Author: Dmitry Krass
Abstract: Inventory problems with transshipments, where facilities are allowed to satisfy some of the demand by transshipping available inventory between each other are notoriously hard to analyze. Yet, transshipments are quite common in practice and have the potential for greatly reducing the system operating costs.
Most of the traditional literature on transshipments has focused on deriving optimal replenishment and transshipment policies (under very restrictive assumptions) and have ignored the location aspects altogether. The inventory location models, on the other hand, have not considered transshipments at all.
A recent ``breakthrough'' in transshipment research has been the application of Infinitesimal Perturbation Analysis (IPA) algorithm - form of approximate dynamic programming - which has allowed for treatment of much more general problems. We show how this technique can be used to integrate location and transshipment models, which yield interesting managerial insights. We also discuss several approaches rooted in traditional location models that allow for a much more efficient implementation of the IPA-based methods.

Author: Zhou Xu
Abstract: We study an extension of the classical traveling salesman problem (TSP) to the situation where k salesmen are dispatched. One needs to decide a route and a depot for each salesman, so as to minimize the total travel distance for the k salesmen to service all customers in a metric graph. As with the TSP, the generalized problem is motivated by a large range of applications. In this talk, we present a [2-1/(2k)]-approximation algorithm for this problem, which improves the existing best approximation ratio of 2.