Binary Integer Programming Example Cal aircraft Manufacturing company What decisions are to be made? 1. Build fac 2. Build factory in SFO 3. Build warehouse in La 4. Build warehouse in SFo I if decision i is yes Introduce 4 binary variables if decision i is no Binary Integer Programming Example Cal aircraft Manufacturing Company 1. Cal wants to expand (TBD) 2. Available capital: $10,000,000 3. Cal wants to maximize"total net present value"(profitability vs time value of money) Build a factory in L.A.? Sam 2 Build a factory in S.F.? 3 Build a warehouse in L.A.? Sam Sam 4 Build a warehouse in S F? S2m What is the objective? Maximize npv. z=9X1+5x+6x3+4 Remaining constraints? Dont go beyond meansWhat decisions are to be made? 1. Build factory in LA 2. Build factory in SFO 3. Build warehouse in LA 4. Build warehouse in SFO 1 if decision i is yes Introduce 4 binary variables xi = 0 if decision i is no Binary Integer Programming Example: Cal Aircraft Manufacturing Company 1. Cal wants to expand (TBD) 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 What is the objective? • Maximize NPV: Z = 9x1 + 5x2 + 6x3 + 4x4 Remaining constraints? • Don’t go beyond means: 6x1 + 3x2 + 5x3 + 2x4 <10 Binary Integer Programming Example: Cal Aircraft Manufacturing Company