Browsing by Author "Öztop, Hande"

Now showing 1 - 14 of 14

Citation - WoS: 10
Citation - Scopus: 13
A Bus Crew Scheduling Problem with Eligibility Constraints and Time Limitations
(ELSEVIER SCIENCE BV, 2017) Hande Oztop; Ugur Eliiyi; Deniz Tursel Eliiyi; Levent Kandiller; Öztop, Hande; Kandiller, Levent; Eliiyi, Uǧur; Eliiyi, Deniz Türsel; HB Celikoglu; AH Lav; MA Silgu
In this study we consider a real life crew scheduling problem (CSP) of a public bus transportation authority where the objective is to determine the optimal number of different types of crew members with a minimum cost that cover a given set of tasks regarding working and spread time limitations. Each driver has a spread time limit from the start time to the end time of his/her shift including the idle times. Additionally a driver cannot exceed the maximum total working time limit. The processing times of the tasks assigned to each driver are included in his/her working time as well as the sequence-dependent setup times. As our study is inspired from a real life CSP the tasks can require different types of vehicles that require different crew capabilities. Therefore there are several crew classes based on the competencies required to use certain vehicle types inducing eligibility constraints in the problem. We formulate a Tactical Fixed Job Scheduling Problem based binary programming model for the problem. In the formulation we consider only processing times of tasks as working time. In order to avoid defining an additional sequence control variable that explodes the model size and in turn ruins solution performance we develop an iterative valid inequality generation scheme which eliminates task sequences exceeding the total working time when setup times are included. The performance of the developed model is investigated through a comprehensive experimentation and the numerical results are reported. The results show that our optimal seeking solution procedure is quite effective in terms of solution time for instances with up to 120 tasks. (C) 2017 The Authors. Published by Elsevier B.V.
A Hybrid Flow Shop Scheduling Problem
(Springer Science and Business Media Deutschland GmbH, 2020) Ayşegül Eda Özen; Gülce Çini; Merve Çamlıca; Nilay Çınar; Hasan Bahtiyar Soydan; Levent Kandiller; Hande Oztop; Çini, Gülce; Özen, Ayşegül Eda; Çamlıca, Merve; Kandiller, Levent; Öztop, Hande; Çınar, Nilay; Soydan, Hasan Bahtiyar; N.M. Durakbasa , M.N. Osman Zahid , R. Abd. Aziz , A.R. Yusoff , N. Mat Yahya , F. Abdul Aziz , M. Yazid Abu , M.G. Gençyilmaz
Hybrid flow shop environment generally refers to the flow shop with multiple parallel machines per stage. Hybrid flow shop scheduling problem (HFSP) is a complex combinatorial optimization problem that came across in many real-life problems. In this study a real-life HFSP of a lubricant company is considered where the aim is to minimize total weighted completion time of the jobs. Apart from classical HFSPs the studied problem has additional constraints such as machine eligibility sequence-dependent setup times and machine capacities. Due to the additional constraints in the system a novel mixed integer linear programming model is proposed for the studied HFSP with three stages. As the problem is NP-hard two constructive heuristic algorithms and an improvement heuristic algorithm are also developed. The performance of the proposed heuristic algorithms is evaluated by comparisons with the optimal results obtained from the mathematical model. The extensive computational results show that proposed heuristic algorithms find near optimal results in reasonable computational times. Sensitivity analysis is also performed for the weight parameter of the problem which indicates that the proposed heuristic algorithms also perform very well for different weight parameter values. Finally the proposed heuristic algorithms are integrated into a user-friendly decision support system using Microsoft Excel VBA interface to provide an efficient scheduling tool for the company. © 2022 Elsevier B.V. All rights reserved.
