Sandra (A.C.C.) van Wijk | American University of Sharjah (original) (raw)

Sandra (A.C.C.) van Wijk

Sandra van Wijk is a visiting assistant professor in Supply Chain Management at American University of Sharjah (Sharjah, UAE) in the Department of Marketing and Information Systems of the School of Business Administration. She is teaching courses on supply chain management, operations management, logistics, and managerial statistics, both in the undergraduate program and in the MBA program.

Sandra's research interests focus on stochastic operations research, supply chain and inventory management, performance analysis of stochastic systems, sustainable operations, and queueing theory.

Before, she was a Postdoctoral Research Fellow at McGill University (Montreal, Canada), Desautels Faculty of Management, working on sustainable operations and closed-loop supply chain management. Also, she held positions as Postdoctoral Researcher at Qatar University (Doha, Qatar), and at the Hamilton Institute (National University of Ireland Maynooth, Maynooth, Ireland).

In 2012, she received her PhD from Eindhoven University of Technology. She worked on the 'Creation of Pooling in Inventory and Queueing Models', resulting in her thesis "Pooling and Polling" (see http://tue.academia.edu/SandraVanWijk/Books). She mainly investigates the efficient use of scarce resources, such as inventory or server capacity. One of the main focuses is the use of lateral transshipments in spare parts inventory models, in this way pooling the inventory between multiple warehouses. Also, she studied the pooling of servers in queueing models. Next to this, she worked on polling models, which are queueing models where multiple queues are served by a single server.

Her PhD research was a joint project of the Mathematics department (Stochastic Operational Research group) and the School of Industrial Engineering (Operations, Planning, Accounting, and Control group). Furthermore, she worked at research institute EURANDOM (Queueing and Performance Analysis track). Her thesis advisors were dr. Ivo Adan and dr. Geert-Jan van Houtum, while she also worked with dr. Onno Boxma and dr. Ton de Kok.

In 2012, she received a Prince Bernhard Scholarship for visiting the computer science department of Carnegie Mellon University (CMU, Pittsburgh, PA, USA), working together with Mor Harchol-Balter and Alan Scheller-Wolf.

Sandra graduated from Eindhoven University of Technology in Industrial and Applied Mathematics (BSc 2006, MSc 2007, PhD 2012). Previously, she worked as a mathematics teacher in high schools, teaching assistant at university, and conducted internships in the Stochastic Operational Research group of Eindhoven University of Technology and at Philips Research Eindhoven.
Supervisors: A.G. de Kok, O.J. Boxma, I.J.B.F. Adan, and G.J. van Houtum
Address: American University of Sharjah,

School of Business Administration,

Department of Marketing and Information Systems,

PO Box 26666,

Sharjah,

UAE

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Books by Sandra (A.C.C.) van Wijk

We study the 'Creation of Pooling in Inventory and Queueing Models'. This research consists of th... more We study the 'Creation of Pooling in Inventory and Queueing Models'. This research consists of the study of sharing a scarce resource (such as inventory, server capacity, or production capacity) between multiple customer classes. This is called pooling, where the goal is to achieve cost or waiting time reductions. For the inventory and queueing models studied, both theoretical, scientific insights are generated, as well as strategies which are applicable in practice.

This monograph consists of two parts: pooling and polling . In the first part, pooling is applied to multi-location inventory models. It is studied how cost reduction can be achieved by the use of stock transfers between local warehouses, so-called lateral transshipments. In this way, stock is pooled between the warehouses. The setting is motivated by a spare parts inventory network, where critical components of technically advanced machines are kept on stock, to reduce down time durations. We create insights into the question when lateral transshipments lead to cost reductions, by studying several models.

Firstly, a system with two stock points is studied, for which we completely characterize the structure of the optimal policy, using dynamic programming. For this, we formulate the model as a Markov decision process. We also derived conditions under which simple, easy to implement, policies are always optimal, such as a hold back policy and a complete pooling policy. Furthermore, we identified the parameter settings under which cost savings can be achieved. Secondly, we characterize the optimal policy structure for a multi-location model where only one stock point issues lateral transshipments, a so-called quick response warehouse. Thirdly, we apply the insights generated to the general multi-location model with lateral transshipments. We propose the use of a hold back policy, and construct a new approximation algorithm for deriving the performance characteristics. It is based on the use of interrupted Poisson processes. The algorithm is shown to be very accurate, and can be used for the optimization of the hold back levels, the parameters of this class of policies. Also, we study related inventory models, where a single stock point servers multiple customers classes.

