Stochastic Activity Month
September 2012
"Stochastic Operations Management"
Workshop Pricing & Staffing
September 101112
SUMMARY  SPEAKERS  SPONSORS  REGISTRATION 
Advances in information technology enable online decision making based on incoming data streams. In operations management, this is relevant for assigning workforce to various different tasks (either answer phone calls or do administration in the next half hour) and for optimizing prices. This requires a blend of techniques from adaptive control theory and statistics, game theory, stochastic modeling and optimization. The keynote speakers are experts on staffing and pricing, both in traditional operations management as well as adjacent areas such as internet pricing and road pricing. Staffing is important in call centers, but also in health care  two emerging key applications are ambulance planning and staffing of emergency wards.
Keynote speakers: Frank Kelly, Marty Reiman, Assaf Zeevi
ORGANIZERS
Onno Boxma  TU Eindhoven 
Assaf Zeevi  Columbia University 
Bert Zwart  CWI/ VU Amsterdam 
Arnoud den Boer  CWI 
Eugene Feinberg  State University of New York at Stony Brook 
Richard Gibbens  Cambridge University 
Moshe Haviv  Hebrew University of Jerusalem 
Frank Kelly  University of Cambridge 
Frank Karsten  TU Eindhoven 
Anton Kleywegt  Georgia Tech 
Vidyadhar Kulkarni  University of North Carolina, Chapel Hill 
Johan van Leeuwaarden  TU/e 
Marty Reiman  AlcatelLucent Bell Labs 
Adam Wierman  Caltech 
Assaf Zeevi  Columbia University 
Bert Zwart  CWI / VU Amsterdam 
Please fill in the online registration form by following the link to the TU/e website. There is no registration fee for this workshop. We do however ask a contribution for participating in the conference dinner (date not yet fixed, most probably Monday sep 10)
Monday September 10
10.00  10.30  Registration  
10.30  11.15  Marty Reiman  Dynamic Pricing for Network Revenue Management  
11.15  11.45  Coffee/tea  
11.45  12.30  Adam Wierman (1)  Congestion and price competition in the cloud  
12.30  14.00  Lunch  
14.00  14.45  Moshe Haviv  Regulating a queue when customers know their demand  
14.45  15.15  Coffee/tea  
15.15  16.00  Frank Karsten 
Resource pooling and cost allocation among independent service providers 

16.00  16.15  Coffee/tea  
16.15  17.00  Johan van Leeuwaarden  Staffing systems with admission control  
18.30   Conference dinner 
Tuesday September 11
10.30  11.15  Assaf Zeevi  Model misspecification and dynamic pricing  
11.15  11.45  Coffee/tea  
11.45  12.30  Bert Zwart  On the Benefits of Price Dispersion in Revenue Management  
12.30  14.00  Lunch  
14.00  14.45  Richard Gibbens 
Staffing banks of supermarket tills/Control policies in energy storage systems 

14.45  15.15  Coffee/tea  
15.15  16.00  Arnoud Den Boer  Two extensions of the singleproduct infiniteinventory dynamic pricing problem under uncertainty  
16.00  16.15  Coffee/tea  
16.15  17.00  Anton Kleywegt  DerivativeFree Optimization Methods for Price Optimization 
Wednesday September 12
10.30  11.15  Eugene Feinberg  Pricebased admission to M/M/k/N queues with multiple customer classes  
11.15  11.45  Coffee/tea  
11.45  12.30  Vidyadhar Kulkarni  Design and analysis of concierge option for a service offering  
12.30  14.00  Lunch  
14.00  14.45  Adam Wierman (2)  Energy procurement in the presence of intermittent sources  
14.45  15.15  Coffee/tea  
15.15  16.00  Frank Kelly  Open questions on pricing for electricity networks  
16.00  16.15  Coffee/tea 
Arnoud den Boer
Two extensions of the singleproduct infiniteinventory dynamic pricing problem under uncertainty
(i) The first extension
considers a firm that sells multiple products, with sufficient inventory. The
demand of a product does not only depend on its own selling price, but also on
the selling prices of other products; in this way we can model substitute or
complementary products.
