance functions of stochastic systems.By exploiting the fact that the performance function we want to optimize is the almost sure limit of a sequence of random functions, it overcomes some of the di culties from which variants of stochastic approximation methods su er.We provide a mathematical framework that makes use of a function space construction to model the dependence of throughput on bu er capacities and maximum ow rates of machines.Using this framework we prove various structural properties of throughput and show how these properties, along with a niceness condition on the steady-state, can be used to prove that the sample-path optimization method converges almost surely when applied to the bu er allocation problem.Among the properties established, monotonicity in bu er capacities and in ma- chine ow rates are especially important.Although monotonicity results of this nature have appeared in the literature for discrete tandem lines, as far as we are aware the kind of analysis we present here has not yet been done for continuous tandem lines.

Strategic Generation Capacity Choice under Demand Uncertainty:Analysis of Nash Equilibria in Electricity Markets

Abstract: We analyze a two-stage game of strategic firms facing uncertain demand and exerting market power in decentralized electricity markets. These firms choose their generation capacities at the first stage while anticipating a perfectly competitive future electricity spot market outcome at the second stage; thus it is a closed loop game. In general, such games can be formulated as an equilibrium problem with equilibrium constraints (EPEC) and examples have been posed in the literature that have multiple or no equilibria. Therefore, it is of interest to define general sets of conditions under which solutions exist and are unique, which would enhance the value of such models for policy andmarket intelligence purposes. In this paper, we consider various types of such a closed loop model regarding the underlying price-demand relations (elastic and inelastic demand), the assumed demand uncertainty with a broad class of continuous distributions, and any finite number of players with symmetric or asymmetric costs. We establish sufficient conditions for the random demand’s probability distribution which guarantee existence and uniqueness of equilibria in most of the cases of this closed loop model. We identify a broad class of commonly used continuous probability distributions satisfying these conditions