Optimum cost sharing of sorted waste collection between households and local authority considering consumer inconvenience: rational basis of shared responsibility

To find the optimum cost-sharing for sorted collections of waste between households and the local authority, an analytical model to evaluate the economic impact of the sorted collection activity has been developed based on the grid city model. The model takes into account the costs of space and handling in households. The sum of these costs and the costs of the local authority for sorted waste collection is minimized with collection frequencies of each sorting category as decision variables. The optimum collection frequencies of each sorting category is expressed by three nondimensional numbers, K, θ and φi, which represent, respectively, the allocation of the variable cost of sorted waste collection between households and the local authority, nonlinearity of space cost function with respect to space, and the volumetic share of the ith sorting category. The optimum collection frequency for each sorting category is proportional to the square root of the volumetric share of that category. When the space cost is linear with the space, the optimum sharing of the variable costs of sorted waste collection between households and the local authority is evenly shared. When the space cost function is a positive, increasing, and convex function with space, more than half of the variable cost of sorted waste collection is borne by the local authority to minimize the total cost.