A company has five factories, and the information about the coordinates of each factory are known. The company wants to locate a warehouse to minimize the sum of Euclidian distances from factories to the warehouse. Is non-linear programming model necessary to solve such a problem?

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BlackTom AI · Accepted Answer

The question asks about locating a warehouse to minimize the sum of Euclidean distances from five factories, which is a classic Fermat-Weber problem.
Option 1: 'No, it is not necessary' — This is the plausible choice. In this setting, the objective is the sum of Euclidean distances, which forms a convex, non-differentiable objective in general. Although nonlinear, there are specialized methods tailored for this problem (e.g., the Weiszfeld algorithm) that do not require formulating and solving a general nonlinear programming (NLP) model. Therefore, you can solve it without resorting to a generic NLP formulation.
Option 2: 'Yes, it is necessary' — This would imply that a general NLP formulation is required for an exact solution. While an NLP can model the problem, it is not strictly necessary because dedicated algorithms exist that directly tackle the Fermat-Weber objective. Relying solely on a generic NLP solver may be less efficient than using a problem-specific approach.
In summary, since the objective is the sum of Euclidean distances and specialized methods like the Weiszfeld algorithm can solve it without formulating a full nonlinear programming model, the statement that an NLP model is necessary is not correct.

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A company has five factories, and the information about the coordinates of each factory are known. The company wants to locate a warehouse to minimize the sum of Euclidian distances from factories to the warehouse. Is non-linear programming model necessary to solve such a problem?

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