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From a mathematical point of view, in the standard transportation problem, why should we assume that the total supply must be equal to the total demand?
This problem should be analyzed from the perspective of operational research, which is a hypothesis about establishing a mathematical model of transportation problems. Why should we assume that the total supply must be equal to the total demand because we want to find the optimal solution (even if the freight is the smallest)? To understand this, you need some basic knowledge of operational research. Let me give you a general idea. You're trying to solve it yourself. In operational research, there is a special chapter on transportation. Thinking: In practice, there are three situations between output and sales. The first output equals the sales volume, and the second output is greater than the sales volume. Because it is a transportation problem, it is necessary to transport the output from different places of origin to different sales places for sale (the output transported to the sales place is the sales volume). Because the output is greater than the sales volume, the output will be redundant, so a virtual sales place is created when modeling. This virtual sales place is the place of origin, that is, it is transported from the place of origin to the place of origin. Even if transportation is needed, the transportation cost is zero, which means no transportation. If you cut a picture, the land sales B5 is virtual, and the output is also virtual. The output itself is not transported. Why do you want to do this? Because the method of finding the optimal solution must use this skill. The third kind of sales volume is greater than the output. Similarly, both A4 and output of a production area are fictitious, so that production and sales are balanced, but the fictitious output cannot be transported to the sales place. The transportation problem itself requires the lowest freight rate. After the mathematical model is established, the methods to be used are 1. Minimum element method (not applicable) 2. (1) Vogel method (the first step is to find the initial solution) (2) closed-loop method (to test the optimal solution) ((1)) potential method.

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