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 theory of supply chains. (English) Zbl 1030.90003
Lecture Notes in Economics and Mathematical Systems. 526. Berlin: Springer. viii, 123 p EUR 32.95/net; $ 47.00; £23.00; sFr 56.50 (2003).

The author investigates supply chains, i.e., networks where suppliers produce goods for generic customers, possibly visiting intermediate suppliers and being altered or combined in the process. The output of each supplier is determined by a function of its inputs. The size of flows of different goods through the network depends on the customer demand, the flow of orders across suppliers, and on the policies that the suppliers use to place orders and replenish their inventories.

The investigations are mainly restricted to a serial supply system where supplier j receives all its input from supplier j+1 and ships all his goods to supplier j-1. It is assumed that the order policy of supplier j is based exclusively on the order history of supplier j-1 on the one hand and its own status on the other hand. The book investigates the instability of such policies, i.e., the increased variability of order sizes and inventory levels with the supplier as j increases.

For analyzing the stability of order policies the concept of stability in the small and stability in the large (as considered in control theory) are introduced, where the former means that any infinitesimal perturbation in the customer demand input when the system is in a steady state generates only infinitesimal order size and inventory perturbations for any supplier j, and the latter means that the order size and the inventory must be bounded for all j at any time.

Necessary and sufficient conditions for policies assuring stability in the small are developed. Moreover, the class of strongly stable policies (being stable in the small and simultaneously in the large) is introduced and algorithms are proposed to determine such a policy in special cases. The techniques are partly taken from the field of traffic flow theory and its its connections to queuing theory are briefly outlined. The theoretic findings are illustrated by means of various examples. Finally, it is shown how to estimate the total cost and arrive at cost-optimal policies. In the concluding chapter some hints for generalizations are given.

MSC:
90B05Inventory, storage, reservoirs
90-02Research monographs (optimization)
90B20Traffic problems