Read the referenced article that fully describes the management science study summarized in the application vignette presented in Section

Briefly describe how the model for a special type of minimum-cost flow problem was applied in this study.

Then list the various financial and nonfinancial benefits that resulted from this study.

An Application Vignette:

Hewlett-Packard (HP) offers many innovative products to meet the diverse needs of more than 1 billion customers. The breadth of its product offering has helped the company achieve unparalleled market reach.

However, offering multiple similar products also can cause serious problems-including confusing sales representatives and customers-that can adversely affect the revenue and costs for any particular product.

Therefore, it is important to find the right balance between too much product variety and too little. With this in mind, HP top management made managing product variety a strategic business priority.

HP has been a leader in applying management science to its important business problems for decades, so it was only natural that many of the company's top management scientists were called on to address this problem as well. The heart of the methodology that was developed to address this problem involved formulating and applying a network optimization model.

After excluding proposed products that do not have a sufficiently high return on investment, the remaining proposed products can be envisioned as flows through a network that can help fill some of the projected orders on the right-hand side of the network.

The resulting model is a special type of minimum cost flow problem (related to the special type discussed in the next two sections).

Following its implementation by the beginning of 2005, this application of a minimum cost flow problem had a dramatic impact in enabling HP businesses to increase operational focus on their most critical products.

This yielded companywide profit improvements of over $500 million between 2005 and 2008, and then about $180 million annually thereafter. It also yielded a variety of important qualitative benefits for HP.

These dramatic results led to HP winning the prestigious first prize in the 2009 Franz Edelman Award for Achievement in Operations Research and the Management Sciences.