433 research outputs found
A Suspension Lemma for Bounded Posets
Let and be bounded posets. In this note, a lemma is introduced that
provides a set of sufficient conditions for the proper part of being
homotopy equivalent to the suspension of the proper part of~. An application
of this lemma is a unified proof of the sphericity of the higher Bruhat orders
under both inclusion order (a known proved earlier by Ziegler) and single step
inclusion order (which was not previously known)
Demand forecasting for companies with many branches, low sales numbers per product, and non-recurring orderings
We propose the new Top-Dog-Index to quantify the historic deviation of the
supply data of many small branches for a commodity group from sales data. On
the one hand, the common parametric assumptions on the customer demand
distribution in the literature could not at all be supported in our real-world
data set. On the other hand, a reasonably-looking non-parametric approach to
estimate the demand distribution for the different branches directly from the
sales distribution could only provide us with statistically weak and unreliable
estimates for the future demand. Based on real-world sales data from our
industry partner we provide evidence that our Top-Dog-Index is statistically
robust. Using the Top-Dog-Index, we propose a heuristics to improve the
branch-dependent proportion between supply and demand. Our approach cannot
estimate the branch-dependent demand directly. It can, however, classify the
branches into a given number of clusters according to an historic oversupply or
undersupply. This classification of branches can iteratively be used to adapt
the branch distribution of supply and demand in the future.Comment: 6 pages, 7 figure
Lotsize optimization leading to a -median problem with cardinalities
We consider the problem of approximating the branch and size dependent demand
of a fashion discounter with many branches by a distributing process being
based on the branch delivery restricted to integral multiples of lots from a
small set of available lot-types. We propose a formalized model which arises
from a practical cooperation with an industry partner. Besides an integer
linear programming formulation and a primal heuristic for this problem we also
consider a more abstract version which we relate to several other classical
optimization problems like the p-median problem, the facility location problem
or the matching problem.Comment: 14 page
Evaluation of a new supply strategy based on stochastic programming for a fashion discounter
Fashion discounters face the problem of ordering the right amount of pieces
in each size of a product. The product is ordered in pre-packs containing a
certain size-mix of a product. For this so-called lot-type design problem, a
stochastic mixed integer linear programm was developed, in which price cuts
serve as recourse action for oversupply. Our goal is to answer the question,
whether the resulting supply strategy leads to a supply that is significantly
more consistent with the demand for sizes compared to the original manual
planning. Since the total profit is influenced by too many factors unrelated to
sizes (like the popularity of the product, the weather or a changing economic
situation), we suggest a comparison method which excludes many outer effects by
construction. We apply the method to a real-world field study: The improvements
in the size distributions of the supply are significant.Comment: 5 pages, 1 tabl
Optimal Opinion Control: The Campaign Problem
Opinion dynamics is nowadays a very common field of research. In this article
we formulate and then study a novel, namely strategic perspective on such
dynamics: There are the usual normal agents that update their opinions, for
instance according the well-known bounded confidence mechanism. But,
additionally, there is at least one strategic agent. That agent uses opinions
as freely selectable strategies to get control on the dynamics: The strategic
agent of our benchmark problem tries, during a campaign of a certain length, to
influence the ongoing dynamics among normal agents with strategically placed
opinions (one per period) in such a way, that, by the end of the campaign, as
much as possible normals end up with opinions in a certain interval of the
opinion space. Structurally, such a problem is an optimal control problem. That
type of problem is ubiquitous. Resorting to advanced and partly non-standard
methods for computing optimal controls, we solve some instances of the campaign
problem. But even for a very small number of normal agents, just one strategic
agent, and a ten-period campaign length, the problem turns out to be extremely
difficult. Explicitly we discuss moral and political concerns that immediately
arise, if someone starts to analyze the possibilities of an optimal opinion
control.Comment: 47 pages, 12 figures, and 11 table
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