Resolving Discrepancies in Reported Flow Amounts in Sewage Sludge Management Network Datasets by Mathematical Programming

Abstract

For further development and infrastructure planning, considerations regarding economically feasible, efficient and appropriate waste management are essential. In current waste management networks and related datasets, errors and discrepancies arise in the reported values, to due to an insufficient detail of used infrastructure, which is often reduced to only several nodes in the case of very complex tasks. This paper presents an optimised multi-criteria mathematical programming model, which enables to obtain data for more detailed infrastructure while preserving the efficiency of the calculation using mathematical modifications and algorithms. The paper describes the method of how to divide the estimated flows in a chosen area among different sources. The optimized robust model minimizes the total sum of absolute deviations from the original data. It also considers logistics in the form of distances and emulates the economic behaviour of subjects in the network. The alternating direction method of multipliers is applied for an original model solution, together with a heuristic used for one set of ambiguous variables. This algorithm facilitates the solving of large instances of the defined problem. The implementation of the algorithm and all computations are done in the Julia programming language involving specialized optimisation libraries. The functionality of the optimised model is shown on the sewage sludge management network dataset of the Czech Republic, which contains approximately 200 entities. Such a dataset leads to the model with approximately 400,000 of decision variables. The results of the presented case study are used for the improvement of the treatment of sludge, a waste produced in wastewater treatment plants. The proposed model is general enough as it can be also used for estimating real waste flow datasets containing a similar type of error as described.