A Linear Bound On The Diameter Of The Transportation Polytope

We prove that the combinatorial diameter of the skeleton of the polytope of feasible solutions of any m× n transportation problem is at most 8 (m+ n− 2). The transportation problem (TP ) is a classic problem in operations research. The problem was posed for the first time by Hitchcock in 1941 [9] and independently by Koopmans in 1947 [12], and appears in any standard introductory course on operations research. The m × n TP has m supply points and n demand points. Each supply point i holds a quantity ri > 0, and each demand point j wants a quantity cj > 0, with m ∑