Analysis of Models for the Stochastic Outpatient Procedure Scheduling Problem

In this paper, we present a new stochastic mixed-integer linear programming model for the Stochastic Outpatient Procedure Scheduling Problem (SOPSP). In this problem, we schedule a day’s worth of procedures for a single provider, where each procedure has a known type and associated probability distribution of random duration. Our objective is to minimize the expectation … Read more

A simplex method for uncapacitated pure-supply infinite network flow problems

We provide a simplex algorithm for a structured class of uncapacitated countably-infinite network flow problems. Previous efforts required explicit capacities on arcs with uniformity properties that facilitate duality arguments. By contrast, this paper takes a “primal” approach by devising a simplex method that provably converges to optimal value using arguments based on convergence of spanning … Read more

Parameter-free Sampled Fictitious Play for Solving Deterministic Dynamic Programming Problems

To facilitate fast solution of deterministic dynamic programming problems, we present a parameter-free variation of the Sampled Fictitious Play (SFP) algorithm. Its random tie-braking procedure imparts a natural randomness to the algorithm which prevents it from “getting stuck” at a local optimal solution and allows the discovery of an optimal path in a finite number … Read more

Simplex Algorithm for Countable-state Discounted Markov Decision Processes

We consider discounted Markov Decision Processes (MDPs) with countably-infinite state spaces, finite action spaces, and unbounded rewards. Typical examples of such MDPs are inventory management and queueing control problems in which there is no specific limit on the size of inventory or queue. Existing solution methods obtain a sequence of policies that converges to optimality … Read more

Robust Linear Optimization With Recourse

We propose an approach to linear optimization with recourse that does not involve a probabilistic description of the uncertainty, and allows the decision-maker to adjust the degree of robustness of the model while preserving its linear properties. We model random variables as uncertain parameters belonging to a polyhedral uncertainty set and minimize the sum of … Read more

Optimizing Call Center Staffing using Simulation and Analytic Center Cutting Plane Methods

We present a simulation-based analytic center cutting plane method to solve a sample average approximation of a call center problem of minimizing staffing costs, while maintaining an acceptable level of service in multiple time periods. We establish convergence of the method when the service level functions are discrete pseudoconcave. An extensive numerical study of a … Read more

Aggregation in Stochastic Dynamic Programming

We present a general aggregation method applicable to all finite-horizon Markov decision problems. States of the MDP are aggregated into macro-states based on a pre-selected collection of “distinguished” states which serve as entry points into macro-states. The resulting macro-problem is also an MDP, whose solution approximates an optimal solution to the original problem. The aggregation … Read more

A fictitious play approach to large-scale optimization

In this paper we investigate the properties of the sampled version of the fictitious play algorithm, familiar from game theory, for games with identical payoffs, and propose a heuristic based on fictitious play as a solution procedure for discrete optimization problems of the form $\max\{u(y):y=(y^1,\ldots,y^n)\in\setY^1\times\cdots\times\setY^n\}$, i.e., in which the feasible region is a Cartesian product … Read more