Çok amaçlı kaynak kısıtlı çoklu proje çizelgeleme problemi ve bir traktör firmasında uygulama
Multi-objective resource constrained multiple project scheduling problem and its application in a tractor company
Yazar: CEMRE NUR DİNÇKURT BİÇER
Danışman: PROF. DR. ÖZGÜR KABAK
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Endüstri Mühendisliği Ana Bilim Dalı / Endüstri Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2024
Konu: Endüstri ve Endüstri Mühendisliği = Industrial and Industrial Engineering

Özet:
Proje yönetiminde, projelerin zamanında ve önceden belirlenen bütçe dahilinde tamamlanması büyük önem taşımaktadır. Proje çizelgeleme sürecini karmaşıklaştıran nokta, genellikle sınırlı kaynaklarla birlikte birden fazla projenin aynı anda yürütülmesidir. Gerçek hayat proje çizelgeleme süreçlerinde; projeleri en kısa sürede, gecikme olmadan ve bütçeyi aşmadan kaynakları en verimli şekilde kullanarak tamamlamak gibi birden fazla amaç aynı anda gerçekleştirilmek istendiğinden durum daha da karmaşık bir hale gelmektedir. Bu tür problemler Kaynak Kısıtlı Proje Çizelgeleme Problemi (KKPÇP) çatısı altında toplanmıştır.
Bu yüksek lisans tez çalışması, birden fazla amacı aynı anda gerçekleştirmeyi ve birden fazla projenin çizelgelenmesini amaçlayan Çok Amaçlı Kaynak Kısıtlı Çoklu Proje Çizelgeleme Problemi üzerine odaklanmaktadır. Bu tür problemler, genellikle birbiriyle çelişen hedeflere sahip olurlar; proje süresinin minimize edilmesi, maliyetlerin düşürülmesi veya kaynak kullanımının dengelenmesi gibi çeşitli amaçlar örnek olarak gösterilebilir. Çok amaçlı KKPÇP çözümü için çeşitli matematiksel modelleme ve optimizasyon teknikleri kullanılmaktadır.
Bu çalışmada, belirli bir zaman dilimi içinde tamamlanması gereken birden fazla projenin, sınırlı kaynaklar göz önünde bulundurularak en iyi şekilde planlanması ve çizelgelenmesi amaçlanmıştır. Ağırlıklı hedef programlama, farklı hedeflerin önem derecelerine göre ağırlıklandırıldığı ve bu hedeflerin aynı anda optimize edilmeye çalışıldığı bir teknik olarak kullanılmaktadır. Bu çalışmada, problemin çözümü için önerilen matematiksel model, OPL dilinde kodlanmış ve ağırlıklı hedef programlama yöntemi kullanılarak ve IBM ILOG CPLEX çözücüsünden faydalanılarak çözülmüştür. CPLEX, özellikle doğrusal programlama problemlerinin ve karmaşık matematiksel modellerin çözümünde etkili bir araç olarak kullanılmaktadır. Matematiksel modelin amaç fonksiyonunda bulunan ağırlıklar duyarlılık analizi yapılarak ve son karar verici tarafından şirketlerin hedefleri doğrultusunda belirlenmiştir. Modelin doğruluğunu ve etkinliğini test etmek amacıyla başta daha küçük bir örnek üzerinde çalışma yapılmıştır.
Bu tez çalışmasında, bir traktör firmasının geliştirdiği traktör projelerinin AR-GE test süreçlerinin çizelgelemesi üzerine çalışılmıştır. Odaklanılan amaçlar; belirli kaynak sayısı ve testlerin öncüllük ilişkileri dikkate alınarak, projelerin toplam gecikme sürelerinin ve toplam fazla mesainin minimize edilmesidir. Her bir projenin birbirinden farklı sayıda ve tipte validasyon test ihtiyacı olduğu, 6 farklı kaynağı kullanan 25 projenin çizelgelenmesi için ağırlıklı hedef programlama matematiksel modeli geliştirilmiştir. Dikkate alınan AR-GE validasyon test süreci kaynak tipleri: Motor & HVAC, Hidrolik & Güç Aktarma Organları, NVH & Araç Doğrulama, Atölye, Saha Testi & Güvenilirlik, Elektrik & Elektronik test mühendislerinden oluşmaktadır. Her proje için, uygulanacak validasyon testlerinin öncüllük-ardıllık ilişkisi, testlerin gerçekleştirileceği süreler ve projelerin tamamlanması gereken gün sayısı gibi parametreler model içerisinde tanımlanmıştır. Yapılan bu çalışma sonucunda; gerçekte toplam 45 gün gecikerek ve toplam 126 adam*gün fazla mesai yapılarak tamamlanan projeler, hiç gecikme yaşanmadan toplam 110 adam*gün fazla mesai yapılarak tamamlanmıştır. Ayrıca kaynak kapasitesinin yeterliliği ile ilgili çeşitli senaryolar denenmiş ve analiz sonuçları paylaşılmıştır.

Abstract:
In today's highly competitive business environment, effective project scheduling has become more critical than ever. As organizations strive to deliver projects on time, within budget and to the desired quality standards, the need for planning and scheduling is essential. Here are a several reasons why project planning is important in project management.
