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This paper presents a mixed integer linear programming model to optimize the costs of maintenance and extra hours for scheduling a fleet of battery electric vehicles (BEVs) so that the products are delivered to prespecified delivery points along a route. On this route, each BEV must have an efficient charging strategy at the prespecified charging points. The proposed model considers the average speed of the BEVs, the battery states of charge, and a set of deliveries allocated to each BEV. The charging points are located on urban roads and differ according to their charging rate (fast or ultra-fast). Constraints that guarantee the performance of the fleet's batteries are also taken into consideration. Uncertainties in the navigation of urban roads are modeled using the probability of delay due to the presence of traffic signals, schools, and public works. The routes and the intersections of these routes are modeled as a predefined graph. The results and the evaluation of the model, with and without considering the extra hours, show the effectiveness of this type of transport technology. The models were implemented in AMPL and solved using the commercial solver CPLEX.

Short-term planning is a decision-making process that aims at ensuring proper performance of electrical distribution systems (EDSs) within a short period of time. In recent years, this process has faced a significant challenge due to the integration of renewable energy based technologies. To handle such complicated planning problem most suitably, sophisticated algorithms are required. This paper proposes a mixed-integer linear programming model to find the optimal short-term plan of EDSs considering siting and sizing of capacitor banks and renewable energy sources, conductor replacement of overloaded circuits, and voltage regulators allocation. Besides considering the economic aspects, the environmental issues are also considered to promote a low carbon emission system. To address the uncertainties of electricity consumption and renewable energy output power, a two-stage robust optimization model is used, and to handle this model more efficiently, the column and constraint generation algorithm is applied. A 135-node distribution system is studied under different conditions to assess the performance of the proposed approach. Results show that the planning actions, for each case study, improve the efficiency of EDS and mitigate the pollutant emissions at the distribution level.

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