Nowadays, robust and efficient solid waste collection is crucial to motivate citizens to participate in the circular economy by sorting recyclable solid waste. Vocational vehicles, including garbage trucks, contribute significantly to CO${}_2$ emissions; therefore, it is strongly recommended, and in the European Union it is mandatory, to replace conventional-fuel-based garbage trucks with electric ones. For providing sustainable and energy-efficient solid waste collection with a heterogeneous fleet, in-depth mathematical computations are needed to support solving complex decision-making problems, including crew rostering and vehicle routing, because the distance and capacity of electric garbage trucks differ from conventional-fuel-based ones. However, the literature on solid waste collection using electric garbage trucks is still relatively scarce. The main contribution of this paper is developing an optimization problem for balancing travel distance assigned to each garbage truck of a heterogeneous fleet. The problem is based on specific requirements of the Municipal Solid Waste Management in Cracow, Poland, where the working time of routes is balanced and the total time of collection service can be minimized. For the problem, an MIP program was developed to generate optimal crew schedules, so that the hitherto network of segregated solid waste pickup nodes can be served using a heterogeneous fleet in which the share of electric garbage trucks is up to 30%. We study the impact of the changed composition of the fleet on modifications in crew rostering due to the shorter range of an electric vehicle compared to a conventional-fuel-based one.

The paper is devoted to optimal vaccination scheduling during a pandemic to minimize the probability of infection. The recent COVID-19 pandemic showed that the international community is not properly prepared to manage a crisis of this scale. Just after the vaccines had been approved by medical agencies, the policymakers needed to decide on the distribution strategy. To successfully fight the pandemic, the key is to find the equilibrium between the vaccine distribution schedule and the available supplies caused by limited production capacity. This is why society needs to be divided into stratified groups whose access to vaccines is prioritized. Herein, we present the problem of distributing protective actions (i.e., vaccines) and formulate two mixed-integer programs to solve it. The problem of distributing protective actions (PDPA) aims at finding an optimal schedule for a given set of social groups with a constant probability of infection. The problem of distributing protective actions with a herd immunity threshold (PDPAHIT) also includes a variable probability of infection, i.e., the situation when herd immunity is obtained. The results of computational experiments are reported and the potential of the models is illustrated with examples.

Nowadays, in the European Union selective solid waste management be-longs to important responsibilities of municipalities. In Solid Waste Management (SWM) the main operational task is to set a schedule for solid waste collection and to find optimal routes for garbage trucks so that the total costs of solid waste collection service can be minimized subject to a series of constraints which guarantee not only fulfillment of SWM’s obligations but also desirable level of quality of that service. Optimization problem of garbage trucks routing is a special case of rich Vehicle Routing Problem as it has to cover following constraints: pickup nodes (clients) must be visited during their predefined time windows; the number and capacity of depots and specialized sorting units can-not be exceeded; each garbage truck can be assigned to at most one depot; each route should be dedicated to collecting one type of segregated solid waste, and the route must be served by a garbage truck which can collect that type of solid waste; availability of garbage trucks and their drivers must be respected; each garbage truck must be drained at a specialized sorting unit before going back to the depot. This paper contributes with a new Mixed-Integer Programming (MIP) model for the Selective Solid Waste Collection Routing Problem (SS-WCRP) with time windows, limited heterogeneous fleet, and different types of segregated solid waste to be collected separately. Utilization of MIP for solving small-sized instance of the Fleet Optimization Problem for Selective Solid Waste Collection (FOPSSWC) is and obtained results are reported.

Municipal Solid Waste Management (MSWM) struggles with significant policy and operational challenges, particularly concerning collection routes for recyclables and fleet composition. Within the European Union, phasing out traditional fuel-based vocational vehicles, like garbage trucks, in favor of zero-emission alternatives, is mandatory to achieve sustainable development objectives. This paper presents a preliminary study on the problem of multi-period fleet transition from combustive fuels towards more eco-friendly fueling types. Initially developed for energy sector, the MARKAL framework was used here to support the technological transition of the fleet. The mixed-integer program was formulated for the Fleet Transition Problem (FTP), a simplified theoretical problem. The objective of the FTP and a mixed-integer linear program used to solve it is minimizing the overall cost of fleet modernization throughout a multi-phase planning horizon so that the sustainable transition of the fleet can be assured. Computational experiments run on randomly generated data instances affirmed the model’s effectiveness in strategizing fleet transition. This research outlines a multi-period model for transitioning to a zero-emission fleet and demonstrates the FTP’s potential for strategic decision-making. Notably, the study observes consistent reductions in permissible emissions across the planning horizon.

The purpose of the study is to investigate the energy performance of a PVT collector in combination with a heat pump. First, a test system combining a heat pump and PVT module is built, and then its performance is carefully measured, assessing the electricity and heat production. The paper focuses on increasing the efficiency of a photovoltaic (PV) panel (as part of the PVT module) by cooling it with a heat pump. The main idea is to use the heat generated by the warming panels as a low-temperature source for the heat pump. The research aims to maximize the use of solar energy in the form of both electricity and heat. In traditional PV systems, the panel temperature rise reduces the solar-to-electric conversion efficiency. Therefore, cooling with a heat pump is increasingly used to keep panels at optimal temperatures and improve performance. The tests confirm that cooling the panels with a heat pump results in an 11.4% improvement in electrical efficiency, an increase from 10.8% to 12.0%, with an average system efficiency of 11.81% and a temperature coefficient of –0.37%/°C. The heat pump achieves a COP of 3.45, while thermal energy from the PVT panel accounts for up to 60% of the heat input when the air exchanger is off. The surface temperature of the PVT panels varies from 11 °C to 70 °C, and cooling enables an increase in electricity yield of up to 20% during sunny periods. This solution is especially promising for facilities with year-round thermal demand (e.g., swimming pools, laundromats).