14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
SPREADSHEETS in EDUCATIONBond UniversityVolume 12 I Issue 2 I 2020Spreadsheet-Based Modeling and Optimization of a Bi-Modal Traveling Salesman Problem 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-casem: Model, Solution, and CaseRoger Grinde,Decision SciencesUniversity of New Hampshireroger.qrinde(a)unh.eduFollow this and additional works at: https.7Zsie.scholasticahQ.comanThis work is licensed under a Creative Commons Attributiọn-Noncommerậal-Nọ Derivative Works 4,0 Licence.Spreadsheet-Based Mod 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-caseeling and Optimization of a Bi-Modal Traveling Salesman Problem: Model, Solution, and CaseRoger Grinde Decision Sciences.University of New Hampshire r14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
o$er.$nnde&unk.eduAbstract'Ibis paper presents a bi-modal routing problem and two-phase spreadsheet-based model and solution approach. Ihe problem is SPREADSHEETS in EDUCATIONBond UniversityVolume 12 I Issue 2 I 2020Spreadsheet-Based Modeling and Optimization of a Bi-Modal Traveling Salesman Problem 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-caseet of peaks, where they have defined a number of hikes from which to choose. The problem is to a) identify the set of hikes in order to minimize a hiking time objective while ascending all peaks, followed by b) sequencing the chosen hikes in order to minimize a driving distance objective The problem 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case essentially combines two well-known problems in Operations Research: the Set Covering Problem and the Traveling Salesman Problem. A mathematical prog14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
ramming formulation is presented, followed by a detailed explanation of the Excel1'1 model and solution approach with Solver1'1, using linear and evolSPREADSHEETS in EDUCATIONBond UniversityVolume 12 I Issue 2 I 2020Spreadsheet-Based Modeling and Optimization of a Bi-Modal Traveling Salesman Problem 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-caseion example all the way up to a semester long project done in several phases A case, spilt mto two parts, is provided in the appendix. The full workbook and a template file is available upon request from the authorKeywords: routing, optimization. Operations Research, traveling salesman, spreadsheet, 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case Excel, Solver, VBA, Simplex Method, evolutionary algorithm1.0 IntroductionIbis paper presents a model and solution of a bi-modal routing problem rela14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
ted to the well-known Traveling Salesman Problem (TSP). Il is bi-modal due Io vehicular and walking travel and is termed lhe Bi-Modal Covering SalesmaSPREADSHEETS in EDUCATIONBond UniversityVolume 12 I Issue 2 I 2020Spreadsheet-Based Modeling and Optimization of a Bi-Modal Traveling Salesman Problem 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-caselated to Optimization, Operations Research, Management Science, Busmess Analytics, and programming at various levels and2various programs (e g., business, engineering, applied mathematics) depending on what aspects of the problem-solving process the instructor wishes to emphasize. From an educationa 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-casel standpoint, the problem has some key differences compared to the TSP, which present questions of how to model it, and then how to find a solution ap14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
proach. The problem can be used to emphasize the modeling aspect, the spreadsheet implementation. VBA enhancements, or some combination of these It coSPREADSHEETS in EDUCATIONBond UniversityVolume 12 I Issue 2 I 2020Spreadsheet-Based Modeling and Optimization of a Bi-Modal Traveling Salesman Problem 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-casese in an MBA course in Management Science with good results.The specific problem arises in hiking, but it is related Io some other variations of the ISP and is applicable to some other bi-modal routing situations. Ihoro are a number of mountain peaks to climb. For this paper, the specific problem of 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case the 48 mountain peaks above 4000 feet in altitude, in the State of New Hampshire, USA, are used (Smith & Dickerman, 2012). The hikers seek to a) iden14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
tify the set of hikes to perform which will ascend each peak in the shortest Inking time; and b) sequence the hikes to minimize the driving distance bSPREADSHEETS in EDUCATIONBond UniversityVolume 12 I Issue 2 I 2020Spreadsheet-Based Modeling and Optimization of a Bi-Modal Traveling Salesman Problem 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-cases are reached by one or more trails, each with trailheads. /X specific, trail may traverse more than one peak and maybe a round-trip trail or a one-way trail. I railheads are connected by a network of roads. I wo hikers utilize two vehicles to roach the trailheads, and then hike one or more hikes fr 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-caseom that trailhead. In the case of one-way hikes, the hikers must stage a vehicle at each end of the hailheadIn this section, related work is discussed14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
