ISSN:
1432-5217
Keywords:
Key words: Transportation problem
;
permutable demand vector
;
computational complexity
;
minimum weight f-factor problem
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Economics
Notes:
Abstract. In this note we investigate the computational complexity of the transportation problem with a permutable demand vector, TP-PD for short. In the TP-PD, the goal is to permute the elements of the given integer demand vector b=(b 1,…,b n) in order to minimize the overall transportation costs. Meusel and Burkard [6] recently proved that the TP-PD is strongly NP-hard. In their NP-hardness reduction, the used demand values b j, j=1,…,n, are large integers. In this note we show that the TP-PD remains strongly NP-hard even for the case where b j∈{0,3} for j=1,…,n. As a positive result, we show that the TP-PD becomes strongly polynomial time solvable if b j∈{0,1,2} holds for j=1,…,n. This result can be extended to the case where b j∈{κ,κ+1,κ+2} for an integer κ.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s001860050031
Permalink
