The Pickup and Delivery Problem with Split Loads and Transshipments: A Branch-and-Cut Solution Approach
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
Authors: Wolfinger, David; Salazar-Gonzalez, Juan-Jose
Abstract
This paper addresses the design of routes for a fleet of vehicles serving customer requests. It is a pickup and delivery problem where each customer location can be visited several times, and load may be transshipped from one vehicle to another at specific locations. The aim is to minimize the sum of travel costs and transshipment costs. We present an arc-based mixed-integer formulation for the problem and propose a branch-and-cut algorithm for solving it. Extensive computational results illustrate the performance of the algorithm. (C) 2020 The Author(s). Published by Elsevier B.V.
An Analysis of Soft X-Ray Structures at Kiloparsec Distances from the Active Nucleus of Centaurus A Galaxy
ASTROPHYSICAL JOURNAL
Authors: Krol, Dominika L.; Marchenko, Volodymyr; Ostrowski, Michal; Stawarz, Lukasz
Abstract
Here we reanalyze the archival Chandra data for the central parts of the Centaurus A radio galaxy, aiming for a systematic investigation of the X-ray emission associated with the inner radio lobes in the system, and their immediate surroundings. In particular, we focus on four distinct features characterized by the soft excess with respect to the adjacent fields. Those include the two regions located at kiloparsec distances from the nucleus to the west and east, the extended bow-shock structure to the south, and a fragment of a thin arc north of the center. The selected north, west, and south features coincide with the edges of the radio lobes, while the east structure is seemingly displaced from the radio-emitting plasma. Our X-ray spectral analysis reveals (i) a power-law emission component with photon index Gamma similar to 2 in the north, east, and south regions, and (ii) a dense (number density similar to 0.3 cm(-3)) and relatively cold (temperature similar to 0.2 keV) gas in the east and west regions. The power-law emission is consistent with the synchrotron continuum generated at the edges of the radio structure, and implies that the efficiency of the electron acceleration at the terminal bow shock does not vary dramatically over the inner lobes' extension. The presence of gaseous condensations, on the other hand, could possibly be understood in terms of a massive outflow from the central regions of the galaxy.