Integer Programming for Decision Making Yes or no"decisions encoded with binary variables 1 if decision is yes 0 if decision is no Binary Integer Programming( BIP: Binary variables linear constraints Binary Integer Programming Example Cal aircraft Manufacturing company Problem Cal wants to expand 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 2. Available capital: S10,000,000 3. Cal wants to maximize"total net present value"(profitability vs time value of money) Pri 1 Build a factory in L. A? Sir Sam 2 Build a factory in S F? Sam 3 Build a warehouse in L.A.? S61 Sam 4 Build a warehouse in S F? S41 S2m“Yes or no” decisions encoded with binary variables: 1 if decision is yes xj 0 if decision is no. Binary Integer Programming (BIP): • Binary variables + linear constraints. Integer Programming for Decision Making Problem: 1. Cal wants to expand: • 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. 2. Available capital: $10,000,000 3. Cal wants to maximize “total net present value” (profitability vs. time value of money) NPV Price 1 Build a factory in L.A.? $9m $6m 2 Build a factory in S.F.? $5m $3m 3 Build a warehouse in L.A.? $6m $5m 4 Build a warehouse in S.F.? $4m $2m Binary Integer Programming Example: Cal Aircraft Manufacturing Company