Furthermore, in the first part, the pooling of server capacity is studied. For a two queue model where the head-of-line processor sharing discipline is applied, we derive the optimal control policy for dividing the servers attention, as well as for accepting customers. Also, a server farm with an infinite number of servers is studied, where servers can be turned off after a service completion in order to save costs. We characterize the optimal policy for this model.

In the second part of the thesis, polling models are studied, which are queueing systems where multiple queues are served by a single server. An application is the production of multiple types of products on a single machine. In this way, the production capacity is pooled between the product types. For the classical polling model, we derive a closed-form approximation for the mean waiting time at each of the queues. The approximation is based on the interpolation of light and heavy traffic results. Also, we study a system with so-called smart customers, where the arrival rate at a queue depends on the position of the server. Finally, we invent two new service disciplines (the gated/exhaustive and the k-gated discipline) for polling models, designed to yield 'fairness and efficiency' in the mean waiting times. That is, they result in almost equal mean waiting times at each of the queues, without increasing the weighted sum of the mean waiting times too much.

Slides of presentation during PhD defense: http://tue.academia.edu/SandraVanWijk/Talks/82570/Pooling_and_Polling_Creation_of_Pooling_in_Inventory_and_Queueing_Models

Papers by Sandra (A.C.C.) van Wijk

Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools, 2008

We consider a polling system where the server cyclically serves the queues according to the follo... more We consider a polling system where the server cyclically serves the queues according to the following discipline: the server does one round of visits to the queues applying the gated service discipline at each of the queues, followed by one round of visits applying the exhaustive service discipline at each of the queues, and this alternating pattern repeats itself. We call this the Gated/Exhaustive service discipline. For this we derive (i) a Pseudo Conservation Law for the weighted sum of the mean waiting times, (ii) the mean steady state waiting times using Mean Value Analysis, (iii) queue length distributions making use of results for Multitype Branching Processes and the concept of so-called Smart Customers, and (iv) the sojourn time distributions.

Performance Evaluation, 2011

A typical polling system consists of a number of queues, attended by a single server in a fixed o... more A typical polling system consists of a number of queues, attended by a single server in a fixed order. The vast majority of papers on polling systems focusses on Poisson arrivals, whereas very few results are available for general arrivals. The current study is the first one presenting simple closed-form approximations for the mean waiting times in polling systems with renewal arrival processes, performing well for all workloads. The approximations are constructed using heavy traffic limits and newly developed light traffic limits. The closed-form approximations may prove to be extremely useful for system design and optimisation in application areas as diverse as telecommunication, maintenance, manufacturing and transportation.

Operations Research Letters, 2013

We study a multi-location inventory problem with a so-called quick response warehouse. In case of... more We study a multi-location inventory problem with a so-called quick response warehouse. In case of a stock-out at a local warehouse, the demand might be satisfied by a stock transfer from the quick response warehouse. We derive the optimal policy for when to accept and when to reject such a demand at the quick response warehouse. We also derive conditions under which it is always optimal to accept these demands. Furthermore, we conduct a numerical study and consider model variations.

In this part of the thesis we focus on pooling of resources. We consider respectively pooling of ... more In this part of the thesis we focus on pooling of resources. We consider respectively pooling of inventory and pooling of server capacity. We start by a discussion on pooling of resources in general, followed by introductions to each of the parts. Finally, we address the connection between pooling and polling models.

This thesis is the result of my final project to obtain the degree of Master of Science in Indust... more This thesis is the result of my final project to obtain the degree of Master of Science in Industrial and Applied Mathematics at the Eindhoven University of Technology. I did the specialization in Statistics, Probability and Operations Research. This document describes the work done during my eight-month internship at Philips Research Eindhoven in the Digital Signal Processing group.