Section 2 presents the problem formulation and outlines the solution approach The spreadsheet implementation (in Excel™ and VBA) is explained in SectSPREADSHEETS in EDUCATIONBond UniversityVolume 12 I Issue 2 I 2020Spreadsheet-Based Modeling and Optimization of a Bi-Modal Traveling Salesman Problem 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-casease study presented, in two parts. Ihe spreadsheet implementation and a template file is available from the author upon request.Ihe TSP and related Vehicle Routing Problem (VRP) have a rich literature due to their many practical applications as well as solution challenges. Examples include Gutin (20 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case07), Applegate et al. (2007), Golden et al. (2008), and Braekers et al (2016). Review of multi-objective problems is done by Jozefowiez et al. (2008).14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
The Covering Tour Problem (CTP) has similarity to the BCSP discussed in this paper, in that there are two node sets. However, in the CTP there is onlSPREADSHEETS in EDUCATIONBond UniversityVolume 12 I Issue 2 I 2020Spreadsheet-Based Modeling and Optimization of a Bi-Modal Traveling Salesman Problem 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case within some critical distance of a visited nodes (e.g., rural health clinics might be one node set, and towns/villages might be the other node set). Current & Schilling3(1989) introduced this problem, and it has been studied by others. Tile problem most directly related to the BCSP presented in thi 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-cases paper is termed the Walking Line of Travel Problem (WLT). It was studied by Levy & Bodin (1988). lhe example provided was to schedule postal carrier14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
s who drive to a parking area, complete a walking tour delivering mail, and return to the vehicle. It differs from the BCSP in that one-way trips are SPREADSHEETS in EDUCATIONBond UniversityVolume 12 I Issue 2 I 2020Spreadsheet-Based Modeling and Optimization of a Bi-Modal Traveling Salesman Problem 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-caseh using traditional optimization software, and computational results.2.0 Problem Formulation and Solution ApproachThe BCSP uses two networks, one for each mode of transportation In the hiking case problem, one network is a sei of parking areas (/’1, p?, ..., Pm) connected by roads. I he other networ 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-casek is a set of peaks ("cities" in the traditional I SP language), denoted by (Cl, (ỳ, Cn) and connected by trails. Some trails have connection points t14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
o parking areas. Each of the peaks must be visited al least once. Figure 1 shows an example. Ihe overall objective isto minimize total weighted travelSPREADSHEETS in EDUCATIONBond UniversityVolume 12 I Issue 2 I 2020Spreadsheet-Based Modeling and Optimization of a Bi-Modal Traveling Salesman Problem 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-caseing one or more hikes (either cyclical or chain hikes, to be discussed shortly), chiving to another parking area and hiking from there, and returning to the home base after all peaks have been visited.Figure 1. Road and Trail Networksihe concept of a single trip visiting one or more peaks (hike in t 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-casehis problem context) is as follows. The car is driven to a parking area Pi. A hike is performed, which visits one or more peaks. Two possibilities exi14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-case
st for the end of the hike. A loop or cyclical hike is when the hikers return to Pi, and then drive to another parking location (or perform another hiSPREADSHEETS in EDUCATIONBond UniversityVolume 12 I Issue 2 I 2020Spreadsheet-Based Modeling and Optimization of a Bi-Modal Traveling Salesman Problem 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-casehain hike, both hikers drive to Pt, the endpoint of the hike, and leave one car. Then they drive to Pl, and depart on the hike. Finishing the hike at P;, they drive back to Pl to retrieve the other carFigure 2. Cyclical HikeChain Trip IllustrationFigure 3. Chain Hike5 14531-spreadsheet-based-modeling-and-optimization-of-a-bi-modal-traveling-salesman-problem-model-solution-and-caseSPREADSHEETS in EDUCATIONBond UniversityVolume 12 I Issue 2 I 2020Spreadsheet-Based Modeling and Optimization of a Bi-Modal Traveling Salesman ProblemGọi ngay
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