A Multi-sided and Multi-model Assembly Line Balancing Problem
(Springer Science and Business Media Deutschland GmbH, 2021) Seda Gemici; Emine Otuzbir; İrem Almila Koçyiğit; Sinem Pekelli; Fethi Tüzmen; Hande Oztop; Levent Kandiller; Pekelli, Sinem; Otuzbir, Emine; Gemici, Seda; Koçyiğit, İrem Almila; Tüzmen, Fethi; Öztop, Hande; Kandiller, Levent; N.M. Durakbasa , M.G. Gençyılmaz
In this paper we study a real-life assembly line balancing problem (ALBP) of a cooler manufacturer brand in Manisa Turkey. The aim of this study is to create an effective assembly line balancing tool for the company which minimizes the number of stations and balances the total workloads of the stations while keeping the number of products produced the same. The studied ALBP is Type-1 ALBP that minimizes the number of workstations given a cycle time which is determined by a bottleneck operation. However different from the standard Type-1 ALBP some of the stations are two-sided stations in the studied assembly line. There are special constraints in the studied ALBP such as concurrent tasks preemptive tasks zone-restricted tasks and parallel tasks. Due to these additional characteristics of the system a novel mixed-integer linear programming (MILP) model is proposed for the studied ALBP to minimize the number of workstations. A secondary objective which balances the workload of the stations is also considered in the proposed MILP model using a lexicographic optimization. The computational experiments show that the proposed MILP model can obtain the optimal solution in reasonable computational time. When the model results are compared with the current system there is a 44% improvement in the number of stations on average. Furthermore a sensitivity analysis is performed to analyze the trade-off between the number of stations and cycle time criteria employing an ε-constraint method. Finally a user-friendly DSS is developed by embedding the proposed MILP model. © 2020 Elsevier B.V. All rights reserved.
Citation - WoS: 50
Citation - Scopus: 56
An energy-efficient permutation flowshop scheduling problem
(Elsevier Ltd, 2020) Hande Oztop; M. Fatih Tasgetiren; D. T. Eliiyi; Quanke Pan; Levent Kandiller; Tasgetiren, M. Fatih; Öztop, Hande; Pan, Quan-Ke; Kandiller, Levent; Eliiyi, Deniz Türsel
The permutation flowshop scheduling problem (PFSP) has been extensively explored in scheduling literature because it has many real-world industrial implementations. In some studies multiple objectives related to production efficiency have been considered simultaneously. However studies that consider energy consumption and environmental impacts are very rare in a multi-objective setting. In this work we studied two contradictory objectives namely total flowtime and total energy consumption (TEC) in a green permutation flowshop environment in which the machines can be operated at varying speed levels corresponding to different energy consumption values. A bi-objective mixed-integer programming model formulation was developed for the problem using a speed-scaling framework. To address the conflicting objectives of minimizing TEC and total flowtime the augmented epsilon-constraint approach was employed to obtain Pareto-optimal solutions. We obtained near approximations for the Pareto-optimal frontiers of small-scale problems using a very small epsilon level. Furthermore the mathematical model was run with a time limit to find sets of non-dominated solutions for large instances. As the problem was NP-hard two effective multi-objective iterated greedy algorithms and a multi-objective variable block insertion heuristic were also proposed for the problem as well as a novel construction heuristic for initial solution generation. The performance of the developed heuristic algorithms was assessed on well-known benchmark problems in terms of various quality measures. Initially the performance of the algorithms was evaluated on small-scale instances using Pareto-optimal solutions. Then it was shown that the developed algorithms are tremendously effective for solving large instances in comparison to time-limited model. © 2020 Elsevier B.V. All rights reserved.
Citation - Scopus: 8
An energy-efficient single machine scheduling with release dates and sequence-dependent setup times
(Association for Computing Machinery Inc acmhelp@acm.org, 2018) Uǧur Eliiyi; M. Fatih Tasgetiren; Damla Kizilay; Hande Oztop; Quanke Pan; Kizilay, Damla; Fatih Tasgetiren, M.; Öztop, Hande; Pan, Quan-Ke; Eliiyi, Uğur
This study considers single machine scheduling with the machine operating at varying speed levels for different jobs with release dates and sequence-dependent setup times in order to examine the trade-off between makespan and total energy consumption. A bi-objective mixed integer linear programming model is developed employing this speed scaling scheme. The augmented ε-constraint method with a time limit is used to obtain a set of non-dominated solutions for each instance of the problem. An energy-efficient multi-objective variable block insertion heuristic is also proposed. The computational results on a benchmark suite consisting of 260 instances with 25 jobs from the literature reveal that the proposed algorithm is very competitive in terms of providing tight Pareto front approximations for the problem. © 2018 Elsevier B.V. All rights reserved.
