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We study a transportation problem with the minimum quantity commitment (MQC), which is faced by a famous international company. The company has a large number of cargos for carriers to ship to the United States. However, the U.S. Marine Federal Commission stipulates that when shipping cargos to the United States, shippers must engage their carriers with an MQC. With such a constraint of MQC, the transportation problem becomes intractable. To solve it practically, we provide a mixed-integer programming model defined by a number of strong facets. Based on this model, a branch-and-cut search scheme is applied to solve small-size instances and a linear programming rounding heuristic for large ones. We also devise a greedy approximation method, whose solution quality depends on the scale of the minimum quantity if the transportation cost forms a distance metric. Extensive experiments have been conducted to measure the performance of the formulations and the algorithms and have shown that the linear rounding heuristic behaves best. [ABSTRACT FROM AUTHOR]

In the global context of reducing the use of fossil fuels and turning to the usage of electric vehicles. The location and ease of charging stations have the crucial impact on early adopters and volunteers who will eventually become mainstream consumers. In this transition, national planning needs to take into account the final network planning of charging stations and the development and evolution of charging station systems, and seek to develop policies to facilitate the transition of vehicles to electric vehicles, making the best solution for each country. In this paper, we first determine that the standard measurement of full electrified electric vehicles should reach 90%. By fitting and forecasting the data of Tesla electrification rate in recent years, we draw the conclusion that it is difficult to realize a complete electrification at present. Based on this conclusion, we estimate that the number of electric vehicle charging stations required in the United States is about 29.7 million under the constraints of demand and service by using the multi-objective programming model. Moreover, we have suggested to countries the factors to be taken into account in the development of electric vehicles and the timing of banning the use of fuel vehicles. Finally, we use the asymmetric Nash negotiation model to discuss the impact of the number of vehicles, population density, road network density, GDP, geographical environment and other factors. The results show that the urban, suburban, and rural areas have reached 63.52%, 23.41%, and 13.07%. [ABSTRACT FROM AUTHOR]