Revisiting the fixed charge transportation problem

Susann Schrenk (1) , Van-Dat Cung (2) , Gerd Finke (2)

1 G-SCOP_OC - Optimisation Combinatoire
2 G-SCOP_ROSP - Recherche Opérationnelle pour les Systèmes de Production

We analyze degeneracy characterizations for two classical problems: the transportation paradox in linear transportation problems and the pure fixed charge transportation problem. Solving the pure constant fixed charge problem is equivalent to finding a basic tree solution with maximum degree of degeneracy. Problems possess degenerate solutions if the equal subsum property is satisfied for the supplies and demands. To determine the existence of degeneracy is an NP-complete problem. But this NP-hardness remains even if all equal-subsums are known in advance. Finally, the paradox is linked to overshipment solutions, which belong to supply and demand configurations that tend to have a high degree of degeneracy.

Domaines: Recherche opérationnelle [math.OC]

Susann Schrenk, Van-Dat Cung, Gerd Finke. Revisiting the fixed charge transportation problem. European Chapter on Combinatorial Optimization (ECCO) XXII, May 2009, Jerusalem, Israel. pp.19. ⟨hal-00414346⟩