Citation - WoS: 33
Citation - Scopus: 37
Ensemble of metaheuristics for energy-efficient hybrid flowshops: Makespan versus total energy consumption
(Elsevier B.V., 2020) Hande Oztop; M. Fatih Tasgetiren; Levent Kandiller; D. T. Eliiyi; Liang Gao; Tasgetiren, M. Fatih; Gao, Liang; Öztop, Hande; Kandiller, Levent; Eliiyi, Deniz Türsel
Due to its practical relevance the hybrid flowshop scheduling problem (HFSP) has been widely studied in the literature with the objectives related to production efficiency. However studies regarding energy consumption and environmental effects have rather been limited. This paper addresses the trade-off between makespan and total energy consumption in hybrid flowshops where machines can operate at varying speed levels. A bi-objective mixed-integer linear programming (MILP) model and a bi-objective constraint programming (CP) model are proposed for the problem employing speed scaling. Since the objectives of minimizing makespan and total energy consumption are conflicting with each other the augmented epsilon (ε)-constraint approach is used for obtaining the Pareto-optimal solutions. While close approximations for the Pareto-optimal frontier are obtained for small-sized instances sets of non-dominated solutions are obtained for large instances by solving the MILP and CP models under a time limit. As the problem is NP-hard two variants of the iterated greedy algorithm a variable block insertion heuristic and four variants of ensemble of metaheuristic algorithms are also proposed as well as a novel constructive heuristic. The performances of the proposed seven bi-objective metaheuristics are compared with each other as well as the MILP and CP solutions on a set of well-known HFSP benchmarks in terms of cardinality closeness and diversity of the solutions. Initially the performances of the algorithms are tested on small-sized instances with respect to the Pareto-optimal solutions. Then it is shown that the proposed algorithms are very effective for solving large instances in terms of both solution quality and CPU time. © 2020 Elsevier B.V. All rights reserved.
Citation - WoS: 9
Citation - Scopus: 14
Iterated greedy algorithms for the hybrid flowshop scheduling with total flow time minimization
(Association for Computing Machinery Inc acmhelp@acm.org, 2018) Hande Oztop; D. T. Eliiyi; M. Fatih Tasgetiren; Quanke Pan; Tasgetiren, M. Fatih; Fatih Tasgetiren, M.; Öztop, Hande; Pan, Quan-Ke; Eliiyi, Deniz Türsel
1 The hybrid flosshop scheduling problem (HFSP) has been extensively studied in the literature due to its complexity and real-life applicability. Various exact and heuristic algorithms have been developed for the HFSP and most consider makespan as the only criterion. The studies on HFSP sith the objective of minimizing total flos time have been rather limited. This paper presents a mathematical model and efficient iterated greedy algorithms IG and IGALL for the HFSP sith total flos time criterion. In order to evaluate the performance of the proposed IG algorithms the sell-knosn HFSP benchmark suite from the literature is used. As the problem is NP-hard the proposed mathematical model is solved for all 87 instances under a time limit on CPLEX. Optimal results are obtained for some of these instances. The performance of the IG algorithms is measured by comparisons sith these time-limited CPLEX results of the mathematical model. Computational results shos that the proposed IG algorithms perform very sell in terms of solution time and quality. To the best of our knosledge for the first time in the literature the results of flos time criterion have been reported for the HFSP benchmark suite. © 2018 Elsevier B.V. All rights reserved.
