Bu çalışmada, bulanık kümeler ve olabilirlik teorilerinden faydalanılarak zaman aralıklı araç rotalama problemi (ZAARP) için bulanık karar ortamında kullanılabilecek bir gürbüz bulanık programlama modeli önerilmiştir. Geçmiş çalışmalar incelendiğinde ZAARP’nin genellikle parametrelerindeki belirsizliklerin ve kısıtlarındaki esnekliklerin göz ardı edilerek modellendiği görülmüştür. Bu tip modellere üretilen çözümler uygulama aşamasında çoğunlukla geçerliliklerini yitirmekte ve kullanıcılar tarafından elle düzeltilmeyi gerektirmektedirler. Stokastik modellerin kullanıldığı çalışmalarda ise önerilen modellerin çok fazla hesaplama yükü gerektirdiği ve parametrelerinin belirlenmesi için problemle ilgili geçmiş verilere ihtiyaç duyulduğu görülmektedir. Bu nedenlerle stokastik modeller de gerçek hayatta karşılaşılan problemlerin çözümünde rahatlıkla kullanılamamaktadır. Bu çalışmada belirsizliklerin ve esnekliklerin modellenmesi için bulanık aralıklar ve bulanık kümeler kullanılmıştır. Gereklilik ve olabilirlik ölçütleri ile planlayıcının belirlediği eşik güvenilirlik ve müşteri tatmini düzeylerine sahip çözümler oluşturulmuştur. Bulanık programlama modeli ile yüksek veri işleme maliyeti düşürülürken modellerin geçerlilikleri de arttırılmıştır. Önerilen modellere çözüm oluşturmak amacıyla karınca kolonisi optimizasyonu tabanlı bir algoritma geliştirilmiştir. Bulanık değerler kesin değerlerin genelleştirilmiş hali olarak ele alındığından geliştirilen algoritma kesin veri ve/veya bulanık veri durumlarında çözüm oluşturabilmektedir. Örnek problemler üzerinde gerçekleştirilen deneylerde planlayıcıların tercih ve önceliklerine göre alternatif çözümlerin üretilebileceği ve oluşturulan çözümler hakkında planlayıcılara ve müşterilere daha fazla bilgi sağlanabileceği gösterilmiştir.

Many companies use fleets of vehicles within their activity in a range of sectors. More often than not, meeting customers’ requirements, taking into account their geographical spread and delivery time windows, as well as managing the company’s operating and financial constraints, turns into a nightmare. The vehicle routing problem with time windows (VRPTW) is a well-known and complex combinatorial optimization problem concerned with finding efficient routes, beginning and ending at a central depot, for a fleet of identical vehicles to serve a number of customers with capacity and time window constraints where each customer is visited exactly once by a vehicle. The capacity constraint signifies that the total load on a route cannot exceed the capacity of the assigned vehicle. The time window constraint signifies that each vehicle must start the service each customer in the period specified by the customer. The objective is to find the feasible solution (hierarchically or not) with minimal number of vehicles or with the minimal total distance. VRPTW has been a subject of intensive research focused mainly on the heuristic and the metaheuristic approaches. The VRPTW is still one of the most difficult problems in combinatorial optimization and this problem contributes directly to a real opportunity to reduce costs in the important area of logistics. Transportation management, and more specifically the vehicle routing, has a considerable economical impact on all logistic systems. However, the classical definitions of the vehicle routing problem often lack handling of uncertain parameters and flexible constraints such as the traveling times between customers and the latest delivery times for the custoners. In addition, a best/optimal solution generated by a heuristic/exact method, for the classical VRPTW do not mean any knowledge to the user about its realization when applicated. Whereas, the solutions generated with the classical models usually became infeasible when implemented and the planners are often involved to make corrections by hand. The natural approach to modeling the uncertainty is a stochastic one. Unfortunately, the stochastic models are often hard to solve. Moreover, it may be hard or expensive to assume any specific probability distributions for the unknown parameters. For these reasons stochastic models are behind the needs of users. Up to past decades, operational research methods seem to be inadequate for the large sized combinatorial optimization problems due to their large computational effort and long solution time. But, recent developments in data processing and communication technologies and recently proposed metaheuristic methods that can generate solutions to large sized combinatorial problems made these classical disadvantages less important for the researchers. Subsequently, validity of used models became a more important issue for the researchers In this study, the fuzzy set and the possibility theories are utilized in order to propose a fuzzy robust programming model for the VRPTW that can be used in the uncertain decision environments. The fuzzy programming model proposed in this study exploit fuzzy sets and fuzzy intervals in order to model flexibilities on latest delivery times and uncertainties for traveling times between customers. A necessity measure is used to generate knowledge about the satisfaction of delivery time constraints when a route is realized by the vehicle. In addition, a possibility measure is used to evaluate the customer satisfaction levels. Using the necessity and the possibility measures, solutions that have the maximum risk level to be unfeasible and the minimum customer satisfaction, which are specified by the user, can be generated. Validities of the models are increased while decreasing the computational effort with fuzzy programming models. In order to generate solutions for the proposed model an ant colony optimization based algorithm is developed. The algorithm is capable of solving both the classical and the fuzzy programming models for the VRPTW. Results of the experimental studies with the benchmark problems indicate that the proposed fuzzy programming model and the ant colony optimization algorithm can be usable for solving practical problems in means of solution time and quality. The proposed approach can be integrated with a decision support system in order to generate alternative solutions achieving the planners’ and the customers’ preferences along with acquiring more information about the realization of the solutions.