A Promising Approach to Optimizing Sequential Treatment Decisions for Depression: Markov Decision Process

Faustmann's formula gives the land value, or the forest value of land with trees, under deterministic assumptions regarding future stand growth and prices, over an infinite horizon. Markov decision process (MDP) models generalize Faustmann's approach by recognizing that future stand states and prices are known only as probabilistic distributions. The objective function is then the expected discounted value of returns, over an infinite horizon. It gives the land or the forest value in a stochastic environment. In MDP models, the laws of motion between stand-price states are Markov chains. Faustmann's formula is a special case where the probability of movement from one state to another is equal to unity. MDP models apply whether the stand state is bare land, or any state with trees, be it even- or uneven-aged. Decisions change the transition probabilities between stand states through silvicultural interventions. Decisions that maximize land or forest value depend only on the stand-price state, independently of how it was reached. Furthermore, to each stand-price state corresponds one single best decision. The solution of the MDP gives simultaneously the best decision for each state, and the forest value (land plus trees), given the stand state and following the best policy. Numerical solutions use either successive approximation, or linear programming. Examples with deterministic and stochastic cases show in particular the convergence of the MDP model to Faustmann's formula when the future is assumed known with certainty. In this deterministic environment, Faustmann's rule is independent of the distribution of stands in the forest. FOR. SCI. 47(4):466–474.

Towards enhanced threat modelling and analysis using a Markov Decision Process

Invisible stock loss often occurs in inventory management systems, which is usually caused by quality deterioration, theft, and misplacement and makes inventory record inaccurate. Inaccurate inventory record will bring significant negative impact on the performance of inventory control and leads to severe stock-out. To eliminate this negative impact, in this paper, we develop a Markov decision process (MDP) model for an inventory control system with invisible stock loss, inaccurate record, and replenishment lead-time. Based on the MDP model, a robust inventory control policy is constructed by using the policy iteration technique. From numerical experiments, we find that the robust policy still has a reorder point/order-up-to level structure i.e., an (s, S) structure, and can significantly reduce the impact of inventory inaccuracy.

Linear programming formulation for non-stationary, finite-horizon Markov decision process models

The past decade has witnessed the shift from calling taxis within sight to using applications to send location information which enables e-hailing platforms to match passengers to drivers out of sight. After receiving orders, e-hailing platforms search for a suitable driver to accept the order to complete the matching. At present, platforms mainly set a fixed matching distance according to passengers’ locations for finding available drivers in this distance, but they do not consider if there are enough drivers available for their passengers. In order to find the properest driver which enables the decrease of passengers’ waiting time (i.e., from the time the passenger places the order to the time the driver accepts the order), we propose a model to dynamically change matching distance. The purpose is to find the best matching distance in different supply (i.e., the number of drivers) and demand (i.e., the number of passengers) circumstances. We obtain the required probability information by extracting data from multiple datasets in different supply and demand regions. Later, a Markov Decision Process (MDP) model is established to solve the optimal dynamically changing matching distance policy. At the same time, we propose a reward function to measure the waiting time of passengers and the distance between the driver and the passenger boarding point. Finally, we compared MDP model with three benchmark models, the model of fixed matching distance, dynamic programming matching distance, and linear matching distance. Through comparison, it is concluded that the policy of dynamically changing matching distance based on the MDP model we proposed is best applied. The policy we proposed balance the waiting time of passengers and the distance between the driver and the passenger boarding point, improve platform efficiency.KeywordsMarkov decision processDynamic matching distanceOrder dispatchUrban computingE-hailing

Dynamic selling of quality-graded products under demand uncertainties

Women with BRCA1/2 mutations have higher risk for breast and ovarian cancers. Available intervention actions include prophylactic surgeries and breast screening, which vary significantly in cost, cancer prevention, and in resulting death from other causes. We present a model designed to yield optimal intervention strategies for mutation carriers between the ages of 30 and 65 and any prior intervention history. A Markov decision process (MDP) model is developed that considers yearly state transitions for the mutation carriers and state dependent intervention actions. State is defined as a vector comprising mutation type, health states, prior intervention actions, and age. A discounted value iteration algorithm is used to obtain optimal strategies from the MDP model using both cost and quality-adjusted life years (QALYs) as rewards. The results from MDP model show that for 30-year-old women with BRCA1 mutation and no prior intervention history, the cost-optimal strategy is a combination of prophylactic mastectomy (PM) and prophylactic oophorectomy (PO) at age 30 with no screening afterwards. Whereas, the QALYs-optimal strategy suggests PO at age 30 and PM at age 50 with screening afterwards. For BRCA2 mutation carriers at age 30, the cost-optimal strategy is PO at age 30, PM at age 40, and yearly screening only after age 56. Corresponding QALYs-optimal strategy is PM at age 40 with screening. Strategies for all other ages (31 to 65) are obtained and presented. It is also demonstrated that the cost-optimal strategies offer near maximum survival rate and near minimum cancer incidence rates by age 70, when compared to other ad hoc strategies.