European Journal of Operational Research, 2012

We consider a continuous-time, single-echelon, multi-location inventory model with Poisson demand... more We consider a continuous-time, single-echelon, multi-location inventory model with Poisson demand processes. In case of a stock-out at a local warehouse, a demand can be fulfilled via a lateral transshipment (LT). Each warehouse is assigned a predetermined sequence of other warehouses where it will request for an LT. However, a warehouse can hold its last part(s) back from such a request. This is called a hold back pooling policy, where each warehouse has hold back levels determining whether a request for and LT by another warehouse is satisfied. We are interested in the fractions of the demand satisfied from stock (fill rate), satisfied via a lateral transshipment, and via an emergency shipment from an external source. From this the average costs of a policy can be determined. We present two approximation algorithms for the evaluation of a given policy, approximating the above mentioned fractions. The first one, the Poisson overflow algorithm, is an extension of algorithms known in the literature. The second one, the On/Off overflow algorithm is new and more sophisticated. Instead of approximating the stream of LTrequests from a warehouse as a Poisson process, we use an interrupted Poisson process. This is a process that is turned alternatingly On and Off for exponentially distributed durations. In a numerical study we show that both algorithms perform very well. The On/Off algorithm is significantly more accurate than the Poisson algorithm, but requires longer computation times.

In this paper we consider a single-server, cyclic polling system with switch-over times. A distin... more In this paper we consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. For this model we study the joint queue length distribution at polling epochs and at server’s departure epochs. We also study the marginal queue length distribution at arrival epochs, as well as at arbitrary epochs (which is not the same in general, since we cannot use the PASTA property). A generalised version of the distributional form of Little’s law is applied to the joint queue length distribution at customer’s departure epochs in order to find the waiting time distribution for each customer type. We also provide an alternative, more efficient way to determine the mean queue lengths and mean waiting times, using Mean Value Analysis. Furthermore, we show that under certain conditions a Pseudo-Conservation Law for the total amount of work in the system ...

We study a polling model where we want to achieve a balance between the fairness of the waiting t... more We study a polling model where we want to achieve a balance between the fairness of the waiting times and the efficiency of the system. For this purpose, we introduce the κ-gated service discipline. It is a hybrid of the classical gated and exhausted disciplines, and consists of using κi gated service phases at queue i before the server switches to the next queue. We derive the distributions and means of the waiting times, a pseudo conservation law for the weighted sum of the mean waiting times, and the fluid limits of the waiting times. Our goal is to optimize the κi’s so as to minimize the differences in the mean waiting times, i.e. to achieve maximal fairness, without giving up too much on the efficiency of the system. From the fluid limits we derive a heuristic rule for setting the κi’s. In a numerical study the heuristic is shown to perform well.

We study a surveillance wireless sensor network (SWSN) comprised of small and low-cost sensors de... more We study a surveillance wireless sensor network (SWSN) comprised of small and low-cost sensors deployed in a region in order to detect objects crossing the field of interest. In the present paper, we address two problems concerning the design and performance of an SWSN: optimal sensor placement and algorithms for object detection in the presence of false alarms. For both problems, we propose explicit decision rules and efficient algorithmic solutions. Further, we provide several numerical examples and present a simulation model that combines our placement and detection methods.

lateral transshipment policy for a two location inventory problem

We consider an inventory model for spare parts with two stockpoints, providing repairable parts f... more We consider an inventory model for spare parts with two stockpoints, providing repairable parts for a critical component of advanced technical systems. As downtime costs for these systems are huge, ready-for-use spare parts are kept on stock, to be able to quickly respond to a breakdown of a system. We allow for lateral transshipments of parts between the stockpoints upon a demand arrival for a spare part. We are interested in the optimal lateral transshipment policy. We consider a continuous review setting, where the initial number of spare parts at each location is given. We assume Poisson demand processes, and allow for asymmetric demand rates and asymmetric costs structures at the two locations. Defective parts are replaced, and returned to the stockpoint for repair. Each location has ample repair capacity, and repair times are exponentially distributed, with the same mean repair time for both locations. Demands are satisfied from own stock, via a lateral transshipment, or via a...

