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15 pages, 5766 KiB

Open AccessCommunication

An Optimal Routing Algorithm for Unmanned Aerial Vehicles

by Sooyeon Kim, Jae Hyun Kwak, Byoungryul Oh, Da-Han Lee and Duehee Lee

Sensors 2021, 21(4), 1219; https://doi.org/10.3390/s21041219 - 9 Feb 2021

Cited by 14 | Viewed by 3531

A delivery service using unmanned aerial vehicles (UAVs) has potential as a future business opportunity, due to its speed, safety and low-environmental impact. To operate a UAV delivery network, a management system is required to optimize UAV delivery routes. Therefore, we create a routing algorithm to find optimal round-trip routes for UAVs, which deliver goods from depots to customers. Optimal routes per UAV are determined by minimizing delivery distances considering the maximum range and loading capacity of the UAV. In order to accomplish this, we propose an algorithm with four steps. First, we build a virtual network to describe the realistic environment that UAVs would encounter during operation. Second, we determine the optimal number of in-service UAVs per depot. Third, we eliminate subtours, which are infeasible routes, using flow variables part of the constraints. Fourth, we allocate UAVs to customers minimizing delivery distances from depots to customers. In this process, we allow multiple UAVs to deliver goods to one customer at the same time. Finally, we verify that our algorithm can determine the number of UAVs in service per depot, round-trip routes for UAVs, and allocate UAVs to customers to deliver at the minimum cost. Full article

(This article belongs to the Special Issue Time-Sensitive Networks for Unmanned Aircraft Systems)

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14 pages, 691 KiB

Open AccessArticle

Comparison of the Sub-Tour Elimination Methods for the Asymmetric Traveling Salesman Problem Applying the SECA Method

by Ramin Bazrafshan, Sarfaraz Hashemkhani Zolfani and S. Mohammad J. Mirzapour Al-e-hashem

Axioms 2021, 10(1), 19; https://doi.org/10.3390/axioms10010019 - 8 Feb 2021

Cited by 18 | Viewed by 7393

Abstract

There are many sub-tour elimination constraint (SEC) formulations for the traveling salesman problem (TSP). Among the different methods found in articles, usually three apply more than others. This study examines the Danzig–Fulkerson–Johnson (DFJ), Miller–Tucker–Zemlin (MTZ), and Gavish–Graves (GG) formulations to select the best asymmetric traveling salesman problem (ATSP) formulation. The study introduces five criteria as the number of constraints, number of variables, type of variables, time of solving, and differences between the optimum and the relaxed value for comparing these constraints. The reason for selecting these criteria is that they have the most significant impact on the mathematical problem-solving complexity. A new and well-known multiple-criteria decision making (MCDM) method, the simultaneous evaluation of the criteria and alternatives (SECA) method was applied to analyze these criteria. To use the SECA method for ranking the alternatives and extracting information about the criteria from constraints needs computational computing. In this research, we use CPLEX 12.8 software to compute the criteria value and LINGO 11 software to solve the SECA method. Finally, we conclude that the Gavish–Graves (GG) formulation is the best. The new web-based software was used for testing the results. Full article

(This article belongs to the Special Issue Multiple-Criteria Decision Making)

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19 pages, 1149 KiB

Open AccessArticle

Capacitated Lot-Sizing Problem with Sequence-Dependent Setup, Setup Carryover and Setup Crossover

by Jangha Kang

Processes 2020, 8(7), 785; https://doi.org/10.3390/pr8070785 - 5 Jul 2020

Cited by 2 | Viewed by 4097

Abstract

Since setup operations have significant impacts on production environments, the capacitated lot-sizing problem considering arbitrary length of setup times helps to develop flexible and efficient production plans. This study discusses a capacitated lot-sizing problem with sequence-dependent setup, setup carryover and setup crossover. A new mixed integer programming formulation is proposed. The formulation is based on three building blocks: the facility location extended formulation; the setup variables with indices for the starting and the completion time periods; and exponential number of generalized subtour elimination constraints (GSECs). A separation routine is adopted to generate the violated GSECs. Computational experiments show that the proposed formulation outperforms models from the literature. Full article

(This article belongs to the Special Issue Advances in Sustainable Supply Chains)

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