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Workshop YEQTIV (Young European Queueing Theorists) "Optimal Control in Stochastic Systems" November 2527, 2010
Thursday November 25
Friday November 26
Saturday November 27
Abstracts Zumbul Atan Supply Disruptions in MultiEchelon Inventory Systems The effect of supply disruptions in multiechelon inventory systems can be more severe than single location systems. In multiechelon systems, a disruption in the supply process of a location can impact all the other locations. Some of them may not receive the inventory they request and the others may need to carry excess inventories which they originally planned to send if disruptions did not happen. For effective management of multiechelon inventory systems subject to disruptions, all locations need to develop strategies for protecting against the damages caused by disruptions. In this study, we analyze twoechelon serial and distribution systems subject to supply disruptions. We consider a range of assumptions and propose algorithms to find the optimal or nearoptimal stocking levels of all the locations in the system. We show how supply disruptions in different parts of the network affect inventory decisions and propose strategies that firms can use to mitigate the effects of these disruptions. Rene Bekker Scheduling admissions and reducing variability in bed demand
With the growing demand for health care resources, the
pressure on the efficient usage of the available bed capacity is increasing.
An efficient use of capacity is however complicated by a considerable degree
of variability, which is typical for the workload at clinical wards.
Surprisingly, studies have shown that the variation in the number of
admitted scheduled (or elective) patients is generally at least as large as
the variation in the number of emergency admissions. The variability in
admission pattern leads to highly variable bed occupancy for both elective
and emergency patients. Moreover, during the weekend the number of elective
admissions is generally very small leading to extra workload fluctuations
over the week. Cagdas Buyukkaramikli Periodic Capacity Management under a Lead Time Performance Constraint In this paper, we study a production system that operates under a lead time performance constraint which guarantees the completion of an order before a predetermined lead time with a certain probability. The demand arrival times and the service requirements for the orders are random. To reduce the capacity related operational costs, the production system under study has the option to use flexible capacity. We focus on periodic capacity policies and model the production system as a queuing system that can change its capacity periodically and choose from two levels of capacity available: a permanent capacity and a permanent plus contingent capacity. The permanent capacity is always employed in the system. Contingent capacity is supplied if needed at the start of a period, and is available during that period, at a cost rate that is decreasing in period length. For a given lead time performance constraint and a permanent/contingent capacity cost structure, we develop a procedure to create a set for candidate period lengths and permanent/contingent capacity levels. Afterwards, we propose a search algorithm that finds the capacity levels and the threshold point that minimizes the capacity related costs for a given period length. Due to the cost structure of the permanent and contingent capacity levels, the behavior of the operational costs changes drastically under different period lengths and different cost structures. In our computational study, we observe that the periodic capacity flexibility reduces the capacity related operational costs significantly (up to 35 %). The percentage savings are higher for more ambitious lead time performance constraints. Moreover, we observe that the use of contingent capacity makes the total system costs more insensitive to the lead time performance requirements.
JanPieter Dorsman Nicolas Gast Mean field for Markov decision processes: from discrete to continuous optimization
In this talk, I will focus on the optimal control of
large stochastic systems. I will explain how to extend classical mean field
methods to study the controlled behavior of large systems. I will show that
under mild assumptions, solving an optimal control problem for a system with
a large number of objects can be reduced to the solving of a problem for a
deterministic system as the number of objects grows large. In practice, this
allows one to evaluate the performance of a policy and provide a way to
asymptotically solve problems that used to be intractable. Itai Gurvich Motivated by callcenter outsourcing problems, we consider a network with multiple call centers overflowing some of their calls to a central call center. Relying on a separation of time scales, we establish heavytraffic approximations and prove an asymptotic independence result which facilitates, in turn, simplified expressions for the customer waitingtime distribution. The asymptotic independence is shown to be useful in solving some callcenter optimization problems. Rene Haijema Onestep policy improvements to reduce the waiting time at traffic lights
We consider a single intersection of roads that is
controlled by traffic lights. For each traffic flow f leading to the
intersection cameras and/or induction loops measure the number of cars
approaching the intersection and their distances as well as the number of
cars (qf) waiting at queue f. We model the control in discrete time to
acknowledge a fixed switchover time when a light changes from green to
yellow to all red. When a light shows green one either keeps it green or
turns it into yellow. Bernd Heidergott
David Hodge Asymptotic optimality of multiaction restless bandits The class of restless multiarmed bandits as proposed by Whittle in the 1980s have long since been known to be very hard to solve optimally. We present an optimality result which borrows greatly from the primary work on optimality of policies in the restless bandit framework, namely the 1990 paper of Weber & Weiss. We extend their framework to bandits with multiple levels of activation and therefore a more general resource constraint too. The work is motivated by a number of recent works of Glazebrook et al. which demonstrate the performance of index heuristics for resource allocation in stochastic systems. Before now these heuristics have only been shown to be optimal for the Whittle relaxation of the standard problem, i.e. to problems where resource is purchased by bandits rather than a fixed resource level is optimally shared. We find that under key assumptions about the solution to a deterministic differential equation the index heuristics above are asymptotically optimal. Gerard Hoekstra Dynamic Traffic Splitting to Parallel Wireless Networks with Partial Information: A Bayesian Approach Contemporary wireless communication networks are based on a wide range of different technologies providing overlapping coverage. This offers users the opportunity to use several networks at the same time. Motivated by this, we consider a networking environment in which users are able to select between the available wireless networks to minimize the mean processing times for file