Abstract
The deployment of grain and oil is related to the daily needs of people and the stability of society. In this paper, we take the shortest path problem and the minimum cost maximum flow problem in graph theory as the theoretical basis. Through the establishment of distance matrix between the reserves station and the deployment warehouse or between reserve station and reserve station, we use the Floyd algorithm to calculate the shortest path between any two points in the matrix to determine the optimal deployment of the emergency plan. Through the establishment of mathematical model of the reserve station and deployment warehouse, we use the minimum cost maximum flow theory to solve the model and to obtain the deployment programs of grain and oil under normal circumstances. Through the combination of shortest path and minimum cost and maximum flow, we give the deployment plan under the general emergency situation and provide a new way for the deployment of the supply of grain and oil in each case.
Highlights
Plenty of grain and oil reserves in each region are important for the protection of non-food consumer demand, regulating the supply and demand balance of domestic food, stabilizing grain prices, responding to major natural disasters or other emergencies, to protect the security and stability of society
When the urgency of the emergency situation is in a lower level, if the whole deployment of grain and oil supplies only takes the time into consideration, and use the shortest path theory to solve the problem, because we only think that we deploy the grain and oil supplies in the shortest possible time in order to meet the demand of the area, without considering the transportation costs, so, the transportation cost will be very high
If the whole deployment of grain and oil supplies only use the minimum cost maximum flow theory to optimize, we can transport grain and oil supplies to reserve station as much as possible at the lowest cost, we cannot guarantee the timeliness of supply, that means we cannot transport the grain and oil supplies to the desired place timely, and it will affect the demand for grain and oil supplies of the desired place
Summary
Plenty of grain and oil reserves in each region are important for the protection of non-food consumer demand, regulating the supply and demand balance of domestic food, stabilizing grain prices, responding to major natural disasters or other emergencies, to protect the security and stability of society. This paper will establish the comprehensive mathematical model of the deployment of grain and oil supplies based on the researches of the shortest path problem and minimum cost maximum flow problem and will analyze and present the deployment plans of grain and oil supplies in an emergency situation, in normal circumstance, and in special circumstance. This can provide some references more or less to the actual deployment of grain and oil supplies
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