Complete solution of a constrained tropical optimization problem with application to location analysis

We present a multidimensional optimization problem that is formulated and solved in the tropical mathematics setting. The problem consists of minimizing a nonlinear objective function defined on vectors over an idempotent semifield by means of a conjugate transposition operator, subject to constraints in the form of linear vector inequalities. A complete direct solution to the problem under fairly general assumptions is given in a compact vector form suitable for both further analysis and practical implementation. We apply the result to solve a multidimensional minimax single facility location problem with Chebyshev distance and with inequality constraints imposed on the feasible location area.Comment: 20 pages, 3 figure

Analytical Modeling Framework to Assess the Economic and Environmental Impacts of Residential Deliveries, and Evaluate Sustainable Last-Mile Strategies

In the last decade, e‐commerce has grown substantially, increasing business‐to‐business, business‐to‐consumer, and consumer‐to‐consumer transactions. While this has brought prosperity for the e-retailers, the ever-increasing consumer demand has brought more trucks to the residential areas, bringing along externalities such as congestion, air and noise pollution, and energy consumption. To cope with this, different logistics strategies such as the introduction of micro-hubs, alternative delivery points, and use of cargo bikes and zero emission vehicles for the last mile have been introduced and, in some cases, implemented as well. This project, hence, aims to develop an analytical framework to model urban last mile delivery. In particular, this study will build upon the previously developed econometric behavior models that capture e-commerce demand. Then, based on continuous approximation techniques, the authors will model the last-mile delivery operations. And finally, using the cost-based sustainability assessment model (developed in this study), the authors will estimate the economic and environmental impacts of residential deliveries under different city logistics strategies.View the NCST Project Webpag

An optimal algorithm for the weighted backup 2-center problem on a tree

In this paper, we are concerned with the weighted backup 2-center problem on a tree. The backup 2-center problem is a kind of center facility location problem, in which one is asked to deploy two facilities, with a given probability to fail, in a network. Given that the two facilities do not fail simultaneously, the goal is to find two locations, possibly on edges, that minimize the expected value of the maximum distance over all vertices to their closest functioning facility. In the weighted setting, each vertex in the network is associated with a nonnegative weight, and the distance from vertex $u$ to $v$ is weighted by the weight of $u$. With the strategy of prune-and-search, we propose a linear time algorithm, which is asymptotically optimal, to solve the weighted backup 2-center problem on a tree.Comment: 14 pages, 4 figure

Layout Optimization of a repair facility using discrete event simulation

Technological advancements in the field of simulation have enabled production managers to model and simulate their facilities under various scenarios, in order to optimize system performance. In particular the reconfiguration of factory layouts can be time consuming and expensive; Discrete Event Simulation (DES) can be used to model and assess various scenarios to assist production managers with layout planning. Significant benefits can be achieved through the use of DES for factory layout optimization including: decreased lead times, reduced manufacturing costs, efficient materials handling and increased profit. This paper presents the development of a DES model in WITNESS for the analysis and factory layout optimization of a repair facility. The aim of the model is to allow decision makers to assess various layouts and configurations with a view to optimize production. The model has been built with a link to an Excel spreadsheet to enable data input and the visualization of Key Performance Indicators (KPIs). Specific functions have been built into the simulation model to set and save new layouts within Excel to facilitate layout optimization. The model will be used to optimize the factory configuration

Location analysis - possibilities of use in public administration

V článku jsou stručně popsána teoretická východiska lokační teorie a možnosti využití v oblasti veřejné správy jako je navrhování sítí a lokace různých zařízení v geografickém prostoru regionů.The paper under consideration describes key theoretical issues of continuous/discrete location theory and possibilities of applications in the area of public administration activities such as networks design and location of different facilities in geographical area of regions

Robust Legged Robot State Estimation Using Factor Graph Optimization

Legged robots, specifically quadrupeds, are becoming increasingly attractive for industrial applications such as inspection. However, to leave the laboratory and to become useful to an end user requires reliability in harsh conditions. From the perspective of state estimation, it is essential to be able to accurately estimate the robot's state despite challenges such as uneven or slippery terrain, textureless and reflective scenes, as well as dynamic camera occlusions. We are motivated to reduce the dependency on foot contact classifications, which fail when slipping, and to reduce position drift during dynamic motions such as trotting. To this end, we present a factor graph optimization method for state estimation which tightly fuses and smooths inertial navigation, leg odometry and visual odometry. The effectiveness of the approach is demonstrated using the ANYmal quadruped robot navigating in a realistic outdoor industrial environment. This experiment included trotting, walking, crossing obstacles and ascending a staircase. The proposed approach decreased the relative position error by up to 55% and absolute position error by 76% compared to kinematic-inertial odometry.Comment: 8 pages, 12 figures. Accepted to RA-L + IROS 2019, July 201