# Formulate the following network problem

(See the attached file for the diagram)

- In the above network, a given flow Q is transferred through the network to a demand node N. The goal is to route the flows in such a way that total channel loss is minimized, where channel loss coefficients clij per unit length are given for each link or arc of length Lij. Ignore the maximum capacities of the links for this. Specify how the arc parameters [lij, uij, cij] for any link (i,j) in this network should be defined, as well as the demand node parameters (i.e., priority and demand), that will result in minimization of total channel loss.

- Instead of Q being specified in the above network, suppose that now the objective is to find the maximum flow that can be delivered to demand node N, assuming that upper bounds uij are now specified on the flow in each link or arc (i,j) and channel losses are ignored. Specify the arc parameters and demand node parameters that would be required to solve this problem [Hint: you may need to add a supply node such as a dummy reservoir].

- How would you define the arc parameters and demand node parameters in order to find the shortest path through this network, assuming each link is of length Lij? We are not trying to route flows in this network, but simply identify the shortest connected path through the network.

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#### Solution Summary

This solution gives a step-by-step explanation on how to formulate the given problem using the network flow model. The solution discussed some basic techniques in the formulation of network flow problem.