downloads in the presence of background traffic. The information available to the user is only the total number of jobs in each network, rather than the pernetwork numbers of foreground and background jobs. This leads to a complex partial information decision problem which is the focus of this talk. A Bayesian learning algorithm is presented that optimally splits a traffic stream that minimizes the expected sojourn time. Oualid Jouni On Queueing Systems with Finite Arrivals This work is motivated in practice by a situation where a finite number of arrivals occur in a service system. Although the importance of such type of systems, a few results are available. We consider single and multiserver models with exponential service times. The source of customers is assumed to be finite to the contrary of standard queueing systems. We obtain the system state probabilities and use them to evaluate several measures of system performance, including the distribution of the waiting time of an arbitrary customer. We then conduct numerical experiments and study the characteristic of these special types of queuing systems. In particular, we analyze the effect of heterogeneity in interarrival times on the performance measures. We show that modeling without accounting such features may lead to inappropriate results. Ger Koole Monotonicity Results in MDP We focus on monotonicity results for dynamic systems that take values in the natural numbers or in moredimensional lattices. The results are mostly formulated in terms of controlled queueing systems, but there are also applications to maintenance systems, revenue management, and so forth. We concentrate on results that are obtained by inductively proving properties of the dynamic programming value function. We give a framework for using this method that unifies results obtained for different models. We also give a comprehensive overview of the results that can be obtained through it, in which we discuss not only (partial) characterizations of optimal policies but also applications of monotonicity to optimization problems and comparisons of systems. Dinard van der Laan Optimal mixing of suboptimal decision rules for MDP control Consider a Markov Decision Process (MDP) with the
restriction that at decision epochs only a finite number of given Markov
decision rules are admissible. Many openloop control problems can be
modeled as an MDP with such a restriction on the admissible decision
rules. Moreover, such model can be considered for closedloop problems
if for example it is difficult to obtain or implement the optimal
control policy. Then the set of admissible Markov decision rules D could
be some suboptimal, but easyimplementable decision rules. Semyon Meerkov Production Systems Engineering: Optimality through Improvability Production Systems Engineering (PSE) is an emerging branch of Engineering intended to uncover fundamental principles that govern production systems and utilize them for the purposes of analysis, continuous improvement, and design. In PSE, the machines are assumed to be unreliable and the buffers are finite. Under these assumptions, production lines are nonlinear stochastic systems. Analyses of their statics, dynamics, and optimal operation are the goals of PSE. In this talk, the main problems of PSE and their solutions will be described along with several applications. In particular, the notion of improvability, which addresses the issue of system optimization through a series of suboptimal steps, will be discussed. A justification of this approach is in the fact that, under insufficient information on the factory floor, the optimality may be unachievable, while the improvability is possible. In addition, the socalled PSE Toolbox, which implements the methods and algorithms developed, will be discussed. A demo of the toolbox can be found at http://www.ProductionSystemsEngineering.com . Ulrich Rieder Markov Decision Processes with Applications Markov Decision Processes are considered w.r.t. the
total reward criterion. We present general verification and structure
theorems for finitestage and infinitestage MDPs. Special attention is
given to the computation of optimal policies. In the second part,
stochastic Flora Spieksma Local uniformisation in the successive approximations method for processor sharing retrial queues
Successive Approximations is an important tool for proving structural
results for average optimal policies in a Markov Decision Process. Its
application requires a uniformisation step, that is not applicable when the
jump rates are unbounded in action and state variables. This occurs in e.g.
call centre models with abandonments and retrial queues. Taoying FarenhorstYuan A Perturbation Analysis Approach to Phantom Estimators There are two distinct philosophies to the implementation and coding of gradient estimators for stochastic cost functions: singlerun computation and parallel systems computation. There is a tradeoff between these two families of estimators. The singlerun estimators are computationally more efficient, but have higher variance than the parallel estimators. In this talk, we discuss the possibility of combining the best of both worlds, namely, low variance and numerical efficiency. Sofia Villar Realstate restless bandit problems: marginal productivity indexation methodology and its application to exible sensor tracking systems
Many control problems of modern technological systems are readily formulated
in the framework of Markov decision processes (MDPs), by considering the
optimal sequential allocation of common resources to a collection of
independent stochastic projects, each modeled as binaryaction MDPs (i.e.
onearmed bandit models), whose state variable naturally moves in a
continuous state space according to transitions which are action speci c.
Under such conditions, the optimal policy solves a multiarmed restless
bandit problem (MARBP). Hence, its practical implementation is hindered both
by the intractability of the conventional dynamic programming (DP) technique
and by particular difficulties of continuous state spaces. A promising
approach to overcome this limitation is based on the design of a priority
index policy resulting from a Lagrangian relaxation and decomposition
approach, introduced by Whittle (1988) and further developed by NinoMora
(2001) into a unifying framework. Chelsea White III
Optimal Control in Stochastic Systems: Challenges for the Future Sandra van Wijk Optimal lateral transshipment policies in spare parts inventory models We consider an inventory model for spare parts, where two stockpoints provide repairable parts for a critical component of advanced technical systems. As downtime costs for these systems are huge, readyforuse spare parts are kept on stock, to be able to quickly respond to a breakdown of a system. We allow for lateral transshipments (stock transfers) of parts between the stockpoints upon a demand arrival. We are interested in the optimal lateral transshipment policy. Using dynamic programming, we completely characterize and prove the structure of this optimal policy. We also derive conditions under which simple policies are optimal. In addition, we discuss similar inventory models for which we are able to derive the same type of results.


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