The Perfect Solution To Flow Problems In Linear Networks

Maximum network flow formulation in linear optimization programming is a very common applied mathematics problem. The Simplex mathematical optimization model is the quintessential linear programming assignment help, in case you find it hard to solve your network flow problems.

The Network Simplex algorithm is the tailor-made solution option as it takes into account the large number of constraints that arise in a linear program derived from a maximum network flow problem.

Every individual programming step is mentioned in specific details below for your academic writing help:

· Note down the linear program form first hand

A linear program generally comes in the form

Z=c0+c1x1+…+cnxn subject to ai1x1+ai2x2+…+ainxn >= or <= or = bi

· Represent the Maximum Flow problem as a Linear Program

First up, list out all the variables that represent flow across the edges of the network. Next up, make a note of all the capacity and conservation constraints and then add an artificial feedback link from the sink to the source for representing the total flow.

In case you find all these too tough to understand, go through your subject material thoroughly or drop your “make my linear optimization assignment for me” message at good assignment assistance websites.

· List all flow variables

The key to converting a max flow problem into a linear program is to represent all flow processes as flow variables. For example, the following diagram represents a flow network.

The constituent flow variables in this network are:

X01 X02 X03

X14 X15

X24 X25 X26

X35

X47

X57

X67

· Keep in mind the constraints

There are two types of constraints in a basic network flow diagram, namely, capacity and flow constraints. Remember, the flow over any link cannot exceed the capacity of that link.

So for the above network flow diagram, every individual flow variable is capacity constrained as follows:

The flow conservation constraints are applicable for every node other than the source and sink node, which do not come under this limitation. For every other node, total flow into a node= total flow out of a node.

That is,

· Obtain the objective function

Your objective is to maximize the flow from source node 0 to sink node7, keeping in mind the applicable constraints.

The linear maximum objective function comes out to be

Max: X01+X02+X03 with a maximum value of 6

And the corresponding max flow is

Well, there you have it! A complete step by step solution to the maximum network flow problem that will come in handy in your linear programming assignment.