We present two algorithms for indoor positioning estimation in peer-to-peer networks. The setup i... more We present two algorithms for indoor positioning estimation in peer-to-peer networks. The setup is a network of two types of devices: reference devices with a known location and blindfolded devices that can determine distances to reference devices and each other. From this information the blindfolded devices try to estimate their positions. A typical scenario is navigation inside a shopping mall where devices in the parking lot can make contact with GPS satellites, whereas devices inside the building make contact with each other, devices on the parking lot, and devices fixed to the building. The devices can measure their in-between distances, with some measurement error, and exchange positioning information. However, other devices might only know their position with some error. We present two algorithms for positioning estimation in such a peer-to-peer network. The first one is purely geometric and is based on Euclidean geometry and intersecting spheres. We rewrite the information t...

We study a surveillance wireless sensor network (SWSN) comp rised of small and low-cost sensors d... more We study a surveillance wireless sensor network (SWSN) comp rised of small and low-cost sensors deployed in a region in order to de ect objects crossing the field of interest. In the present paper, we addre ss two problems concerning the design and performance of an SWSN: optimal se nsor placement and algorithms for object detection in the presence of f alse alarms. For both problems, we propose explicit decision rules and effici nt algorithmic solutions. Further, we provide several numerical examples and present a simulation model that combines our placement and detection met hods.

We consider an inventory model for spare parts. Two stockpoints provide repairable parts for a cr... more We consider an inventory model for spare parts. Two stockpoints provide repairable parts for a critical component of advanced technical systems. As downtime costs for these systems are huge, ready-for-use spare parts are kept on stock, to be able to quickly respond to a breakdown of a system. We allow for lateral transshipments of parts between the stockpoints upon a demand arrival for a spare part. We are interested in the optimal lateral transshipment policy. Using dynamic programming, we completely characterize and prove the structure of the 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.

This report summarises progress made towards the problem submitted by Rusal Aughinish at the 93rd... more This report summarises progress made towards the problem submitted by Rusal Aughinish at the 93rd European Study Group with Industry. Rusal Aughinish is a company that refines alumina from bauxite. The problem presented to the study group was to review the percentage of time that the company’s inner berth was occupied and how to minimise this percentage. A number of different approaches were taken with this aim in mind. Firstly, data supplied by Rusal Aughinish was analysed. This analysis found that there is an optimal loading rate (with respect to eliminating demurrage costs) and suggested bands of optimal ship sizes. Further to these studies, two models of Rusal Aughinish’s shipping process were developed by the group: a simulation model and an analytical model. Both models were found to replicate the shipping process reasonably well and were, hence, used to study alumina output, berth occupancy and demurrage costs.

In this paper we consider a single-server, cyclic polling system with switch-over times. A distin... more In this paper we consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. For this model we study the joint queue length distribution at polling epochs and at the server’s departure epochs. We also study the marginal queue length distribution at arrival epochs, as well as at arbitrary epochs (which is not the same in general, since we cannot use the PASTA property). A generalised version of the distributional form of Little’s law is applied to the joint queue length distribution at customer’s departure epochs in order to find the waiting time distribution for each customer type. We also provide an alternative, more efficient way to determine the mean queue lengths and mean waiting times, using Mean Value Analysis. Furthermore, we show that under certain conditions a Pseudo-Conservation Law for the total amount of work in the sys...

International Journal of Production Research

We consider a small traditional retailer that is managing its inventory under strict cash constra... more We consider a small traditional retailer that is managing its inventory under strict cash constraints, mainly because typically informal loans are offered to customers. These stores are widely present in emerging markets, and we refer to them as nanostores (also called ‘mom-and-pop stores’). As the suppliers require immediate payments for goods delivered, a nanostore can only replenish products to the level for which it has on-hand cash available. To improve delivery efficiency, a supplier might offer a nanostore credit for its replenishments. However, currently, suppliers are often reluctant to do so as these nanostores quickly go bankrupt or disappear, hence defaulting on all outstanding credits. The objective of this paper is to determine when it is beneficial to offer supplier credits. We propose a multi-period, stochastic inventory model, and numerically compare scenarios with and without supplier credits. Our study shows that even in the presence of this risk, suppliers often have good incentives to provide these credits, even if interest is not incurred. For this to hold, the operations of the retailer should be (a little) profitable in the first place, for which we provide analytical conditions.

