Abstract
A few theoretical results are given for the fractional programming problem where the objective function is the product of an affine function and a linear fractional function and where the feasible region is a polytope. Moreover, a simplex-like algorithm is proposed to solve the same problem when the feasible region is bounded. The algorithm is based on the exploration of a set of suitably defined optimal level solutions.
Riassunto
Nel lavoro vengono esposti alcuni risultati teorici per un problema di programmazione frazionaria nel quale la funzione oggetto è data dal prodotto tra una funzione affine e una funzione lineare definita su una regione ammissibile poliedrica. Viene inoltre formulato un algoritmo di tipo simplesso che consente la risoluzione del problema qualora la regione ammissibile sia limitata. Tale algoritmo è basato sulla esplorazione di un insieme opportunamente definito di soluzioni ottime di livello.
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This research was partially supported by MURST.
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Ellero, A., Tomasin, E.M. A parametric simplex-like algorithm for a fractional programming problem. Rivista di Matematica per le Scienze Economiche e Sociali 16, 77–88 (1993). https://doi.org/10.1007/BF02095126
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DOI: https://doi.org/10.1007/BF02095126