Effective project scheduling allows for optimal allocation of resources, including human resources, materials, and equipment. By identifying what resources are needed and when they are needed, project managers can ensure that resources are not over-allocated or underutilized. This helps in avoiding bottlenecks and minimizing idle time, ultimately leading to cost savings and increased efficiency. Time is a critical factor in any project. Scheduling helps in breaking down the project into manageable tasks with specific deadlines. This detailed planning enables project managers to track progress, identify delays early, and implement corrective measures promptly. Timely completion of tasks is essential to meet the overall project deadline, which can have significant implications for client satisfaction and competitive advantage. A well-thought-out schedule is essential for maintaining control over the project budget. By mapping out the timeline and understanding the sequence of activities, project managers can estimate costs more accurately and monitor spending against the budget. By planning each step of the project and anticipating potential obstacles, project managers can develop contingency plans and risk mitigation strategies. This proactive approach helps in addressing issues before they escalate, ensuring the project stays on track. A clear and detailed project schedule serves as a communication tool that aligns the entire project team. It provides a common understanding of the project timeline, responsibilities, and deliverables. Project schedules provide a baseline against which performance can be measured. By comparing actual progress to the planned schedule, project managers can assess how well the project is adhering to the plan. Any deviations from the schedule can be quickly identified and addressed. Clients and stakeholders are often more satisfied when they see a clear and structured plan for project delivery. Meeting deadlines and delivering on commitments are key to building and maintaining strong client relationships.
By optimizing resources, managing time and budget, mitigating risks, enhancing communication, and ensuring accountability, effective scheduling helps organizations achieve their project goals and maintain a competitive edge in the market. As the complexity of projects continues to grow, the importance of precise and strategic scheduling will only increase.
In project management, it is crucial that projects are completed on time and within the predetermined budget. Complicating the project scheduling process is the simultaneous execution of multiple projects, often with limited resources. In real-life project scheduling processes, the situation becomes even more complex as multiple objectives need to be achieved simultaneously, such as completing projects in the shortest time, without delays and within budget, using resources in the most efficient way. This type of problem is categorized as of Resource Constrained Project Scheduling Problem (RCPSP).
RCPSP is a complex and critical challenge in project management, especially when resources such as manpower, equipment or materials are limited. This problem involves scheduling project activities within a given time frame while respecting resource constraints and predefined priority relationships between tasks. The objective is usually to minimize the total project duration (makespan) while ensuring that no resource is over-allocated at any time. This involves balancing the trade-offs between starting activities as soon as possible and the availability of resources.
There are several variants of the RCPSP, each introducing additional complexities and considerations such as; Single Mode RCPSP, Multi-Mode RCPSP, RCPSP with Irregular Objective Function, Stochastic RCPSP, Multi-Project RCPSP, Multi-Objective RCPSP.
Various objective functions are employed in Multi- Objective RCPSP to address the multiple goals. Some of the common objectives include: minimizing makespan, minimizing total costs, maximizing resource utilization, minimizing delays, maximizing quality, enhancing customer satisfaction.
This master's thesis focuses on the Multi-Objective RCPSP, which aims to achieve multiple objectives simultaneously and schedule multiple projects. Such problems often have conflicting objectives, such as minimizing project duration, reducing costs or balancing resource utilization. Various mathematical modeling and optimization techniques have been used for solving Multi-Objective RCPSP.
In this study, we aim to optimize the planning and scheduling of multiple projects that need to be completed within a given time frame, taking into account limited resources. Weighted goal programming is used as a technique in which different goals are weighted according to their importance and these goals are optimized simultaneously.
Weighted Goal Programming (WGP) is a multi-objective optimization method that seeks to find the best solution by satisfying a set of goals to varying degrees, each with an assigned weight indicating its relative importance. Unlike traditional linear programming, which optimizes a single objective function, WGP deals with multiple objectives by converting them into goals that need to be achieved.
In this study, the mathematical model proposed for the solution of the problem is coded in optimization programming language (OPL) and solved using weighted goal programming method and IBM ILOG CPLEX solver. CPLEX is used as an effective tool especially for solving linear programming problems and complex mathematical models. The weights in the objective function of the mathematical model were determined by sensitivity analysis and by the final decision maker in line with the objectives of the companies. In order to test the accuracy and efficiency of the model, a smaller example was initially studied.
In this thesis, the scheduling of R&D testing processes of tractor projects developed by a tractor company was studied. The focused objective functions are to minimize the total delay time and total overtime of the projects. In this model, after determining parameters such as the total number of projects, total resource capacity and deadlines of the projects, which validation tests are needed in which project and how many people are needed in total from which resource type are determined. After all these, the antecedence-predecedence relationships of the tests were determined and the objective function was created. The developed mathematical model is supported by the weighted goal programming method. Since it is aimed to achieve more than one objective at the same time, total delay time and total overtime amounts are modeled by weighting.
The weight coefficients in the objective function are determined by sensitivity analysis method, which is used to show the effect of changing the coefficient values in the linear programming problem on the solution of the problem. By changing the weight coefficients, the effect on the optimal result was examined. The results obtained were evaluated by the decision maker and weight coefficients of 0.8 for total project delay time and 0.2 for total overtime time were added to the model in line with the company's objectives.
Mathematical model is developed for scheduling 25 projects using 6 different resources, where each project requires a different number and type of validation tests. The R&D validation test process resource types considered are: Engine & HVAC, Hydraulics & Powertrain, NVH & Vehicle Validation, Workshop, Field Test & Reliability, Electrical & Electronics test engineers. The capacity of the resources types are 5, 6, 6, 3, 4 and 4 respectively.
For each project, parameters such as the antecedent-successor relationship of the validation tests to be performed, the duration of the tests to be performed and the number of days to complete the projects were defined in the model. As a result of this study; projects that were actually completed with a total of 45 days delay and 126 man/day overtime were completed with a total of 110 man/day overtime without any delay. In addition, various scenarios regarding the adequacy of resource capacity were tested and the results of the analysis were shared.