NETWORK OPTIMIZATION MODELS:CONCLUSIONS

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CONCLUSIONS

Networks of some type arise in a wide variety of contexts. Network representations are very useful for portraying the relationships and connections between the components of systems. Frequently, flow of some type must be sent through a network, so a decision needs to be made about the best way to do this. The kinds of network optimization models and algorithms introduced in this chapter provide a powerful tool for making such decisions.

The minimum cost flow problem plays a central role among these network optimization models, both because it is so broadly applicable and because it can be solved extremely efficiently by the network simplex method. Two of its special cases included in this chap- ter, the shortest-path problem and the maximum flow problem, also are basic network optimization models, as are additional special cases discussed in Chap. 9 (the transportation problem and the assignment problem).

Whereas all these models are concerned with optimizing the operation of an existing network, the minimum spanning tree problem is a prominent example of a model for op- timizing the design of a new network.

The CPM method of time-cost trade-offs provides a powerful way of using a network op- timization model to design a project so that it can meet its deadline with a minimum total cost.

This chapter has only scratched the surface of the current state of the art of network methodology. Because of their combinatorial nature, network problems often are extremely

difficult to solve. However, great progress has been made in developing powerful modeling techniques and solution methodologies that have opened up new vistas for important applications. In fact, relatively recent algorithmic advances are enabling us to solve successfully some complex network problems of enormous size.

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