Approximate solution of a profit maximization constrained virtual business planning problem |
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Affiliation: | 1. Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS-INPT-UPS, Toulouse, France;2. IFP Energies nouvelles, Rond-point de l’échangeur de Solaize, BP 3, Solaize 69360, France |
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Abstract: | A virtual business problem is studied, in which a company-contractor outsources production to specialized subcontractors. Finances of the contractor and resource capacities of subcontractors are limited. The objective is to select subcontractors and distribute a part of the demanded production among them so that the profit of the contractor is maximized. A generalization of the knapsack problem, called Knapsack-of-Knapsacks (K-of-K), is used to model this situation, in which items have to be packed into small knapsacks and small knapsacks have to be packed into a large knapsack. A fully polynomial time approximation scheme is developed to solve the problem K-of-K. |
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Keywords: | Virtual business planning Knapsack problem Dynamic programming Fully polynomial time approximation scheme |
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