European Journal of Operational Research

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Slides of presentation during PhD defense: http://tue.academia.edu/SandraVanWijk/Talks/82570/Pooling_and_Polling_Creation_of_Pooling_in_Inventory_and_Queueing_Models

Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools, 2008

Performance Evaluation, 2011

Operations Research Letters, 2013

European Journal of Operational Research, 2012

lateral transshipment policy for a two location inventory problem

In this paper we consider a single-server, cyclic polling system with switch-over times. A distin... more In this paper we consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. For this model we study the joint queue length distribution at polling epochs and at the server’s departure epochs. We also study the marginal queue length distribution at arrival epochs, as well as at arbitrary epochs (which is not the same in general, since we cannot use the PASTA property). A generalised version of the distributional form of Little’s law is applied to the joint queue length distribution at customer’s departure epochs in order to find the waiting time distribution for each customer type. We also provide an alternative, more efficient way to determine the mean queue lengths and mean waiting times, using Mean Value Analysis. Furthermore, we show that under certain conditions a Pseudo-Conservation Law for the total amount of work in the sys...

International Journal of Production Research

European Journal of Operational Research

Downtime of machines is an expensive cost factor for many companies. For this reason, spare parts... more Downtime of machines is an expensive cost factor for many companies. For this reason, spare parts are kept on stock, to be able to quickly respond to breakdowns. We study spare parts inventory models, allowing for stock transfers between the local warehouses, so-called lateral transshipments. In this way, we create pooling of inventory. We investigate when lateral transshipments lead to cost reductions, how these can be optimally applied, and when simple, easy to implement policy are optimal.

I present a basic introduction to polling models, discussing the model, applications, and techniq... more I present a basic introduction to polling models, discussing the model, applications, and techniques for deriving main performance characteristics.

Downtime of machines is an expensive cost factor for many companies. This especially holds for te... more Downtime of machines is an expensive cost factor for many companies. This especially holds for technically advanced machines that are used in the primary processes of their users. Examples include trucks for a transportation company, medical equipment in hospitals, and machines in a production line of manufacturing facilities. To reduce down times, and hence loss of revenue, spare parts are kept on stock at locations close to these machines, to be able to quickly respond to a breakdown. Spare parts, however, can be extremely expensive, while demand rates are very low. We study the resulting multi-location inventory system. In order to reduce costs, we allow for stock transfers between the local warehouses, so-called lateral transshipments. Case studies in literature have shown that cost reduction up till 50% are possible by the use of lateral transshipments, but might also lead to increasing costs. Currently, there is a lack of insights into when exactly costs can be saved. For this, we start by studying a system with two stock points, for which we completely characterized the structure of the optimal policy. We derived conditions under which simple, easy to implement, policies are always optimal. Furthermore, we identiﬁed the parameter settings under which one can gain most from lateral transshipments. For more than two stock points, we characterized the optimal policy structure for a system where only one stock point issues lateral transshipments. Based on these results, we propose a simple to implement, parameterized policy for the general multi- location setting. For this, we constructed an approximation algorithm for the performance characteristics, and well-performing heuristics for the setting of the parameters.

We consider an inventory system with multiple stock points. When a demand occurs at a stock point... more We consider an inventory system with multiple stock points. When a demand occurs at a stock point and there is a part on stock, the demand can be immediately satised. Otherwise, one may apply a lateral transshipment, in which case a part is shipped from a nearby stock point, if it has a part available. The demand is lost otherwise. Both options have a cost, and the optimal choice may depend on the stock levels of all stock points in the system. For inventory problems with lateral transshipments, currently only limited insights are available on optimal policy structures. It is known that a lot of costs can be saved via lateral transshipments; see in particular Kranenburg [2006], who showed a cost reduction of 50% for a spare parts inventory control problem at ASML, an original equipment manufacturer in the semiconductor industry, compared to the situation without lateral transshipments. But, there is a lack of insights into when exactly costs can be saved via lateral transshipments. This depends on the parameters settings, such as the costs for a lateral transshipment.

In previous research, we solved the two location problem, for which we completely characterized the structure of the optimal policy. We derived conditions under which simple, easy to implement, policies are always optimal. Furthermore, we identifed the parameter settings under which one can gain most from lateral transshipments. Currently, we are focusing on multi-location models, with more than two stock points. For a special case, where only one stock point issues lateral transshipments, we characterized the optimal policy structures. However, our current techniques do not straightforwardly generalize to the general multi-location model. Hence, we have to restrict the possibilities for stock transfers in our model. Firstly, we only allow lateral transshipments when a location is stocked-out, although this can be suboptimal in the two location model. Secondly, we probably have to limit or restrict the transshipments between the stock points.

