Markov decision process (MDP) is a decision making framework where a decision maker is interested in maximizing the expected discounted value of a stream of rewards received at future stages at various states which are visited according to a controlled Markov chain. Many algorithms including linear programming methods are available in the literature to compute … Read more
In recent years, robust Markov decision processes (MDPs) have emerged as a prominent modeling framework for dynamic decision problems affected by uncertainty. In contrast to classical MDPs, which only account for stochasticity by modeling the dynamics through a stochastic process with a known transition kernel, robust MDPs additionally account for ambiguity by optimizing in view … Read more
Markov decision process (MDP) models have been used to obtain non-stationary optimal decision rules in various applications, such as treatment planning in medical decision making. However, in practice, decision makers may prefer other strategies that are not statistically different from the optimal decision rules. To benefit from the decision makers’ expertise and provide flexibility in … Read more
Crowd-shipping has gained significant attention as a last-mile delivery option over the recent years. In this study, we propose a variant of dynamic crowd-shipping model with in-store customers as crowd-shippers to deliver online orders within few hours. We formulate the problem as a Markov decision process and develop an approximate dynamic programming (ADP) policy using … Read more
Problem definition: Effective hypertension management is critical to reducing consequences of atherosclerotic cardiovascular disease, a leading cause of death in the United States. Clinical guidelines for hypertension can be enhanced using decision-analytic approaches, capable of capturing many complexities in treatment planning. However, model-generated recommendations may be uninterpretable/unintuitive, limiting their acceptability in practice. We address this … Read more
In this paper, we discuss Optimal Control and Markov Decision Process (MDP) formulations of multistage optimization problems when the involved probability distributions are not known exactly, but rather are assumed to belong to specified ambiguity families. The aim of this paper is to clarify a connection between such distributionally robust approaches to multistage stochastic optimization. … Read more
In the daily dispatching of urban deliveries, a delivery manager has to consider workload balance among the couriers to maintain workforce morale. We consider two types of workload: incentive workload, which relates to the delivery quantity and affects a courier’s income, and effort workload, which relates to the delivery time and affects a courier’s health. … Read more
Robust Markov decision processes (MDPs) allow to compute reliable solutions for dynamic decision problems whose evolution is modeled by rewards and partially-known transition probabilities. Unfortunately, accounting for uncertainty in the transition probabilities significantly increases the computational complexity of solving robust MDPs, which severely limits their scalability. This paper describes new efficient algorithms for solving the … Read more
We propose a dynamic version of the classical node packing problem, also called the stable set or independent set problem. The problem is defined by a node set, a node weight vector, and an edge probability vector. For every pair of nodes, an edge is present or not according to an independent Bernoulli random variable … Read more
In classical Markov Decision Processes (MDPs), action costs and transition probabilities are assumed to be known, although an accurate estimation of these parameters is often not possible in practice. This study addresses MDPs under cost and transition probability uncertainty and aims to provide a mathematical framework to obtain policies minimizing the risk of high long-term … Read more