eCommons Community:
http://hdl.handle.net/1813/525
20150704T15:29:06Z

Ful lling Orders in a MultiEchelon Capacitated Online Retail System: PART TWO, realtime purchasing and ful llment decision making
http://hdl.handle.net/1813/40146
Title: Ful lling Orders in a MultiEchelon Capacitated Online Retail System: PART TWO, realtime purchasing and ful llment decision making
Authors: Li, Juan; Muckstadt, John
Abstract: When ful lling customer orders, online retailers must operate their multiwarehouse systems with great
care to ensure that these orders are satis ed in a timely and cost e ective manner. We worked closely with
a major online retailer to design an e ective and e cient ful llment system. This included establishing
policies and procedures for ordering, receiving, storing and shipping of goods. Internal warehousing and
transportation practices were addressed, and new approaches for managing inventories were established. In
this paper we focus on one type of inventory management problem faced by the company when making
daily purchasing and allocation decisions. These decisions are of two types, the positioning of inventories in
their multiechelon system and the detailed manner in which they use inventories to ful ll speci c customer
orders. After reviewing some of the key attributes of models that address the two types of decision problems,
we present a computationally tractable approach for solving these problems for a system that must ful ll
many hundreds of thousands of orders daily.
20150513T00:00:00Z

Asymptotic Normality of Degree Counts in a Preferential Attachment Model
http://hdl.handle.net/1813/39933
Title: Asymptotic Normality of Degree Counts in a Preferential Attachment Model
Authors: Resnick, Sidney; Samorodnitsky, Gennady
Abstract: Preferential attachment is a widely adopted paradigm for understanding
the dynamics of
social networks. Formal statistical inference,
for instance GLM techniques, and model
verification methods will require knowing test statistics are asymptotically
normal even though node or count based
network data is nothing like classical data from
independently replicated experiments. We therefore study asymptotic
normality of degree counts for a sequence of growing simple undirected
preferential attachment graphs. The methods of proof rely on
identifying martingales and then exploiting the martingale central
limit theorems.
20150428T00:00:00Z

Functional central limit theorem for negatively dependent heavytailed stationary infinitely divisible processes generated by conservative flows
http://hdl.handle.net/1813/39288
Title: Functional central limit theorem for negatively dependent heavytailed stationary infinitely divisible processes generated by conservative flows
Authors: Jung, Paul; Owada, Takashi; Samorodnitsky, Gennady
Abstract: We prove a functional central limit theorem for
partial sums of symmetric stationary long range dependent heavy tailed
infinitely divisible processes with a certain type of negative
dependence. Previously only positive dependence could be treated. The
negative dependence involves cancellations of the Gaussian second
order. This
leads to new types of {limiting} processes involving stable random
measures, due to heavy tails, MittagLeffler processes, due to long
memory, and Brownian motions, due to the Gaussian second order
cancellations.
20150406T00:00:00Z

MultiPeriod Stock Allocation Via Robust Optimization
http://hdl.handle.net/1813/39275
Title: MultiPeriod Stock Allocation Via Robust Optimization
Authors: Jackson, Peter; Muckstadt, John
Abstract: In this paper we revisit a longstanding multiechelon inventory allocation problem from a robust optimization perspective. We formulate the problem as a one warehouse, Nretailer, multiperiod, stock allocation problem in which holding costs are identical at each location and
no stock is received from outside suppliers for the duration of the planning horizon. Stock may be transferred from the central warehouse to
the retailers instantaneously and without cost at the beginning of each
period for which the central warehouse still has stock on hand. No other
stock transfers are allowed. Under this setup, the only motive for holding inventory at the central warehouse for allocation in future periods is
the socalled riskpooling motive. The dynamic programming formulation
of this problem requires a state space too large for practical computation. Various approximation methods have been proposed for variants of
this problem. We apply robust optimization to this problem extending
the typical uncertainty set to capture the risk pooling phenomenon and
extending the inventory policy to allow for an adaptive, nonanticipatory
shipment policy. We show how to represent the uncertainty set compactly
so that it grows by no more than the square of the number of retailers.
The problem can be solved using Benders decomposition in the general
case. In the special case of no initial retailer inventories, two periods, and
identical retailers, a relaxed form of the problem admits a closed form
solution with surprising insights. Summarizing the experimental results
of the paper, we see both confirmation of the value of the robust optimization approach as well as managerial insights into the design and operation
of multiechelon inventory systems.
20150325T00:00:00Z

Climbing down Gaussian peaks
http://hdl.handle.net/1813/39077
Title: Climbing down Gaussian peaks
Authors: Adler, Robert; Samorodnitsky, Gennady
Abstract: How likely is the high level of a continuous Gaussian random field on
an Euclidean space to
have a ``hole'' of a certain dimension and depth? Questions of this
type are difficult, but in this paper we make progress on questions
shedding new light in existence of holes. How likely is the field to
be above a high level on one compact set (e.g. a sphere) and to be
below a fraction of that level on some other compact set, e.g. at the
center of the corresponding ball? How likely is the field to be below that
fraction of the level anywhere nside the ball? We work on the
level of large deviations.
20150128T00:00:00Z

