Computation - Operations Research Models and Methods

Computation

Mathematical Programming

Network Programming

Example Problem

Constructing the Network

Solving the Problem


Network Flow

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Network Flow Programming

This important class of linear programming models has the advantage that elements of a problem can be described by a picture rather than a series of algebraic expressions as for the general linear programming model. Even if a particular problem cannot entirely be expressed as a network flow problem, very often major components of the problem can be expressed as a network. For an "almost" network model, the problem can be described using this model construct, and the worksheet or the Solver model modified to incorporate nonstandard features.

A network is a collection of nodes and arcs. Flow enters and leaves at the nodes and passes through the arcs. Generally there are lower and upper bounds on arc flows. Each arc has a unit cost and the arc cost is the flow multiplied by the unit cost. The goal is to find the flow that minimizes total cost.

Each arc has a gain factor that multiplies the flow entering the arc to obtain the flow that leaves the arc. A network with all gains equal to 1 is called a pure network. If some gains are other than 1, the network is called a generalized network.