Optimizing Bond Purchase for Soil Decontamination in Flatbush, Texas

1. Flatbush Case Study Team Outliers Josel Cates Danielle Ross Vince Tam Lulu Xu

2. The Problem • City of Flatbush, Texas is responsible for decontaminating soil surrounding their petroleum pumping facility • Will purchase zero coupon and regular bonds to pay for the clean up

3. The Problem Cont. • Funding the clean-up • Coupon and principal payments, and cash balances carried forward (which earn 4% interest) • Will be self financing • How much of each bond type should Flatbush buy to minimize total costs?

4. Solution structure Determined: Total annual receipts of bond dividends per year Total income from maturing bonds per year Total funds available per year Cash left per year

5. Solution • Used Solver to minimize Total Cost by changing the number of bonds purchased • Subject to constraints: • Cash left is between 0 and 4 million • Cash left in the last period is <25,000 • Optimal Total Cost = $16,580,197.87

6. Shadow Price • Shadow Price is "the marginal utility of relaxing a constraint, or, equivalently, the marginal cost of strengthening a constraint" • Can tell us how much we should be willing to pay for additional units of input • Zero shadow price indicates that the constraint is not binding • Strictly positive shadow price indicates potential benefits by increasing amount of input, and vise versa • In this nonlinear optimization problem, we look at lagrange multiplier

7. Shadow Price Cont. • Year 1 cash left (cell B25) has a shadow price of 0 • Increasing upper bound constraint by 1, total cost stays the same • Year 15 cash left (cell P25) has a shadow price of -0.178 • Increasing upper bound constraint by 1, total cost decreases by 0.178 • Year 4 cash left (cell E25) has a shadow price of 0.032 • Increasing lower bound constraint by 1, total cost increases by 0.032