Çok periyotlu araç rotalama problemi için mantık temelli bir Benders ayrıştırma yöntemi

Öz

Çok periyotlu araç rotalama problemi, müşteri taleplerinin birden fazla döneme yayılan bir planlama ufku içinde karşılanmasını gerektiren, klasik araç rotalama probleminin daha genel ve karmaşık bir türüdür. Bu problemde hem rotalama hem de müşteri ziyaret sıklıklarının belirlenmesi gerekir, bu da onu pratikte karşılaşılan lojistik uygulamaları için oldukça önemli hale getirmektedir. Bu çalışmada problem için yönsüz kesi temelli bir tam sayılı programlama formülasyonu önerilmiş ve mantık temelli Benders ayrıştırmasına dayalı özgün bir kesin çözüm yöntemi geliştirilmiştir. Ana problem genelleştirilmiş atama problemi şeklinde tanımlanırken, alt problemler her dönem için bağımsız araç rotalama problemleri olarak ele alınmıştır. Çalışmada iki farklı algoritma versiyonu sunulmuş, biri kesen düzlem tabanlı yinelemeli bir çözüm süreci takip ederken, diğeri ise ticari çözücünün geri çağırma fonksiyonundan faydalanmaktadır. Yapılan hesaplama deneyleri, her iki algoritmanın da küçük ölçekli örneklerde etkin olduğunu, özellikle ikinci versiyonun büyük ölçekli örneklerde çok daha üstün performans gösterdiğini ortaya koymuştur. Elde edilen bulgular, mantık temelli Benders ayrıştırmasının çok periyotlu araç rotalama probleminin çözümünde umut vadeden bir yöntem olduğunu göstermektedir.

Anahtar Kelimeler

• Araç rotalama
• Çok periyotlu rotalama
• Mantık temelli Benders ayrıştırma
• Kesin çözüm algoritmaları

A Logic-Based Benders decomposition framework for the multi-period vehicle routing problem

Öz

The period vehicle routing problem is a generalized and a more complex version of the classical vehicle routing problem where customer demands must be fulfilled over a planning horizon spanning multiple periods. In this problem, both routing and customer visit frequency decisions must be addressed simultaneously, which makes it highly relevant for real-life logistics and distribution settings. This study proposes an undirected cut-based mathematical model for the problem and develops a logic-based Benders decomposition framework as a novel exact solution method. The master problem is formulated as a generalized assignment problem, while the subproblems are defined as independent vehicle routing problems for each period. Two algorithmic variants are presented: one follows a cutting plane-based, iterative cut solution process while the other exploits callback functionalities of a commercial solver. Computational experiments demonstrate that both approaches are effective on small instances, while the second variant achieves superior performance on larger instances. The results highlight the potential of logic-based Benders decomposition as a promising approach for solving the period vehicle routing problem.

Anahtar Kelimeler

• Vehicle routing
• Multi-period routing
• Logic-based Benders decomposition
• Exact algorithms

Kaynakça

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