Lecture

Networks: Supply and Demand

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Description

This lecture explains the concepts of supply and demand in network theory, using examples from logistics to illustrate how nodes inject and absorb flows. The instructor defines divergence as the difference between total outgoing and incoming flows at a node, categorizing nodes as supply, demand, or transiting based on the sign of their divergence. The lecture concludes with a discussion on circulation, where all nodes have a divergence of zero, indicating flow balance throughout the network.

In MOOC

Optimization: principles and algorithms - Network and discrete optimization

Introduction to the mathematical concept of networks, and to two important optimization problems on networks: the transshipment problem and the shortest path problem. Short introduction to the modeling power of discrete optimization, with reference to classical problems. Introduction to the branch and bound algorithm, and the concept of cuts.

Official source

Related concepts (18)

Supply and demand

In microeconomics, supply and demand is an economic model of price determination in a market. It postulates that, holding all else equal, in a competitive market, the unit price for a particular good, or other traded item such as labor or liquid financial assets, will vary until it settles at a point where the quantity demanded (at the current price) will equal the quantity supplied (at the current price), resulting in an economic equilibrium for price and quantity transacted.

Aggregate demand

In macroeconomics, aggregate demand (AD) or domestic final demand (DFD) is the total demand for final goods and services in an economy at a given time. It is often called effective demand, though at other times this term is distinguished. This is the demand for the gross domestic product of a country. It specifies the amount of goods and services that will be purchased at all possible price levels. Consumer spending, investment, corporate and government expenditure, and net exports make up the aggregate demand.

Effective demand

In economics, effective demand (ED) in a market is the demand for a product or service which occurs when purchasers are constrained in a different market. It contrasts with notional demand, which is the demand that occurs when purchasers are not constrained in any other market. In the aggregated market for goods in general, demand, notional or effective, is referred to as aggregate demand. The concept of effective supply parallels the concept of effective demand.

Divergence (statistics)

In information geometry, a divergence is a kind of statistical distance: a binary function which establishes the separation from one probability distribution to another on a statistical manifold. The simplest divergence is squared Euclidean distance (SED), and divergences can be viewed as generalizations of SED. The other most important divergence is relative entropy (also called Kullback–Leibler divergence), which is central to information theory.

F-divergence

In probability theory, an -divergence is a function that measures the difference between two probability distributions and . Many common divergences, such as KL-divergence, Hellinger distance, and total variation distance, are special cases of -divergence. These divergences were introduced by Alfréd Rényi in the same paper where he introduced the well-known Rényi entropy. He proved that these divergences decrease in Markov processes.

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