zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A static approximation for dynamic demand substitution with applications in a competitive market. (English) Zbl 1167.90330
Summary: We propose a static approximation of dynamic demand substitution behavior based on a fluid network model and a service-inventory mapping. This approximation greatly enhances our ability to analyze the interdependent inventory/service, price, and product assortment decisions in noncompetitive and competitive scenarios with demand substitution. We demonstrate that the approximation is well behaved and then apply it to two previously intractable applications. First, we study a price and service competition between single-product retailers. After establishing a unique pure-strategy Nash equilibrium, we find that competition results in lower price, higher demand, and a higher level of inventory. We also observe that the aggregate profit and inventory level increase to positive constants as the number of retailers goes to infinity. Second, we study a duopolistic competition on price, service, and product assortment. We establish a pure-strategy Nash equilibrium for the product assortment competition and identify a condition for uniqueness. We find that competition on both price and product assortment results in lower price and less variety for each competitor, but the total number of products and the aggregate inventory level in a duopoly market are both likely to be higher than in a monopolistic market.
MSC:
90B05Inventory, storage, reservoirs
90B15Network models, stochastic (optimization)