Puzzle—Chain-Reaction: A Puzzle to Demonstrate TSP Formulation

A Time Bucket Formulation for the TSP with Time Windows

The Traveling Salesman Problem with Time Windows (TSPTW) is the problem of finding a minimum-cost path visiting a set of cities exactly once, where each city must be visited within a given time window. We present an extended formulation for the problem based on partitioning the time windows into sub-windows, which we call buckets. We present cutting planes for this formulation that are computat...

A Multi-commodity Pickup and Delivery Open-tour m-TSP Formulation for Bike Sharing Rebalancing Problem

Bike sharing systems (BSSs) offer a mobility service whereby public bikes, located at different stations across an urban area, are available for shared use. An important point is that the distribution of rides between stations is not uniformly distributed and certain stations fill up or empty over time. These empty and full stations lead to demand for bikes and return boxes that cannot be fulfi...

On Asymmetric TSP: Transformation to Symmetric TSP and Performance Bound

We show that an instance of traveling salesman problem (TSP) of size n with an asymmetric distance matrix can be transformed into an instance of TSP of size 2n with a symmetric distance matrix. This is an improvement over earlier transformations of this kind which triple the size of the problem. Next we use this transformation to obtain a Hamiltonian tour of a general TSP (which may be asymmetr...

A rare type of reaction to tattoo materials: A granuloma annulare-like reaction

Granuloma annulare represents a reaction pattern that is recognized as idiopathic in many cases but is attributed to a variety of inciting factors in some cases. In this report, we present a case of granuloma annulare-like pattern reaction to tattoo pigment.

A statistical approach to the tsp