Transshipment station location problem in the context of solid waste management of the Brazilian state of Rio Grande do Norte

The problem of solid waste management grows according to the constant changes in the consumption patterns of society and the development of the current economic model. These factors cause an increase in waste generation and, consequently, have a negative impact on the environment and public health since the final disposal of these materials is often inadequate. In Brazil, Law No. 14.026/2020 imposed new deadlines for deactivating open-air dumps nationwide. However, many cities still perform the disposal incorrectly, mainly due to financial constraints that make it impossible to invest in the construction, operation and maintenance of alternatives, such as Sanitary Landfills (SL). In Rio Grande do Norte (RN), Brazil, the State Plan for Solid Waste (SPSW) implemented the inter-municipal consortiums intending to reduce costs through the union of several municipalities. Each consortium has a city designated to receive the SL and a set of cities able to receive Transshipment Stations (TSs) to temporarily store the solid waste, enabling and reducing waste transportation costs between the cities and the SL. A city can also deliver the waste directly to the SL if it is advantageous in terms of cost. Each TS has a storage capacity that depends on the number of buckets to be deployed at the station.In this context, the TS Location Problem (TSLP) arises. In this problem, we aim to determine (i) in which cities the TSs will be installed, (ii) the number of buckets to allocate at each TS, (iii) and the assignment of cities to TSs or SL. The objective is to find a solution that minimizes the total cost, composed of the fixed cost of installing a TS, the total cost of deploying buckets at the installed TS, the delivery cost between the cities and the TSs or the SL and between the TSs and the SL. The problem considers that the cities deliver solid waste on a daily basis, that solid waste can be stored for at most two days at the TSs, and that all deliveries are made at the end of the day. Furthermore, the TSLP considers that each city has a vehicle to make deliveries of the city's waste to the TS or SL, and that an unlimited fleet of vehicles able to carry at most a single bucket is available to make one delivery per day from a TS to the SL. To solve the TSLP, we propose a Mixed Integer Linear Programming model. The model was solved using Gurobi solver for a set of real instances. The solutions obtained will be validated and implemented within the RN SPSW