As a typical scenario in future generation communication network applications, UAV-assisted communication can perform autonomous data delivery for massive machine type communication (mMTC), where the data generated from Internet of Things (IoT) devices can be carried and delivered to the corresponding locations with no direct communication channels to the IoT devices. Wireless energy transfer technique can recharge the UAV when the system is in operation, assisting the UAV to continuously collect and deliver data. In this work, we formulate a Markov decision process (MDP) model to describe the energy and data transfer optimization problem for the UAV. To maximize the long-term utility of the UAV, the MDP model is solved by value iteration algorithm to obtain the optimal strategies of the UAV to collect data, deliver data, and receive transferred energy to replenish on-device battery energy storage. Furthermore, to tackle the issues of system state uncertainties, partially observable states, and large state space in UAV-assisted communication systems, we extend the MDP model and solve it by using a Q -learning and a deep reinforcement learning (DRL) schemes. Simulations and numerical results validate that, compared with baseline schemes, the proposed MDP model with DRL based scheme can achieve better wireless energy and data transfer strategies in terms of the higher long-term utility of the UAV.

Markov decision process (MDP) models are widely used for modeling sequential decision-making problems that arise in engineering, economics, computer science, and the social sciences. Many real-world problems modeled by MDPs have huge state and/or action spaces, giving an opening to the curse of dimensionality and so making practical solution of the resulting models intractable. In other cases, the system of interest is too complex to allow explicit specification of some of the MDP model parameters, but simulation samples are readily available (e.g., for random transitions and costs). For these settings, various sampling and population-based algorithms have been developed to overcome the difficulties of computing an optimal solution in terms of a policy and/or value function. Specific approaches include adaptive sampling, evolutionary policy iteration, evolutionary random policy search, and model reference adaptive search. This substantially enlarged new edition reflects the latest developments in novel algorithms and their underpinning theories, and presents an updated account of the topics that have emerged since the publication of the first edition. Includes: innovative material on MDPs, both in constrained settings and with uncertain transition properties; game-theoretic method for solving MDPs; theories for developing roll-out based algorithms; and details of approximation stochastic annealing, a population-based on-line simulation-based algorithm. The self-contained approach of this book will appeal not only to researchers in MDPs, stochastic modeling, and control, and simulation but will be a valuable source of tuition and reference for students of control and operations research.

In the coronavirus epidemic, many Chinese hospitals have established buffer zones to prevent the spread and transmission of the virus. The buffer zone is a monitored and separate area where the patients who need hospitalizations after the quick treatments in the emergency department can temporarily wait for the Covid-19 test and receive some healthcare services to stabilize their conditions. Because the beds in the buffer zones are limited, the managers face the patient admission control problem for the buffer zone. This management and control problem is challenging since the patient arrivals are uncertain, and the patients’ conditions are different. In this paper, we build the infinite- and finite-horizon Markov decision process (MDP) models for this problem. We use the uniformization method to discretize the patient flow. We propose various iteration algorithms to solve the MDP models and obtain the optimal and threshold policies. Numerical experiments validate the advantages of the policies obtained by the algorithms in this paper over the current policies of hospitals. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The ongoing COVID-19 pandemic has been causing enormous damage to people’s health, jobs, and well-being. COVID-19 has affected almost all countries globally and has changed the operation mode of the healthcare system, especially the hospitals. The hospitals are the frontlines of healthcare service and the battle with the COVID-19 pandemic. This article is motivated by our collaborations with hospitals in Shanghai, China. In China, many hospitals establish buffer zones: a monitored area where the patients who need hospitalizations after the quick treatments in the emergency department can temporarily wait for the Covid-19 test and receive some healthcare services to stabilize their conditions. Because the zone’s capacity is limited, the managers must make dynamic patient admission control decisions according to multiple factors, such as patients’ health conditions and the usage of beds in the zone. We propose two MDP models to solve this complex problem. Several iteration algorithms are designed to solve the MDP models and obtain the optimal and threshold policies. Based on hospitals’ real-life data, we show the methods presented in this paper can help hospital managers make more reasonable decisions. Although we focus on the hospital’s buffer zone in China, the methodology and approach for this problem can be extended to other practical hospital management scenarios in the coronavirus pandemic. For example, For example, some hospitals have admission control problems for coronavirus patients due to hospital capacity limitations. The hospital has to decide if a patient is accepted as an inpatient or suggested to home quarantine. In such a case, the admission control problem can also be solved by the methodologies in the paper.

