Integrated Mathematical Model for Two-Echelon Location-Routing Problem and Application in a Public Institution

Öz

The location-routing problem (LRP) is among the most important optimization problems related to logistics planning decisions at the strategic and tactical levels. In this paper, we have introduced an original two-echelon LRP in line with the characteristics of a real transportation network encountered in a public institution in Turkey. The aim of the study is to design a transportation network to minimize transportation costs through an integrated solution approach that simultaneously considers location and routing decisions in the two-echelon LRP. For this purpose, we have developed an integer linear programming model for integrated solution of the two-echelon LRP. The variable closed vehicle routing has been defined in accordance with the characteristics of the addressed problem. The proposed model determines both the number and location of transfer centers (TC) to be included into the transportation network, assigns the demand centers to these TCs, and generates variable closed vehicle routes for each one of them. In the model, the total distance traveled along the transportation network is minimized as the primary objective, and the total number of used vehicles as the secondary one. The developed model has been implemented into the transportation problem of the public institution and the transportation network generated by the solution of the model has been compared with the existing network. The obtained results show that significant improvements can be achieved through proposed transportation network design.

Anahtar Kelimeler

• Two-Echelon Location-Routing Problem
• Facility Location Problem
• Vehicle Routing Problem
• Mathematical Model.

İki Kademeli Lokasyon-Rotalama Problemi İçin Bütünleşik Matematiksel Model ve Kamuda Bir Uygulama

Öz

Lokasyon-rotalama problemi (LRP), stratejik ve taktik düzeydeki lojistik planlama kararlarına ilişkin en önemli optimizasyon problemlerinin başında gelmektedir. Bu çalışmada, ülkemizdeki bir kamu kurumunda karşılaşılan gerçek bir taşıma ağının özelliklerinden yola çıkılarak iki kademeli özgün bir LRP tanımlanmıştır. Çalışmanın amacı, iki kademeli LRP’de lokasyon ve rotalama kararlarını eş zamanlı olarak ele alan bütünleşik bir çözüm yaklaşımı aracılığıyla taşıma maliyetlerini en aza indirmeye yönelik bir taşıma ağının tasarlanmasıdır. Bu amaç doğrultusunda, iki kademeli LRP’nin bütünleşik bir şekilde çözümü için tamsayılı bir doğrusal programlama modeli geliştirilmiştir. Çalışmada incelenen problemin özelliklerine uygun olarak değişken kapalı uçlu araç rotalama tanımı yapılmıştır. Önerilen modelde, taşıma ağında yer alacak aktarma merkezi (AKM) sayısı ve lokasyonlarının belirlenmesine, talep merkezlerinin bu AKM’lere atanmasına ve her bir AKM için değişken kapalı uçlu araç rotalarının oluşturulmasına çalışılmıştır. Modelde birinci öncelikli amaç olarak taşıma ağı boyunca katedilen toplam mesafenin, ikinci öncelikli amaç olarak ise kullanılan toplam araç sayısının minimize edilmesi hedeflenmiştir. Geliştirilen model, kamu kurumunda karşılaşılan taşıma problemine uygulanmış ve modelin çözümü sonucunda oluşturulan taşıma ağı mevcut ağ ile karşılaştırılmıştır. Elde edilen çözüm sonuçları, önerilen taşıma ağı yoluyla sistem performansında önemli düzeyde iyileştirmelerin sağlanabileceğini göstermiştir.

Anahtar Kelimeler

• İki Kademeli Lokasyon-Rotalama Problemi
• Tesis Lokasyon Problemi
• Araç Rotalama Problemi
• Matematiksel Model.

Kaynakça

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