For this model, we want to prove that a so-called hold back pooling strategy is optimal. In this case a stock point can hold it last part(s) back from a lateral transshipment, which is determined by its hold back level. Then, we want to gain insights in the optimal settings of these hold back levels. That is, we want to optimize the lateral transshipment policy within the class of hold back policies. Moreover, from an implementation point of view, such a simple, parameterized policy may be much more attractive than an overall optimal policy. Furthermore, we investigate the gap between the optimal hold back policy and the overall optimal policy.

We consider a polling system where the server cyclically serves the queues in one of the two foll... more We consider a polling system where the server cyclically serves the queues in one of the two following ways: either the server does the entire round of visits to the queues applying the gated service discipline at each of the queues (serve exactly those customers in a queue present upon arrival), or it does the entire round of visits applying the exhaustive service discipline at each of the queues (serve all customers in a queue until it has become empty). We call this a polling systems with gated and exhaustive cycles. We study the case of a fixed, repeating pattern for the disciplines of a cycle, e.g. repedeatly gated-gated-exhaustive. We derive a Pseudo Conservation Law for the weighted sum of the mean waiting times, the mean steady state waiting times using Mean Value Analysis and Smart Customers, the queue length distributions making use of results for Multitype Branching Processes, and the sojourn time distributions. Moreover, we derive an approximate evaluation using an interpolation of light traffic and heavy traffic results. We use this to optimize the pattern, o.a. to balance the waiting times in each of the queues. As a model variation, we study the system where a coin toss decides the discipline of a cycle.

Motivated by a workload control setting, we study a model where two types of customers are served... more Motivated by a workload control setting, we study a model where two types of customers are served by a single server according to the head-of-line processor sharing discipline. Regular customers and opportunity customers are arriving to the system according to two independent Poisson processes, each requiring an exponentially distributed service time. The regular customers will queue, incurring some holding costs. On contrary, an opportunity customer has to be taken into service directly, or is lost otherwise. There can be at most one opportunity customer in the system. The server can work on both one regular and one opportunity customer at the same time, where one can decide on how the server speed is split out. Moreover, one can decide whether to accept or reject an opportunity customer, incurring penalty costs for the latter. In this way, one has partial control about the workload in the system. We formulate the model as a Markov decision problem. We prove that the optimal policy, minimizing the expected discounted long-run cost, has a monotone structure in the number of regular customers. That is, the optimal policy for accepting an opportunity customer is described be a threshold, and the fraction of the server's attention devoted to the opportunity customer is a monotone decreasing function. Further, we generalize our model to the case where opportunity customers will queue as well, and to the case where also regular customers can be rejected.

We study a surveillance wireless sensor network (SWSN) comprised of small and low-cost sensors. T... more We study a surveillance wireless sensor network (SWSN) comprised of small and low-cost sensors. These are deployed in a region in order to detect objects crossing the ﬁeld of interest. We address two problems concerning the design and performance of an SWSN: optimal sensor placement and algorithms for object detection in the presence of false alarms. For both problems, we propose explicit decision rules and e"cient algorithmic solutions. Further, we provide several numerical examples and present a simulation model that combines our placement and detection methods. The problem was presented to the Study Group Mathematics with Industry in 2008 by Thales.

We consider an inventory system with multiple stock points. When a demand occurs at a stock point... more We consider an inventory system with multiple stock points. When a demand occurs at a stock point and there is a part on stock, the demand can be immediately satisﬁed. Otherwise, one may apply a lateral transshipment, in which case a part is shipped from a nearby stock point if it has a part on stock. The demand is lost otherwise. Both options have a cost, and the optimal choice may depend on the stock levels of all stock points in the system. For inventory problems with lateral transshipments, currently only limited insights are available on optimal policy structures. It is known that a lot of costs can be saved via lateral transshipments; see in particular Kranenburg [2006], who showed a cost reduction of 50% for a spare parts inventory control problem at ASML, compared to the situation without lateral transshipments. But, there is a lack of insights into when exactly costs can be saved via lateral transshipments. This depends on the parameters settings, such as the costs for a lateral transshipment.