Citation - WoS: 3
Citation - Scopus: 5
Mathematical models for the periodic vehicle routing problem with timewindows and time spread constraints
(Ramazan Yaman, 2021) Damla Kizilay; Hande Öztop; Zeynel Abidin ÇİL; Kizilay, Damla; Öztop, Hande; Çil, Zeynel Abidin
The periodic vehicle routing problem (PVRP) is an extension of the well-knownvehicle routing problem. In this paper the PVRP with time windows and timespread constraints (PVRP-TWTS) is addressed which arises in the high-valueshipment transportation area. In the PVRP-TWTS period-specific demands of thecustomers must be delivered by a fleet of heterogeneous capacitated vehicles overthe several planning periods. Additionally the arrival times to a customer shouldbe irregular within its time window over the planning periods and the waiting timeis not allowed for the vehicles due to the security concerns. This study proposes novel mixed-integer linear programming (MILP) and constraint programming(CP) models for the PVRP-TWTS. Furthermore we develop several validinequalities to strengthen the proposed MILP and CP models as well as a lowerbound. Even though CP has successful applications for various optimizationproblems it is still not as well-known as MILP in the operations research field.This study aims to utilize the effectiveness of CP in solving the PVRP-TWTS. This study presents a CP model for PVRP-TWTS for the first time in the literature to the best of our knowledge. Having a comparison of the CP and MILP models can help in providing a baseline for the problem. We evaluate the performance ofthe proposed MILP and CP models by modifying the well-known benchmark setfrom the literature. The extensive computational results show that the CP modelperforms much better than the MILP model in terms of the solution quality. 4
Citation - WoS: 79
Citation - Scopus: 94
Metaheuristic algorithms for the hybrid flowshop scheduling problem
(PERGAMON-ELSEVIER SCIENCE LTD, 2019) Hande Oztop; M. Fatih Tasgetiren; Deniz Tursel Eliiyi; Quan-Ke Pan; Tasgetiren, M. Fatih; Fatih Tasgetiren, M.; Öztop, Hande; Pan, Quan-Ke; Eliiyi, Deniz Türsel
The hybrid flowshop scheduling problem (HFSP) has been widely studied in the literature as it has many real-life applications in industry. Even though many solution approaches have been presented for the HFSP with makespan criterion studies on HFSP with total flow time minimization have been rather limited. This study presents a mathematical model four variants of iterated greedy algorithms and a variable block insertion heuristic for the HFSP with total flow time minimization. Based on the well-known NEH heuristic an efficient constructive heuristic is also proposed and compared with NEH. A detailed design of experiment is carried out to calibrate the parameters of the proposed algorithms. The HFSP benchmark suite is used for evaluating the performance of the proposed methods. As there are only 10 large instances in the current literature further 30 large instances are proposed as new benchmarks. The developed model is solved for all instances on CPLEX under a time limit and the performances of the proposed algorithms are assessed through comparisons with the results from CPLEX and the two best-performing algorithms in literature. Computational results show that the proposed algorithms are very effective in terms of solution time and quality. Additionally the proposed algorithms are tested on large instances for the makespan criterion which reveal that they also perform superbly for the makespan objective. Especially for instances with 30 jobs the proposed algorithms are able to find the current incumbent makespan values reported in literature and provide three new best solutions. (C) 2019 Elsevier Ltd. All rights reserved.
