The transportation problem is a fundamental problem in Operations Research, where items need to be transported from supply nodes (each with a given supply) to demand nodes (each with a given demand) in the cheapest possible way. Here, we are interested in a generalization of the transportation...

Given a weighted graph G = (V, E), the Equitable Traveling Salesman Problem (ETSP) asks for two perfect matchings in G such that (1) the two matchings together form a Hamiltonian cycle in G and (2) the absolute difference in costs between the two matchings is minimized. The problem is shown to...