The Bronx division of the New York City Economic Development Corporation (“EDC”) is considering an expansion of entrepreneurial programs into local communities. Three locations are available for incubators: a small start-up site in the East Bronx, a medium size site for more mature ventures in Central Bronx, and a larger site for existing and new ventures in the South Bronx. The following table summarizes the number of jobs, site start-up costs, and annual returns associated with each site: East Bronx Central Bronx South Bronx Jobs 9 17 35 Costs $150,000 $275,000 $450,000 Returns $85,000 $125,000 $175,000 The EDC has $2,000,000 available to pay start-up costs for new operations in the coming year. Additionally, there are five possible ventures for the East Bronx, seven possible ventures for the Central Bronx location, and three possible ventures for the South Bronx. The EDC wants to plan its expansion in a way that maximizes annual returns and the number of jobs created.
1. Formulate, implement in a spreadsheet, and interpret the construction of an MOLP for this problem.
2. Determine the best possible value for each objective in the problem. Compare and contrast the results across objectives.
3. Implement a goal programming version of the model to determine the solution that minimizes the maximum percentage deviation from the optimal objective function values. What solution do you obtain? Interpret this solution versus each of the results from separate objective values in question 2.
4. Suppose EDC management considers maximizing jobs three times as important as maximizing returns. What solution does this suggest and why? Include in your discussion the opportunity costs of objectives and the value of increasing or decreasing maximum number of ventures for each site.