Citation - WoS: 21
Citation - Scopus: 24
Metaheuristics with restart and learning mechanisms for the no-idle flowshop scheduling problem with makespan criterion
(Elsevier Ltd, 2022) Hande Oztop; M. Fatih Tasgetiren; Levent Kandiller; Quanke Pan; Tasgetiren, M. Fatih; Öztop, Hande; Kandiller, Levent; Pan, Quan-Ke
The no-idle permutation flowshop scheduling problem (NIPFSP) extends the well-known permutation flowshop scheduling problem where idle time is not allowed on the machines. This study proposes a new mixed-integer linear programming (MILP) model and a new constraint programming (CP) model for the NIPFSP with makespan criterion. To the best of our knowledge this study presents a CP model for the NIPFSP for the first time in the literature. We also compare the performance of the proposed MILP and CP models with a well-known MILP model from the literature. Since the studied problem is NP-hard we also develop a new iterated greedy algorithm with restart and learning mechanisms (IG_RL) and a new iterated local search with restart and learning mechanisms (ILS_RL) as metaheuristics for the problem. In the proposed algorithms all the parameters are determined by a learning mechanism in a self-adaptive way. Furthermore a restart mechanism is employed in the proposed IG_RL and ILS_RL algorithms to guarantee the variety of the initial solutions and to assist the algorithm in avoiding the local optima. A variable neighborhood descent procedure is also embedded in the proposed algorithms. We use two well-known benchmark sets i.e. VRF and Ruiz benchmark suites to evaluate the performance of proposed solution methods. For almost half of the 240 small VRF instances optimal results are reported by the MILP and CP models whereas time-limited model results are reported for the rest. The results on small instances show that the proposed MILP and CP models outperform the MILP model from literature where the CP model performs better than both MILP models. We compare the performance of the proposed IG_RL and ILS_RL algorithms with the state-of-the-art metaheuristics from the literature on both large VRF instances and Ruiz benchmark instances. The computational results show the effectiveness and superiority of the proposed ILS_RL and IG_RL algorithms for solving the NIPFSP. Primarily this study improves the current best-known solutions for 102 out of the 250 Ruiz benchmark instances. Additionally this study reports the NIPFSP results for the well-known VRF benchmark set for the first time in the literature. © 2021 Elsevier B.V. All rights reserved.
Multi-Objective Green Hybrid Flowshop Scheduling Problems
(2020) Öztop, Hande; Kandiller, Levent; Taşgetiren, Mehmet Fatih
Literatürde, hibrid akış tipi çizelgeleme problemi çeşitli üretim verimliliği bazlı amaç fonksiyonları düşünülerek yaygın bir şekilde çalışılmıştır. Ancak, hibrid akış tipi çizelgeleme problemi için enerji tüketimi ve çevresel etkileri dikkate alan çalışmalar literatürde oldukça azdır. Bu tez, makinelerin değişen hız seviyelerinde çalışabildiği hibrid akış tipi atölyelerindeki, maksimum tamamlanma zamanı ve toplam enerji tüketimi amaç fonksiyonları arasındaki çelişkiyi ele almaktadır. Bu tezde, enerji-verimli hibrid akış tipi çizelgeleme problemi için, hız ölçeklendirme yöntemi kullanılarak, özgün iki-amaçlı karma-tamsayılı doğrusal programlama ve iki-amaçlı kısıt programlama model formülasyonları önerilmiştir. Bu tezde, hız ölçeklendirme yönteminin hem iş-bazlı hem de iş-tezgah (matris)-bazlı versiyonları çalışılmıştır. Maksimum tamamlanma zamanını ve toplam enerji tüketimini minimize etme amaç fonksiyonları birbirleriyle çeliştiklerinden dolayı, Pareto-optimal