We deploy a parametric demand model, with unknown parameters that can be
estimated with maximum quasilikelihood estimation.
Just as in the singleproduct case, the firm needs to actively experiment with
selling prices in order to eventually learn all unknown parameters. If it would
instead use "certaintyequivalent pricing"  always selecting prices that are
optimal w.r.t. available parameter estimates , then the parameter estimates may
never converge to their true value. Optimal price experimentation can be
achieved by deviating from the certainty equivalent price such that a certain
amount of price dispersion is guaranteed. In the singleproduct case, this can
be done by requiring a lower bound on the sample variance of chosen prices.
In the multidimensional case, price dispersion is measured by the smallest
eigenvalue of a statistical design matrix. We show how the growth rate of this
eigenvalue can be controlled by requiring the selling prices to satisfy a simple
quadratic constraint, and discuss the performance of the resulting pricing
policy.
(ii) The second extension considers a firm that sells a finite number of
products during a finite time period. This is one of the moststudied situations
in dynamic pricing and revenue management problems. In contrast to the previous
setting, a certaintyequivalent pricing policy performs extremely well, and no
active price experimentation is necessary. The reason is that this system
satisfies an "endogenous learning property": the continuously changing marginal
value of inventory implies that the optimal prices are fluctuating over time.
The resulting large amount of price dispersion causes the parameter estimates to
converge very quickly to their true values, which makes the certaintyequivalent
pricing policy structurally better than any pricing policy can achieve in
setting (i).
Eugene Feinberg
We study optimal admission to an M/M/k/N queue with several customer types. The reward structure consists of two functions: prices that customers are willing to pay for services and of holding costs. Both functions may depend on a customer type. This paper studies average rewards per unit time and describes the structures of stationary optimal, canonical, bias optimal, and Blackwell optimal policies. Similar to the case without holding costs, bias optimal and Blackwell optimal policies are unique, coincide, and have a trunk reservation form with the largest optimal control level for each customer type. Problems with one holding cost function for all customer types have been studied previously. The problem with holding costs depending on customer types is more difficult. In particular, there may exist canonical policies that do not have the trunk reservation structure. This is impossible when holding costs do not depend on customer classes.
Richard Gibbens
Staffing banks of supermarket tills/Control policies in energy storage systems
This talk will address two
separate topics. The first topic will be a case study of staffing a bank of
supermarket tills under dynamic workloads such as to meet a customerrelated key
performance indicator. We use actual measured data of customer arrivals and
service times gathered from multiple tills and present results on daily
workloads, staffing levels and discuss open problems.
The second topic is work in progress studying control policies for balancing
large scale energy storage networks. We consider a simplified version of the
problem which can be formulated as a minimum cost circulation problem with buy
and sell market prices for energy and a storage device limited by power
constraints on energy flowing in and out as well as a overall storage capacity.
We study this simplified problem in some detail using actual data on prices and
a spectrum of storage parameters as preparation for a fuller model which we
shall sketch. Joint work with Andrei Bejan, Janusz Bialek, James Cruise, Chris
Dent, Frank Kelly and Stan Zachary.
Moshe Haviv
Regulating a queue when customers know their demand
Selfish customers do not join
the queue at a rate which is socially optimal. Hence, some queueing systems call
for regulations. For the unobservable (not necessarily FCFS) M/G/1 queue and
homogeneous customers with respect to waiting costs and service rewards, we show
how this can be done in the case that customers know their service requirements
by the imposition of an entry, holding or service fee. We commenced with a
unified approach, imposing minimal assumptions on the waiting functions and
state the socially optimal fees.
We show that customers are always worse off under a flat entry free. As for
holding vs. service fees, the answer depends on the queueing regime and/or the
actual service requirement.
For example, under FCFS, service fees are preferable to all. Finally, a similar
question is looked at but from the point of view of a profit maximizer. We show
that this scheme leads to an excessive entry fee which implies under utilization
of the server.