Numerical Validation of Fill Rate Estimation Methods for Two and ThreeDemand Class Rationing Policies with OneforOne Replenishment and General Lead Time Distributions
http://hdl.handle.net/1813/39019
Title: Numerical Validation of Fill Rate Estimation Methods for Two and ThreeDemand Class Rationing Policies with OneforOne Replenishment and General Lead Time Distributions
Authors: Vicil, Oguzhan; Jackson, Peter
Abstract: In this report, we conduct numerical simulations of two and threedemand class inventory threshold rationing systems under oneforone replenishment policies. The performance metrics of interest are the fill rates of the high priority demand classes (the gold fill rate in the two demand
class system and the platinum and gold fill rates in the threedemand class system).
Our main interest is in the sensitivity of these fill rates to the form of the replenishment lead time probability distribution and the resulting quality of approximation methods used to estimate
these fill rates. We consider three approximation methods: what we call the single cycle approach attributed to Dekker et al and Deshpande et al, the embedded Markov chain approach of Fadigloglu and Bulut, and the continuous time Markov chain approach of Vicil and Jackson.
We confirm the superiority of the embedded Markov chain approach for the case of constant lead times but we find that the fill rates are relatively insensitive to the form of the lead time distribution and both latter approaches, the embedded Markov chain approach and the continuous time Markov chain approach, perform well over wide ranges of lead time variability. For the
threedemand class system, we demonstrate that it is possible to achieve highly differentiated fill rates by demand class and show that these fill rates can be estimated with high accuracy using the continuous time Markov chain approach, provided the fill rate of the lowest priority demand class (the silver fill rate) is not too low.
20150108T00:00:00Z

Timechanged extremal process as a random sup measure
http://hdl.handle.net/1813/37941
Title: Timechanged extremal process as a random sup measure
Authors: Lacaux, CĂ©line; Samorodnitsky, Gennady
Abstract: A functional limit theorem for the partial maxima of a long memory
stable sequence produces a limiting process that can be described as a
betapower time change in the classical Fr\'echet
extremal process, for beta in a subinterval of the unit
interval. Any such power time change in the extremal process
for 0<beta<1 produces a process with stationary
maxincrements. This deceptively simple time change hides the much
more delicate structure of the resulting process as a selfaffine
random sup measure. We uncover this structure and show that in a
certain range of the parameters this random measure arises as a limit
of the partial maxima of the same long memory stable sequence, but in
a different space. These results open a way to construct a whole new
class of selfsimilar Fr\'echet processes with stationary
maxincrements.
20141009T00:00:00Z

Tauberian Theory for Multivariate Regularly Varying Distributions with Application to Preferential Attachment Networks
http://hdl.handle.net/1813/36712
Title: Tauberian Theory for Multivariate Regularly Varying Distributions with Application to Preferential Attachment Networks
Authors: Resnick, Sidney; Samorodnitsky, Gennady
Abstract: AbelTauberian theorems relate power
law behavior of distributions and their transforms. We formulate and
prove a multivariate version for nonstandard regularly varying
measures on R_+^p and then apply it to
prove that the joint distribution of in and outdegree in a directed edge
preferential attachement model has jointly regularly varying
tails.
20140625T00:00:00Z

Nonstandard regular variation of the indegree and the outdegree in the preferential attachement model
http://hdl.handle.net/1813/36711
Title: Nonstandard regular variation of the indegree and the outdegree in the preferential attachement model
Authors: Samorodnitsky, Gennady; Resnick, Sidney; Towsley, Don; Davis, Richard; Willis, Amy; Wan, Phyllis
Abstract: For the directed edge preferential attachment network growth model
studied by Bollobas et al. (2003) and
Krapivsky and Redner (2001), we prove that the joint distribution of
indegree and
outdegree
has jointly regularly varying
tails.
Typically the marginal tails of the indegree distribution and the outdegree
distribution have different regular variation indices and so the joint
regular variation is nonstandard.
Only marginal regular variation has been
previously established for this distribution in the cases where the
marginal tail indices are different.
20140625T00:00:00Z

General inverse problems for regular variation
http://hdl.handle.net/1813/34411
Title: General inverse problems for regular variation
Authors: Damek, Ewa; Mikosch, Thomas; Rosinski, Jan; Samorodnitsky, Gennady
Abstract: Regular variation of distributional tails is known to be preserved by
various linear transformations of some random structures.
An inverse problem for regular
variation aims at understanding whether the regular variation of a
transformed random object is caused by regular variation of components
of the original random structure. In this paper we build up on previous
work and derive results in the multivariate case and in
situations where regular variation is
not restricted to one particular direction or quadrant.
20131002T00:00:00Z