For this, we studied a system with two stock points, for which we completely characterized the structure of the optimal policy. We derived conditions under which simple, easy to implement, policies are always optimal. Furthermore, we identiﬁed the parameter settings under which one can gain most from lateral transshipments. For more than two stock points, we characterized the optimal policy structure for a system where only one stock point issues lateral transshipments. Moreover, we constructed an approximation algorithm for the general multi- location setting, determining the performance when executing a given policy. This can also be used for the optimization of parameters within a given class of policies, as from an implementation point of view, a simple parameterized policy may be much more attractive than an overall optimal policy. Furthermore, we investigated the gap between the optimal policy within a given class of parameterized policies and the overall optimal policy.

We consider a continuous-time, single-echelon, multi-location inventory model with Poisson demand... more We consider a continuous-time, single-echelon, multi-location inventory model with Poisson demand processes. In case of a stock-out at a local warehouse, a demand can be fulfilled via a lateral transshipment (LT). Each warehouse is assigned a predetermined sequence of other warehouses where it will request for an LT. However, a warehouse can hold its last part(s) back from such a request. This is called a hold back pooling policy, where each warehouse has hold back levels determining whether a request for and LT by another warehouse is satisfied. We are interested in the fractions of the demand satisfied from stock (fill rate), satisfied via a lateral transshipment, and via an emergency shipment from an external source. From this the average costs of a policy could be determined. We present two approximation algorithms for evaluation of a given policy, approximating the mentioned fractions. The first one, the Poisson overflow algorithm, is an extension of algorithms known in the literature. The second one, the On/Off overflow algorithm is new and more sophisticated. Instead of approximating the stream of LT-requests from a warehouse as a Poisson process, we use an interrupted Poisson process. This is a process that is turned alternatingly On and Off for exponentially distributed durations. In a numerical study we show that both algorithms perform very well. The On/Off algorithm is significantly more accurate than the Poisson algorithm, but requires longer computation times.

We consider an inventory model for spare parts, where two stockpoints provide repairable parts fo... more 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, ready-for-use 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.

We study a multi-location inventory model where, in case of stock-outs, emergency lateral transsh... more We study a multi-location inventory model where, in case of stock-outs, emergency lateral transshipments can take place from a so-called quick response warehouse. We characterize and proof the structure of the optimal policy, we prove conditions under which it simplifies, and we evaluate the performance of simple heuristics as approximations for the optimal policy.

We consider a polling system, where a single server cyclically serves the queues, with positive s... more We consider a polling system, where a single server cyclically serves the queues, with positive switch-over times. Our goal is to minimize the differences in the mean waiting times at each of the queues, i.e. to achieve maximal fairness, without giving up too much on the efficiency of the system. For this, we introduce the k-Gated service discipline, which can be seen as a hybrid version of the well known exhaustive discipline (very efficient, less fair) and gated discipline (less efficient, usually more fair). Upon arrival of the server at queue i, it services the queue consecutively an integer number of times, k_i, according to the gated discipline. That is, a first gate closes and only the customers before this gate are served, then a second gate closes, and again only the customers before this gate are served, etcetera, until this is done k_i times, or until the queue becomes empty. We derive the distribution of the waiting times, a pseudo conservation law for the weighted sum of the mean waiting times, and the fluid limits of the waiting times. The latter we use for optimization of the k_i's, and we provide heuristics for well working settings.

We consider a single-server, cyclic polling system with switch-over times. A distinguishing featu... more We consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. We refer to this as 'smart customers', as an example of this is the situation where arriving customers choose which queue they join, based on the current position of the server. For this system, we derive the waiting time distribution for each customer type, by applying a generalized version of the distributional form of Little’s law to the joint queue length distribution at departure epochs. We also provide an alternative, more efficient way to determine the mean queue lengths and mean waiting times, using Mean Value Analysis for polling systems. Under certain conditions, a Pseudo-Conservation Law for the total amount of work in the system holds. Typical features of the model under consideration are demonstrated in several numerical examples, for instance the optimal queue for customers to join.