çözümleri elde etmek için genişletilmiş epsilon kısıt yöntemi kullanılmıştır. Küçük örnekler için Pareto-optimal eğriye oldukça yakın yaklaşımlar elde edilirken, büyük örnekler için ise önerilen karma-tamsayılı doğrusal programlama ve kısıt programlama model formülasyonları belirli bir süre limiti altında çözülerek baskın olmayan çözüm kümeleri elde edilmiştir. Ayrıca, çalışılan problemin NP-zor sınıfına ait bir problem olmasından dolayı, enerji-verimli hibrid akış tipi çizelgeleme probleminin hem iş-bazlı hem de matris-bazlı versiyonları için özgün iki-amaçlı metasezgisel algoritmalar özgün bir yapıcı sezgisel ile birlikte önerilmiştir. Problemin iş-bazlı versiyonu için iki tip yinelemeli açgözlü algoritma, bir değişken blok yerleştirme sezgiseli ve dört tip bütünleşik-metasezgisel algoritmalar önerilmiştir. Ayrıca, problemin matris-bazlı versiyonu için iki tip yinelemeli açgözlü algoritma, bir değişken blok yerleştirme sezgiseli ve bir bütünleşik-metasezgisel algoritma önerilmiştir. Bunların yanı sıra, bu tez, hibrid akış tipi çizelgeleme problemi için iki özgün sezgisel amaç fonksiyonu değeri hesaplama yöntemi de önermektedir. Literatürde oldukça bilinen hibrid akış tipi çizelgeleme problemi örnekleri kullanılarak, önerilen iki-amaçlı metasezgisellerin performansları birbirleriyle ve karma-tamsayılı doğrusal programlama ve kısıt programlama model formülasyonlarının çözümleri ile; çözümlerin sayısallığı, çeşitliliği ve yakınlığı açılarından kıyaslanmıştır. Öncelikle, metasezgisellerin performansı küçük örnekler üzerinde Pareto-optimal çözümler ile kıyaslanarak test edilmiştir. Ardından, önerilen metasezgisellerin büyük örnekleri çözmek adına hem çözüm kalitesi hem de çözüm süresi açısından oldukça etkin olduğu gösterilmiştir.
Süt Sevkiyat Problemi için Matematiksel Modeller
(2021) Sinem Özkan; Damla Kizilay; Hande Öztop; DAMLA YÜKSEL; Yüksel, Damla; Kizilay, Damla; Özkan, Sinem; Öztop, Hande
Bu çalışma küçük ölçekli bir dağıtım şirketi için şişelenmiş süt sevkiyat problemini ele almaktadır. Şişelenmiş süt sevkiyat problemi ile birçok gerçek\rhayat uygulamasında karşılaşabilmektedir. Sosyal sorumluluk projesi kapsamında şirketler ve belediyeler dahil olmak üzere birçok organizasyon \rçocuklar için ilkokullara ve yoksul ailelere ücretsiz olarak süt dağıtmaktadır. Bu şirketler genellikle belli bir kapasiteye sahip araçlar kullanarak ve\rmüşterilerin (okullar ve aileler) uygun oldukları saat aralıklarını dikkate alarak dağıtım yapmaktadır. Planlama sürecinde genellikle akaryakıt ve\rdepolama maliyetleri gibi masraflar en aza indirilmek istenmektedir. Bu kısıtlar altında problemin teslim zaman aralığı ve araç kapasitesi kısıtlı\raraç rotalama problemi (CVRPTW) olduğu ortaya çıkmaktadır. Temel hedeflerden biri araçların yakıt tüketimini azaltmak için araç türünü dikkate\ralarak toplam seyahat mesafesini en aza indirmektir. Diğer bir amaç ise zamanında teslim edilemeyen sütlerin depolama maliyetini azaltmak için \rmüşterilere uygun zaman aralıklarına göre hizmet vermek ve geç ürün teslimlerini azaltmaktır. Bu hedeflere ulaşmak amacıyla probleme özgü\rkarmaşık tam sayılı doğrusal programlama (MILP) ve kısıt programlama (CP) modelleri geliştirilmiştir. Matematiksel modelleri doğrulamak ve\rkarşılaştırmak için literatürde oldukça bilinen veri setleri üzerinde probleme özgü parametreler dikkate alınarak bazı değişiklikler yapılmıştır. Detaylı\ranalizlere ve sonuçlara göre her iki modelin de çalışılan problem için oldukça rekabetçi olduğu gözlemlenmiştir. Ancak uzun planlama vadesine\rsahip veri örnekleri için MILP modelinin CP modelinden çözüm kalitesi ve çözüm süresi açısından daha iyi performans gösterdiği görülmüştür.
