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"Shone, Rob"
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A conservative index heuristic for routing problems with multiple heterogeneous service facilities
We consider a queueing system with N heterogeneous service facilities, in which admission and routing decisions are made when customers arrive and the objective is to maximize long-run average net rewards. For this type of problem, it is well-known that structural properties of optimal policies are difficult to prove in general and dynamic programming methods are computationally infeasible unless N is small. In the absence of an optimal policy to refer to, the Whittle index heuristic (originating from the literature on multi-armed bandit problems) is one approach which might be used for decision-making. After establishing the required indexability property, we show that the Whittle heuristic possesses certain structural properties which do not extend to optimal policies, except in some special cases. We also present results from numerical experiments which demonstrate that, in addition to being consistently strong over all parameter sets, the Whittle heuristic tends to be more robust than other heuristics with respect to the number of service facilities and the amount of heterogeneity between the facilities.
Journal Article
Defying death in the mountains
An exploration of survival after mountaineering accidents, including discussions of three specific incidents. Presented in graphic novel format.
Book
Containment of socially optimal policies in multiple-facility Markovian queueing systems
We consider a Markovian queueing system with N heterogeneous service facilities, each of which has multiple servers available, linear holding costs, a fixed value of service and a first-come-first-serve queue discipline. Customers arriving in the system can be either rejected or sent to one of the N facilities. Two different types of control policies are considered, which we refer to as 'selfishly optimal' and 'socially optimal'. We prove the equivalence of two different Markov Decision Process formulations, and then show that classical M/M/1 queue results from the early literature on behavioural queueing theory can be generalized to multiple dimensions in an elegant way. In particular, the state space of the continuous-time Markov process induced by a socially optimal policy is contained within that of the selfishly optimal policy. We also show that this result holds when customers are divided into an arbitrary number of heterogeneous classes, provided that the service rates remain non-discriminatory.
Journal Article
Defying death in the wilderness
True stories of survival in the wilderness are told in this graphic novel format.
Book
Dynamic Repair and Maintenance of Heterogeneous Machines Dispersed on a Network: A Rollout Method for Online Reinforcement Learning
We consider a problem in which a single repairer is responsible for the maintenance and repair of a collection of machines, positioned at different locations on a network of nodes and edges. Machines deteriorate according to stochastic processes and incur increasing costs as they approach complete failure. The times needed for repairs to be performed, and the amounts of time needed for the repairer to switch between different machines, are random and machine-dependent. The problem is formulated as a Markov decision process (MDP) in which the objective is to minimize long-run average costs. We prove the equivalence of an alternative formulation based on rewards and use this to develop an index heuristic policy, which is shown to be optimal in certain special cases. We then use rollout-based reinforcement learning techniques to develop a novel online policy improvement (OPI) approach, which uses the index heuristic as a base policy and also as an insurance option at decision epochs where the best action cannot be selected with sufficient confidence. Results from extensive numerical experiments, involving randomly-generated network layouts and parameter values, show that the OPI heuristic is able to achieve close-to-optimal performance in fast-changing systems with state transitions occurring 100 times per second, suggesting that it is suitable for online implementation.
Paper
Werewolves
In this book, readers discover legends of werewolves that have been told throughout the world from France to the United States.
Book
Stochastic dynamic job scheduling with interruptible setup and processing times: An approach based on queueing control
We consider a stochastic, dynamic job scheduling problem, formulated as a queueing control problem, in which a single server processes jobs of different types that arrive according to independent Poisson processes. The problem is defined on a network, with jobs arriving at designated demand points and waiting in queues to be processed by the server, which travels around the network dynamically and is able to change its course at any time. In the context of machine scheduling, this enables us to consider sequence-dependent, interruptible setup and processing times, with the network structure encoding the amounts of effort needed to switch between different tasks. We formulate the problem as a Markov decision process in which the objective is to minimize long-run average holding costs and prove the existence of a stationary policy under which the system is stable, subject to a condition on the workload of the system. We then propose a class of index-based heuristic policies, show that these possess intuitively appealing structural properties and suggest how to modify these heuristics to ensure scalability to larger problem sizes. Results from extensive numerical experiments are presented in order to show that our heuristic policies perform well against suitable benchmarks.
Paper
A Bi-Objective Markov Decision Process Design approach to redundancy allocation with dynamic maintenance for a parallel system
The reliability of a system can be improved by the addition of redundant elements, giving rise to the well-known redundancy allocation problem (RAP). We propose a novel extension to the RAP called the Bi-Objective Integrated Design and Dynamic Maintenance Problem (BO-IDDMP) which allows for future dynamic maintenance decisions to be incorporated. This leads to a problem with first-stage redundancy design decisions and second-stage sequential maintenance decisions under uncertainty. To the best of our knowledge, this is the first use of a continuous-time Markov Decision Process Design framework to formulate a problem with non-trivial dynamics, as well as its first use alongside bi-objective optimization. A general heuristic optimization methodology for bi-objective MDP Design problems is developed, and then applied to the BO-IDDMP. The efficiency and accuracy of our methodology are demonstrated against an exact mixed-integer linear programming solver. The heuristic is shown to be orders of magnitude faster in the majority of cases, and in only 2 out of 84 cases produces a solution that is dominated by the exact method. The inclusion of dynamic maintenance policies is shown to yield stronger and better-populated Pareto fronts, allowing more flexibility for the decision-maker. The impacts of varying parameters unique to our problem are also investigated.
Paper
A New Simheuristic Approach for Stochastic Runway Scheduling
We consider a stochastic, dynamic runway scheduling problem involving aircraft landings on a single runway. Sequencing decisions are made with knowledge of the estimated arrival times (ETAs) of all aircraft due to arrive at the airport, and these ETAs vary according to continuous-time stochastic processes. Time separations between consecutive runway landings are modeled via sequence-dependent Erlang distributions and are affected by weather conditions, which also evolve continuously over time. The resulting multi-stage optimization problem is intractable using exact methods and we propose a novel simheuristic approach, based on the application of methods analogous to variable neighborhood search (VNS) in a high-dimensional stochastic environment. Our model is calibrated using flight tracking data for over 98,000 arrivals at Heathrow Airport. Results from numerical experiments indicate that our proposed simheuristic algorithm outperforms an alternative based on deterministic forecasts under a wide range of parameter values, with the largest benefits being seen when the underlying stochastic processes become more volatile and also when the on-time requirements of individual flights are given greater weight in the objective function.
Paper