Frank Karsten
Resource pooling and cost allocation among independent service providers
We study a situation where several independent service providers collaborate by complete pooling of their resources and customer streams into a joint service system. These service providers may represent such diverse organizations as hospitals that pool beds or maintenance firms that pool repairmen. We model the service systems as Erlang delay systems (M/M/s queues) that face a fixed cost rate per server and homogeneous delay costs for waiting customers. We examine rules to fairly allocate the collective costs of the pooled system amongst the participants by applying concepts from cooperative game theory. (A brief introduction to cooperative game theory will be provided during the presentation.) We consider both the case where players' numbers of servers are exogenously given and the scenario where any coalition picks an optimal number of servers. By exploiting new structural properties of the continuous extension of the classic Erlang delay function, we analyze whether the games under consideration possess a core allocation (i.e., an allocation that gives no group of players an incentive to split off and form a separate pool).
Frank Kelly
Open questions on pricing for electricity networks
In future electricity
networks there is expected to be substantially more supply from renewable
sources (wind, solar, tidal, etc).
There is currently no clear consensus on whether the intermittency of many
renewable sources can be handled by means such as demand management and storage.
This talk will aim to stimulate discussion on some of the pricing issues that
may, or may not, be relevant.
Anton Kleywegt
DerivativeFree Optimization Methods for Price Optimization
Consider the problem of
choosing prices for a number of products in a setting in which the demands as a
function of prices are not known.
Recently several researchers have studied versions of this problem, mostly with
a single product and a parametric family of demand functions, and proposed
methods to estimate the demand function parameters while controlling the price
in such a way that the regret will be small. Another line of research does not
restrict attention to a parametric family of demand functions, and does not
attempt to learn the demand functions, but only searches for the optimal price
through a sequence of local approximations. This type of approach to
optimization has been called derivativefree optimization, and has been studied
for some time. However, the pricing problem has introduced new aspects to
derivativefree optimization. The talk will provide an overview of
derivativefree optimization with random objective function observations, with
particular aspects introduced by the multiple product pricing problem.
Vidyadhar Kulkarni
Design and analysis of concierge option for a service offering
Concierge Medicine is the most visible implementation of a new trend of introducing a feebased premier option in a service offering. This is usually done for the purposes of segmenting customers based on their willingness or ability to wait for the service. Using a realistic yet representative model setup, we perform a detailed analysis to (i) determine the conditions (fees, cost structure, etc.) under which the concierge option is profitable for the service provider, (ii) quantify benefits accrued by the premier customers; and (iii) evaluate the resulting impact on the other customers. We show that, under a wide range of system parameters, introducing a concierge option benefits every one and also compute the magnitude of these benefits. These benefits are larger when the variance in the customer waiting costs is high and the system utilization is high. We complement these results with data on the adoption of MDVIP (the most popular concierge medical service in the US) and show that the areas where it was adopted have higher median incomes and older population and thus are amenable to higher (by about 9\%) revenues for the service provider.
Johan van Leeuwaarden
Staffing systems with admission control
In manyserver
systems it is crucial to staff the right number of servers so that targeted
service levels are met. These staffing problems typically lead to constraint
satisfaction problems that are hard to solve. During the last decade, a powerful
manyserver asymptotic theory has been developed to solve such problems and
optimal staffing rules are known to obey the squareroot staffing principle. We
develop manyserver asymptotics in the socalled QED regime, and present
refinements to manyserver asymptotics and squareroot staffing for a Markovian
queueing model with admission control and retrials.
(joint work with Florin Avram and Guido Janssen)
Martin I. Reiman
Dynamic Pricing for Network
Revenue Management
We consider a dynamic pricing problem that arises in a revenue management
context. It involves several resources and several demand classes, each of which
uses a particular subset of the resources. The arrival rates of demand are
determined by prices, which can be dynamically controlled. When a demand
arrives, it pays the posted price for its class and consumes a quantity of each
resource commensurate with its class. The time horizon is finite: at time T the
demands cease, and a terminal reward (possibly negative) is received that
depends on the unsold capacity of each resource. The problem is to choose a
dynamic pricing policy to maximize the expected total reward.
