What is Mathematical Optimization?
Decisionmakers are often faced with the daunting question, “How do I optimally allocate my shared resources”? With mathematical optimization, the computer calculates many scenarios by altering the decision variables (such as number of FTE, product mix, etc.). When the calculation is complete, the computer will report the optimal combination of input variables and the expected outcome.
Decisionmakers are often faced with the daunting question, “How do I optimally allocate my shared resources”? With mathematical optimization, the computer calculates many scenarios by altering the decision variables (such as number of FTE, product mix, etc.). When the calculation is complete, the computer will report the optimal combination of input variables and the expected outcome.
Staff Scheduling Demonstration:
The example to the right is a randomly generated data set of a transportation company’s individual start and stop times. The staff share common job tasks and can only work one job at a time. There are three shift types (8 hour, 10 hour and 12 hour shifts). The objective is for the computer to select the optimal combination of shifts that covers the demand while using the fewest number of shifts as possible. 
NOTE: This app is not available to demo because of the coding language (which is currently not compatible with the server)

Graph Interpretation
The graph to the right is called a "hourly census". An hourly census measures “how many staff are simultaneously being utilized at each hour of the day”. The xaxis represents the hour of the week (starting on Sunday) and the black line represents the average census demand per hour. The color shading represents the standard deviations from the demand (busier days). For example, on Monday at 2:00 PM (hour 62), two trucks are simultaneously in use. The computer will select the optimal staffing schedule to meet the designated demand per hour (the red and white line represents the estimated schedule’s capacity when using the computer’s recommendation). 
Examples of Popular Optimization Problems

Product Mix

Investment

Traveling Salesman

Knapsack

Cover Set
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Scenario:
The Sweet Apple company makes 10 apple based products. Each product has a unique selling price but share the same resources (such as FTE, equipment, and ingredients, etc.) Question: How much of each product is necessary to maximize profit (i.e., maximizing the number of products produced while minimizing wasted resources such as ingredients leftover)? 
Scenario:
An investor has $70,000 to divide among several stocks. Each stock alternative has their own expected return and minimal investment requirements. The investor would like to diversify their portfolio to reduce risk. Question: How should the investor partition the $70,000 in order to maximize the return while meeting the minimal investment requirements? 
Scenario:
A UPS store has 300 packages to deliver in 20 different zip codes. It would be wasteful to revisit the same zip code multiple times. The truck needs to return to home base by the end of the day. Question: What route should the delivery truck take in order to reduce overlapping routes while returning to the original starting point? 
Scenario:
You are given a bag with a limited weight capacity, each item has a weight and value. You would like make only one trip and understand that some items will be left behind. Question: Determine which items to bring in your bag such that the weight limit of the bag is exceeded, but the total value of the items is as large as possible. How many of which items do you choose? 
Scenario:
A company would like to add several new packaging distribution hubs to service different 12 cities across the country. The company’s strategic plan is to have at least one hub within 300 miles of each city. Question: In what locations should the hubs be placed in order to cover the 12 cities but with the fewest number of hubs as possible? 