Vehicle Edge Computing (VEC) leverages compact cloud computing at the mobile network edge to meet the processing and latency needs of vehicles. By bringing computation closer to the vehicles, VEC reduces data transmission, minimizes latency, and boosts performance for compute-intensive applications. However, during peak hours of urban road traffic, the scarce computational resources available at edge servers could pose challenges in fulfilling the processing needs of vehicles. Introducing Unmanned Aerial Vehicles (UAVs) as supplementary edge computing nodes could significantly mitigate the aforementioned issue. In this paper, we propose a flexible edge computing framework in which a fleet of UAVs function as mobile computational service providers, offering computation offloading services to multiple vehicles. We design and optimize a computation offloading model for the UAV-enabled vehicle edge computing environment. The proposed model tackles the task offloading challenge, aiming to optimize UAV revenue and task processing efficiency while considering the constraints of UAVs’ restricted computational power and energy resources. Towards this end, our model jointly considers two key factors: task partitioning and computational resource allocation. To tackle the challenges posed by the aforementioned non-convex optimization problem, we construct a Markov Decision Process (MDP) model for the multi-UAV-enabled mobile edge computing system and introduce an innovative Multi-Agent Deep Reinforcement Learning (MADRL) framework addressing the decision-making challenge represented by MDP model. Comprehensive simulation outcomes illustrate that our devised task offloading technique outperforms other optimization methods.

MS3 Reproduction of Published Health Economic Obesity Models: Assessment of Facilitators, Hurdles and Barriers

This paper presents a decision-making framework based on an integrated artificial reasoning framework and Markov decision process (MDP). The integrated artificial reasoning framework provides a physics-based approach that converts system information into state transition models, and the analysis result will be represented by the transition probabilities that can be used with an MDP to find a traceable and explainable optimal pathway. A dynamic Bayesian network (DBN) is well suited for representing the structure of an MDP. The causality information among process variables (or among subsystems) is mathematically represented in a DBN by the conditional probabilities of the node’s states provided different probabilities of the parent node’s states. To define node states in a physically understandable manner, we used multilevel flow modeling (MFM). An MFM follows the fundamental energy and mass conservation laws and supports the selection of process variables that represent the system of interest so that causal relations among process variables are properly captured. An MFM-based DBN supports developing state transition models in an MDP to capture the effect of process variables of system having physical relations. The operators of the target system can capture stochastic system dynamics as multiple subsystem state transitions based on their physical relations and uncertainties coming from component degradation or random failures. We analyzed a simplified exemplary system to illustrate an optimal operational policy using the suggested approach.

The stochastic nature of wireless communication suggests a Markov Decision Process (MDP) as a formalism for identifying and evaluating spectrum control policies. However, in practice numerous factors influence the success or failure of a transmission, so that the applicability of particular MDP models to real spectrum management problems must itself be examined. This paper presents a series of model validation studies in which correspondence between an MDP model and a discrete-event simulation (DES) model is evaluated. We test several hypotheses that together provide a foundation and an exemplar for the idea of using MDPs to guide management of shared spectrum. We conclude that there is sufficient similarity between the performance predictions made by the MDP model and the DES model that MDPs can be used effectively to determine spectrum control policies.

This paper extends finite state and action space Markov Decision Process (MDP) models by introducing a new type of measurement for the outcomes of actions. The new measurement allows to sequentially observe the next-state transition for taking an action, i.e., the actions are ordered and the next action outcome in the sequence is observed only if the current action is not chosen. The sequentially-observed MDP (SO-MDP) shares some properties with a standard MDP: among history dependent policies, Markovian ones are still optimal. SO-MDP policies have the advantage of producing better rewards than standard optimal MDP policies due to additional measurements. Computing these policies, on the other hand, is more complex and we present a linear programming based synthesis of the optimal decision policies for the finite horizon SO-MDPs. A simulation example of multiple autonomous agents is also provided to demonstrate the SO-MDP model and the proposed policy synthesis method.