The Uniform Parallel Machine Scheduling Problem: A Case Study
(Springer Science and Business Media Deutschland GmbH, 2020) Ege Duran; Gizem Görgülü; Ayben Pınar Kuruç; İpek Gülhan; Murat Doğruyol; Hande Oztop; Adalet Oner; Öner, Adalet; Gülhan, İpek; Doğruyol, Murat Can; Kuruç, Ayben Pınar; Duran, Ege; Görgülü, Gizem; Öztop, Hande; M.N. Osman Zahid , R. Abd. Aziz , A.R. Yusoff , N. Mat Yahya , F. Abdul Aziz , M. Yazid Abu , N.M. Durakbasa , M.G. Gençyilmaz
In this study the uniform parallel machine scheduling problem with non-common due dates and sequence-dependent setup times is addressed for a real-life problem in the dye house of a hood manufacturer company. The aim of this study is to create an efficient scheduling tool for the company which minimizes lateness (earliness and tardiness) in the system and reduces the buffer stock caused by the lateness. A mathematical model is developed for the problem and optimal results are obtained for the small-sized instances. As the studied problem is NP-hard three heuristic algorithms are also proposed to solve larger instances. The performance of the proposed algorithms is evaluated with a detailed computational experiment. Furthermore a user-friendly decision support system (DSS) is developed using Excel VBA interface and proposed solution approaches are embedded in the DSS. The developed DSS enables users to make an efficient scheduling in very short computational time and provides the results with detailed schedule reports and Gantt charts. As this problem can be faced in various industrial areas the proposed solution approaches can also be applied to different sectors and factories. © 2022 Elsevier B.V. All rights reserved.
Toplu taşımada araç ve sürücü çizelgeleme problemleri
(2016) Öztop, Hande; Kandiller, Levent; Eliiyi, Deniz Türsel
Bu tezde, toplu taşıma operasyonlarının araç ve sürücü çizelgeleme aşamaları, bir toplu taşıma idaresinin gerçek hayat probleminden esinlenilerek çalışılmıştır. Problemde amaç önceden belirlenmiş seferleri ve araç atamalarından kaynaklanacak ölü kilometre seferlerini, sürücülerin toplam çalışma ve vardiya sürelerini dikkate alarak taşımacılığı minimum maliyetle karşılamak için gereken farklı tipteki araç ve sürücülerin sayısını optimal şekilde belirlemektir. Her iki alt problem için tamsayılı programlama modelleri geliştirilmiştir. Sürücü çizelgelemede, toplam çalışma süresini aşan görev sıralamalarını elemek üzere tekrarlamalı geçerli eşitsizlik yaratma yöntemi geliştirilmiştir. Her alt problem için geliştirilen çözüm yöntemlerinin performansları detaylı deneylerle araştırılmıştır ve sonuçlar önerilen optimal arama çözüm yöntemlerinin çözüm süreleri açısından oldukça etkili olduğunu göstermiştir. Bunun yanında, bütüncül problem için sıralı ve entegre olmak üzere iki yaklaşım önerilmiştir. Entegre yaklaşımda tamsayılı bir programlama modeli geliştirilmiş ve küçük boyutlu örnek problemler optimal olarak çözülmüştür. Ancak üstel artan çözüm süreleri nedeniyle büyük boyutlu problemler makul süreler içerisinde çözülememiştir. Bu nedenle araç ve sürücü çizelgeleme problemleri için geliştirilmiş olan tamsayılı programlama modellerinin sırayla çözüldüğü bir sıralı yaklaşım önerilmiştir. Bu yaklaşımın performansı kapsamlı sayısal deneyle araştırılmıştır ve sonuçlar sıralı yaklaşımın en fazla 120 sefere sahip örnekler için oldukça etkin ve verimli olduğunu göstermiştir. Ayrıca sıralı yaklaşım küçük boyutlu örnekler üzerinden entegre yaklaşım ile kıyaslanmıştır ve sonuçlar sıralı yaklaşımın çok makul sürede optimale yakın sonuçlar bulmada oldukça etkin olduğunu göstermiştir.