The Bank Hapoalim Group is Israel's largest banking group, providing services throughout the country. As of the

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The Bank Hapoalim Group is Israel's largest banking group, providing services throughout the country. As of the beginning of 2012, it had approximately 300 branches and eight regional business centers in Isreal. It also operates worldwide through many branches, offices, and subsidiaries in major financial centers in North and South America and Europe.

A major part of Bank Hapoalim's business involves providing investment advisors for its customers. To stay ahead of its competitors, management embarked on a restructuring program to provide these investment advisors with state-of-the-art methodology and technology. An OR team was formed to complete this.

The team concluded that it needed to develop a flexible decision-support system for the investment advisors that could be tailored to meet the diverse needs of every customer. Each customer would be asked to provide extensive information about his or her needs, including choosing among various alternatives regarding his or her investment objectives, investment horizon, choice of an index to strive to exceed, preference with regard to liquidity and currency, etc. A series of questions also would be asked to ascertain the customer's risk-taking classification.

The natural choice of the model to drive the resulting decision-support system (called the Opti-Money System) was the classical nonlinear programming model for portfolio selection described in this section of the book, with modifications to incorporate all the information about the needs of the individual customer. This model generates an optimal weighting of 60 possible asset classes of equities and bonds in the portfolio, and the investment advisor then works with the customer to choose the specific equities and bonds within these classes.

During the first year of full implementation, the bank's investment advisors held some 133,000 consultation sessions with 63,000 customers while using this decision-support system. The annual earnings over benchmarks to customers who follow the investment advice provided by the system totalapproximately US$244 million, while adding more than US$31 million to the bank's annual income.

Briefly describe how nonlinear programming was applied in this study. Then list the various financial and nonfinancial benefits that resulted from this study.