We describe a related, and much simpler, ?diffusion control problem?, the
solution to which provides an asymptotically optimal control as the resource
capacities and arrival rates grow large. This diffusion control is obtained as a
perturbation of an even simpler, deterministic, ?fluid optimization problem?,
which we also present. We show how to solve both the fluid optimization problem
and diffusion control problem in the context of two ?airline? motivated
problems.
(joint work with Rami Atar (Technion))
Adam Wierman (1)
Congestion and price
competition in the cloud
Abstract: The cloud marketplace has evolved into a highly complex economic
system made up of a variety of services. As a result of this complicated
marketplace, the performance delivered to users by cloud services depends on the
the resource allocation design of the service itself and the strategic
incentives resulting from the multitiered economic interactions among cloud
providers. In this talk I will present work developing and analyzing some new
models capturing the interaction this multitiered interaction in a manner that
exposes the interplay of congestion, pricing, capacity provisioning, and
performance. This talk will present joint work with Jonatha Anselmi, Urtzi
Ayesta, Jayakrishan Nair, and Bert Zwart.
Adam Wierman (2)
Energy procurement in the presence of intermittent sources
The increasing penetration of
intermittent, unpredictable renewable energy sources, such as wind energy, poses
significant challenges for the utility companies trying to incorporate renewable
energy into their portfolios. As a result, there is considerable discussion
about how electricity markets should be restructured in order to facilitate the
integration of renewable energy into the grid. Suggestions include adding
additional markets, moving markets, closer to realtime, etc. In this talk, I
will discuss how the optimal energy procurement of a utility company changes as
a result of an increasing penetration of intermittent renewable resources, and
what impact this should have on electricity market structure.
(Joint with Sachin Adlakha and Jayakrishnan Nair)
Bio: Adam Wierman is a Professor in the Department of Computing and Mathematical
Sciences at the California Institute of Technology, where he is a member of the
Rigorous Systems Research Group (RSRG). His research interests center around
resource allocation and scheduling decisions in computer systems and services.
He received the ACM SIGMETRICS Rising Star award in 2011, and has been
corecipient of best paper awards at ACM SIGMETRICS, IEEE INFOCOM, IFIP
Performance, IEEE Green Computing Conference, and ACM GREENMETRICS.
Additionally, he has received multiple teaching awards, including the Associated
Students of the California Institute of Technology (ASCIT) Teaching Award.
Assaf Zeevi
Model misspecification and dynamic pricing
Sequential pricing problems
typically entail some modeling of consumer purchasing behavior, or in more
aggregate form, the demand curve. There is a growing literature, most of it
recent, that is concerned with the impact of not knowing the demand curve a
priori, and learning it on the fly (a problem often referred to as learning and
earning).
In such problem instances, the decision maker constructs a class of demand
models which is then calibrated to observed sales and in turn provides the basis
for subsequent pricing decisions.
In this talk we will be concerned with the following aspect of this dynamic
optimization problem under model uncertainty:
what happens if the assumed class of demand models does not encompass the true
underlying demand curve, i.e, if the model is misspecified.
(joint work with Omar Besbes, Columbia University)
Assaf Zeevi is the Henry Kravis
Professr at the Graduate School of Business, Columbia University, and currently
serves as Vice Dean for Research. He graduated from Stanford in 2001, and since
then has been a faculty at Columbia. His research is broadly focused on the
formulation and analysis of mathematical models of complex systems. He is
particularly interested in the areas of stochastic modeling and statistics and
their synergistic application to problems arising in service operations, revenue
management, information services, and financial engineering.
Bert Zwart
On the Benefits of Price Dispersion in Revenue Management
For a stylized model in dynamic pricing,
it can be shown that the socalled 'certainty equivalent pricing' policy, where
estimating consumer behavior and optimizing profit are completely decoupled,
does not lead to optimal profit.
Thus, it is necessary to develop algorithms that ensure that the right amount of
price experimentation is undertaken so as to learn and exploit consumer behavior
as efficiently as possible.
Our key tool is a new result on L2 convergence rates for maximum likelihood
estimators for generalized linear models with adaptive design.
(joint work with Arnoud den Boer)