Issue link: https://read.dmtmag.com/i/35322
Where to Go? The basic economics of determining the optimal allocation of a waste stream in the MIN-EXP model is to determine the facility with the lowest total cost per ton capable of handling that waste stream, and allocate all the waste in that stream to that facility. If capacity is reached at that facility, the remainder is allocated to the facility with the next-lowest total cost until capacity is reached, and so on. Some waste may go to more-distant facilities if the combination of tipping fees and surcharges is low enough that it more than compensates for the cost of shipping a greater distance. Mode of transportation is decisive in calculating transportation costs—rail costs a fraction of truck transportation. The original, primal LP problem states an issue directly. For the MIN-EXP model, the primal LP problem determines the cost-minimizing allocation of waste streams to available disposal sites. But every LP prob- lem has an associated dual LP problem, which puts valuations on resources that constrained the primal LP optimal solution. The parameters of the dual LP objective function are taken from the constraints of the primal LP prob- lem (see “Authors’ Note,” page 21). Furthermore, the lFigure 4. Composting capacity is the most-significant constraint in the San Francisco Bay Area. parameters of the primal LP objective function appear in the constraints of the dual LP problem (with the direction of the inequalities reversed). The map in Figure 3 shows all possible disposal sites. The central shipping point is indicated with a blue dot. Of the eight sites, only three are used in the base-case optimal solution. The actively used sites are indicated with yellow dots. Total expenditure on waste disposal at this expenditure-minimizing solution is $498,030, and a total of 198,500 ton-miles are hauled, but this isn’t the minimum ton-miles to dispose of these waste streams. The MIN-HAUL LP problem has all the same constraints, but minimizes ton-miles rather than mini- mizing expenditure on disposal. Total expenditure on waste disposal at this ton- mile minimizing solution is more than it was for the expenditure-minimizing solution, $546,602, but the ton-miles hauled decrease to 130,940. All the same facilities are used, but as much waste as possible is disposed of at the closest facility, Newby Island. The Newby Island facility reached capacity for recycling and composting at the ton-miles optimal solution, and the remainder of each stream goes to the near- est respective facilities. Generally, minimizing expenditure on waste lFigure 3. A visualization shows the optimal solution to the primal LP problem in the base case. 20 GEO W ORLD / JUL Y 2O11 removal doesn’t result in minimal carbon emis- sions or a level of carbon emissions that reflect a balance of costs and benefits to society. The expenditure-minimizing solution is dominated by the tipping fees and jurisdiction surcharges that typically don’t reflect the social costs and benefits of transportation emissions. Resource Optimization