Rainer E. Burkard, Günter Rote, Günther Ruhe, and Norbert
Algorithmische Untersuchungen zu bikriteriellen kostenminimalen Flüssen in
Wissenschaftliche Zeitschrift der Technischen Hochschule Leipzig 33 (1989),
333–341, (Zbl 706.90024).
Finding optimal flows in networks is one of the most common tasks in
Operations Research. With few exceptions, this problem has so far been treated
with a single objective function only. Many practical problems involve,
however, several competing objectives.
In this paper we design and analyze algorithms for bicriteria minimum-cost
flows. We present some complexity estimates, which lay the basis for
the development of algorithms. We present some general results about the
approximation of convex functions. We describe an exact algorithm and different
realizations of the Sandwich approximation scheme, and we give results of
numerical test calculations.
Last update: March 9, 2012.