Binary Integer Programming Example Cal aircraft Manufacturing company LA factory(x ), SFO factory(x2), LA warehouse(x,), SFO warehouse (x4) Build new factory in Los Angeles, San Francisco, or both Build new warehouse(only one Warehouse must be built close to city of a new factory What are the constraints between decisions? Only one warehouse x exclusive-orx 2. Warehouse in LA only if Factory is in LA 3. Warehouse in Sfo only if factory is in SFO Implies x Encoding Choices: An Example Mutually exclusive choices Example: at most 2 decisions in a group can be yes LP EncodingLA factory(x1), SFO factory(x2), LA warehouse(x3),SFO warehouse (x4) • Build new factory in Los Angeles, San Francisco, or both. • Build new warehouse (only one). • Warehouse must be built close to city of a new factory. What are the constraints between decisions? 1. Only one warehouse: x3 exclusive-or x3 x3 + x4 < 1 2. Warehouse in LA only if Factory is in LA: x3 implies x1 x3 – x1 < 0 3. Warehouse in SFO only if Factory is in SFO: x4 implies x2 x4 - x2 < 0 Binary Integer Programming Example: Cal Aircraft Manufacturing Company • Mutually exclusive choices • Example: at most 2 decisions in a group can be yes: LP Encoding: x1 +…+ xk < 2. Encoding Choices: An Example