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Paradox in a non-linear capacitated transportation problem. (English) Zbl 1274.90039

Summary: We discuss a paradox in fixed charge capacitated transportation problem where the objective function is the sum of two linear fractional functions consisting of variables costs and fixed charges respectively. A paradox arises when the transportation problem admits of an objective function value which is lower than the optimal objective function value, by transporting larger quantities of goods over the same route. A sufficient condition for the existence of a paradox is established. Paradoxical range of flow is obtained for any given flow in which the corresponding objective function value is less than the optimum value of the given transportation problem. Numerical illustration is included in support of the theory.

MSC:

90B06 Transportation, logistics and supply chain management
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