Browsing by Author "Uzun, Gozde Onder"

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New formulations for multiple traveler minimum latency problem with time windows
(2022) Uzun, Gozde Onder; Kara, Imdat; ABH-1078-2021
In this paper, new mathematical models for homogeneous and heterogeneous multiple traveler minimum latency problem with time windows (kLPTW), named as M2 and M4 are developed. These models are computationally compared with existing models named as M1 and M3 for kLPTW in terms of CPU times and percentage deviation from linear programming relaxation values. A short summary of the computational analysis is given in table A below. In Table A, k is the number of travelers. The first column under the number of traveler cell shows the average CPU times of problems solved in time limit and the second column shows the average percentage deviations. We observed that, our formulations are superior than the existing formulations for all the problems for both kLPTW types with respect to each performance criteria. Purpose: The aim of this study is to develop new mathematical formulations for homogeneous and heterogeneous multiple traveler minimum latency problem with time windows. Theory and Methods: Based on the mixed integer linear programming, mathematical models with polynomial number of decision variables and constraints are developed. Benchmark instances from the literature are solved with existing formulations and proposed new formulations by using CPLEX 12.5.0.1. CPU times and percentage deviation from linear programming relaxation values are considered as performance criteria. Results: We solved 125 problems with varying number of nodes and time windows. In all the problem solved proposed formulations are better than the existing formulations in terms of both of the performance criteria. Conclusion: The proposed formulations for homogeneous and heterogeneous multiple traveler minimum latency problem with time windows are superior than the existing formulations and able to solve the problems up to 100 nodes with narrow time windows. Proposed formulations may be used to solve small and moderate real-life problems very easily. They may also be used for testing the performance of the heuristics constructed for kLPTW.
New Formulations for The Traveling Repairman Problem with Time Windows
(2018) Kara, Imdat; Uzun, Gozde Onder; ABH-1078-2021
New formulations for the traveling repairman problem with time windows
(2021) Uzun, Gozde Onder; Kara, Imdat; ABH-1078-2021
The Traveling Repairman Problem (TRP) is one of the most important variants of the Traveling Salesman Problem (TSP). The objective function of TRP is to find a Hamiltonian path or tour starting from the origin while minimizing the total latency (waiting or delay time) for all customers. The latency of a customer is defined as the time passed from the beginning of a tour (or path) until a customer?s service is completed. TRP with time windows (TRPTW) is the case where the earliest and latest times for visiting each customer are restricted by prescribed time windows. The literature on TRPTW is scarce. We only found one formulation for TRPTW and one formulation for its variant. In this paper, we propose four new mathematical models for TRPTW with O(n2) binary variables and O(n2) constraints. We computationally analyze the performance of existing and new formulations by solving symmetric and asymmetric benchmark instances with CPLEX 12.5.0.1 and compare the results in terms of CPU times and optimality gap. We observed that our two formulations were extremely faster than existing formulations, and they could optimally solve symmetric instances up to 150 nodes and asymmetric instances up to 131 nodes within seconds.
An optimization for milling operation of Kevlar fiber-epoxy composite material using factorial design and goal programming methods
(2019) Ic, Yusuf Tansel; Elaldi, Faruk; Kececi, Baris; Uzun, Gozde Onder; Limoncuoglu, Nur; Aksoy, Irem; 0000-0003-0592-6868; 0000-0002-2730-5993; AAI-1081-2020; AAG-5060-2019; F-1639-2011; AAC-4793-2019
Kevlar fiber-epoxy composite material is extensively used in manufacturing areas because of the advantages of composite material's characteristics. It is usually processed by traditional machining methods but the drawbacks for determination of optimum cutting parameters might cause some material deformations during machining process. In this study, the cutting parameters are concurrently optimized by using the integrated 2k factorial design and goal programming methods for minimum delamination and minimum surface roughness of Kevlar fiber-epoxy composite and the best machining parameters have been obtained for the material. The results were compared with the results of the multi-criteria decision-based Taguchi methods.
Traveling Repairmen Problem: A Biogeography-Based Optimization
(2022) Uzun, Gozde Onder; Dengiz, Berna; Kara, Imdat; Karasan, Oya Ekin
Traveling Repairman Problem (TRP), which is also known by names cumulative traveling salesman problem, the deliveryman problem and the minimum latency problem, is a special variant of Traveling Salesman Problem (TSP). In contrast to the minimization of completion time objective of TSP, the desired objective of TRP is to minimize the cumulative latency (waiting time or delay time) of all customers. In this paper, a generalized version of TRP with multi depots and time windows, namely Multi Depot Traveling Repairman Problem with Time Windows (MDTRPTW) is considered. A group of homogeneous repairmen initiate and finish their visit tours at multiple depots. Each customer must be visited exactly by one repairman within their provided earliest end latest times. Being a challenging Nondeterministic Polynomial-hard (NP-hard) optimization problem, exact solution approaches are not expected to scale to realistic dimensions of MDTRPTW. Thus, we propose a biogeography-based optimization algorithm (BBOA) as a metaheuristic approach to solve large size MDTRPTW problems. The proposed metaheuristic is analyzed in terms of solution quality, coefficient of variation as well as computation time by solving some test problems adapted from the related literature. The efficacy of the proposed solution methodology is demonstrated by solving instances with 288 customers within seconds.