The Metropolis city council is examining four landfill sites as candidates for use in the city's solid waste disposal network. The monthly costs per ton have been calculated for operating at each site and for transportation to each site from the various collection areas. The waste production amounts of each collection site have also been estimated. In addition, the amortized monthly cost for the facility at each proposed site has been evaluated, together with the monthly maximum amount of waste that can be handled at each landfill site. The associated data is shown in Table 2. The Metropolis city council wants to ensure that the waste of each collection area is directed to exactly one landfill site. 13 From collection Transportation cost per ton to landfill site Monthly area L1 L2 L3 L4 tons A $14 $16 $10 $8 500 B 12 11 12 14 700 8 9 11 1500 D 15 14 1000 E 8 12 10 11 1800 F 11 8 6 1200 Operating cost/ton $8 $10 $9 $11 Fixed cost/month $1000 $800 $700 $900 Monthly capacity (tons) 4000 3000 4000 3000 10 12 10 Table 2: Landfill data 1. Write a mixed integer linear program to help metropolis find an optimal configuration that minimizes monthly system cost. 2. Solve your model with AMPL. 3. Assume that city council allowed collection areas to send their waste to multiple landfills. Would you expect the resulting system to be less costly or more costly than the system you obtained in Part (2)? Explain briefly. The Metropolis city council is examining four landfill sites as candidates for use in the city's solid waste disposal network. The monthly costs per ton have been calculated for operating at each site and for transportation to each site from the various collection areas. The waste production amounts of each collection site have also been estimated. In addition, the amortized monthly cost for the facility at each proposed site has been evaluated, together with the monthly maximum amount of waste that can be handled at each landfill site. The associated data is shown in Table 2. The Metropolis city council wants to ensure that the waste of each collection area is directed to exactly one landfill site. 13 From collection Transportation cost per ton to landfill site Monthly area L1 L2 L3 L4 tons A $14 $16 $10 $8 500 B 12 11 12 14 700 8 9 11 1500 D 15 14 1000 E 8 12 10 11 1800 F 11 8 6 1200 Operating cost/ton $8 $10 $9 $11 Fixed cost/month $1000 $800 $700 $900 Monthly capacity (tons) 4000 3000 4000 3000 10 12 10 Table 2: Landfill data 1. Write a mixed integer linear program to help metropolis find an optimal configuration that minimizes monthly system cost. 2. Solve your model with AMPL. 3. Assume that city council allowed collection areas to send their waste to multiple landfills. Would you expect the resulting system to be less costly or more costly than the system you obtained in Part (2)? Explain briefly
