Discounted Traveling Purchaser Problem in Market Chains

Öz

This study addresses the traveling purchaser problem (TPP), which is a well-known extension of the traveling salesman problem as presented in the literature. In TPP, a purchaser traveling from a central depot visits a number of markets at different locations to satisfy a given product demand and then returns to the depot. The aim of the problem is to find a procurement and route plan that minimizes the total procurement and transportation cost of the purchaser. In this study, TPP is extended by considering the promotional practices of chain markets. In this context, the purchaser may earn a discount from a market chain if he/she makes a certain number of market visits and purchases a certain amount of products. In this way, a reduction in the total cost of the purchaser can be achieved. In order to solve the problem, which is called the market chain discounted traveling purchaser problem (MCD-TPP), a tabu search (TS) algorithm is proposed. A problem set has been generated to test the effectiveness of the developed TS in solving the MCD-TPP. In the computational experiments, the TS is compared to the GUROBI solver. The results show that TA is able to produce more efficient results in shorter times.

Anahtar Kelimeler

• Traveling purchaser problem
• Mathematical modelling
• Tabu search algorithm

ZİNCİR MARKET HARCAMALARINDA İNDİRİMLİ GEZGİN SATIN ALICI PROBLEMİ

Öz

Bu çalışma literatürde iyi bilinen gezgin satıcı probleminin genişletilmiş bir versiyonu olan gezgin satın alıcı problemi (GSAP) dikkate almaktadır. GSAP’de merkezi bir depodan dolaşıma çıkan satın alıcı belirli ürün talebini karşılamak üzere farklı lokasyonlarda bulunan marketleri ziyaret ederek tekrar depoya geri dönmektedir. Problemde amaç satın alıcının toplam dolaşım ve satın alma maliyetini minimize edecek satın alma ve rota planının bulunmasıdır. Yapılan bu çalışmada GSAP, zincir marketlerin promosyon uygulamaları dikkate alınarak genişletilmiştir. Bu kapsamda, gezgin satın alıcı belirli zincir market grubundan belirli sayıda ve belirli miktarda satın alma işlemi yapması durumunda indirim kazanabilmektedir. Bu sayede satın alıcının toplam maliyetinde bir düşüş sağlanabilmektedir. Zincir market harcamalarında indirimli gezgin satın alıcı problemi (ZMHİ-GSAP) olarak adlandırılan problemin çözümü için bir tabu arama (TA) algoritması geliştirilmiştir. Geliştirilmiş olan TA’nın ZMHİ-GSAP’nin çözümünde etkinliğini test edebilmek için bir problem seti üretilmiştir. Yapılan sayısal çalışmalarda TA, GUROBI çözücüsü ile karşılaştırılmıştır. Elde edilen sonuçlar, TA’nın kısa sürelerde daha etkin sonuçlar üretebildiğini göstermiştir.

Anahtar Kelimeler

• Gezgin satın alıcı problemi
• Matematiksel modelleme
• Tabu arama algoritması

Kaynakça

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