Approximation Algorithms for Stochastic Inventory Control Models

Approximation Algorithms for Stochastic Inventory Control Model

Solving variational inequalities defined on a domain with infinitely many linear constraints

We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper assumptions, the convergence results for both methods are given. We also provide numerical examples to illustrate the proposed method

Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes

New algorithms for computing of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can be applied to processes with asymptotically coupled and uncoupled finite phase spaces.Comment: 83 page

Comparative Statics for the Consumer Problem

Discrete comparative statics, Lattice programming, Income effects, Consumer theory, C610, D110,

Approximation algorithms for stochastic inventory control models

In this paper we address the long-standing problem of finding computationally efficient and provably good inventory control policies in supply chains with correlated and nonstationary (time-dependent) stochastic demands. This problem arises in many domains and has many practical applications such as dynamic forecast updates (for some applications see Erkip et al. 1990 and Lee et al. 1999). We consider two classical models, the periodic-review stochastic inventory control problem and the stochastic lot-sizing problem with correlated and non-stationary demands. Here the correlation is inter-temporal, i.e., what we observe in the current period changes our forecast for the demand in future periods. We provide what we believe to be the first computationally efficient policies with constant worst-case performance guarantees; that is, there exists a constant C such that, for any given joint distribution of the demands, the expected cost of the policy is guaranteed to be within C times the expected cost of an optimal policy. More specifically, we provide a worst-case performance guarantee of 2 for the periodic-review stochastic inventory control problem, and a performance guarantee of 3 for the stochastic lot-sizing problem. The models. The details of the periodic-review stochastic inventory control problem ar