Two classical transportation problems revisited: Pure constant fixed charges and the paradox

Two classical transportation problems revisited: Pure constant fixed charges and the paradox

We analyze degeneracy characterizations for two classical problems: the transportation paradox in linear transportation problems and the pure constant 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 ...

The Transportation Paradox Revisited

The transportation paradox is related to the classical transportation problem. For certain instances of this problem an increase in the amount of goods to be transported may lead to a decrease in the optimal total transportation cost. Thus this phenomenon has also been named the more-for-less-paradox. Even though the paradox has been known since the early days of linear programming, it has got ...

Fixed-charge transportation problems on trees

We consider a class of fixed-charge transportation problems over graphs. We show that this problem is strongly NP-hard, but solvable in pseudo-polynomial time over trees using dynamic programming. We also show that the LP formulation associated to the dynamic program can be obtained from extended formulations of single-node flow polytopes. Given these results, we present a unary expansion-based...

CLASSICAL k-SERVER QUEUES REVISITED: SOME PROBLEMS

The talk surveys both recent and ‘classical’ studies of k-server queueing systems. There will not be time to do justice to more than a selection of the following topics. 1. EXISTENCE. Kiefer and Wolfowitz’ (1955) proof of the existence of a stationary regime for the GI/GI/k FCFS system relies on ‘An Essential Lemma’. In reality it hinges on a strong law of large numbers, of which variants are u...

Two selection problems revisited