Alejandro Toriello Analysts predict impending shortages in the health care workforce, yet wages for health care workers already account for over half of U.S. health expenditures. It is thus increasingly important to adequately plan to meet health workforce demand at reasonable cost. Using infinite linear programming methodology, we propose an infinite-horizon model for health workforce planning in … Read more
We consider two linear relaxations of the asymmetric traveling salesman problem (TSP), the Held-Karp relaxation of the TSP’s arc-based formulation, and a particular approximate linear programming (ALP) relaxation obtained by restricting the dual of the TSP’s shortest path formulation. We show that the two formulations produce equal lower bounds for the TSP’s optimal cost regardless … Read more
We propose a dynamic traveling salesman problem (TSP) with stochastic arc costs motivated by applications, such as dynamic vehicle routing, in which a decision’s cost is known only probabilistically beforehand but is revealed dynamically before the decision is executed. We formulate the problem as a dynamic program (DP) and compare it to static counterparts to … Read more
We consider cooperative traveling salesman games with non-negative asymmetric costs satisfying the triangle inequality. We construct a stable cost allocation with budget balance guarantee equal to the Held-Karp integrality gap for the asymmetric traveling salesman problem, using the parsimonious property and a previously unknown connection to linear production games. We also show that our techniques … Read more
We propose a framework of lower bounds for the asymmetric traveling salesman problem (TSP) based on approximating the dynamic programming formulation with diff erent basis vector sets. We discuss how several well-known TSP lower bounds correspond to intuitive basis vector choices and give an economic interpretation wherein the salesman must pay tolls as he travels between … Read more
We consider optimization problems with some binary variables, where the objective function is linear in these variables. The stability region of a given solution of such a problem is the polyhedral set of objective coefficients for which the solution is optimal. A priori knowledge of this set provides valuable information for sensitivity analysis and re-optimization … Read more