A Novel Perspective on Resolving the Discounted Transportation Problem

Nurdan Kara

Article Details

A Novel Perspective on Resolving the Discounted Transportation Problem

Authors:

Nurdan Kara

Publisher:

Afyon Kocatepe University

Main Topics:

Matematikte Optimizasyon

Journal:

Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi Vol.25 Issue 4, pp.798-803

Document Type:

Article

Publication Date:

4/2025

Document Language:

English

Document ID (Org No.):

2001354988

pISSN:

2149-3367

Keywords:

Abstract:

 The transportation problem, a fundamental optimization problem, aims to optimize profits or reduce costs by transporting products from suppliers to destinations. Nevertheless, a new level of complexity is introduced when the cost per unit of transportation is based on the quantity of goods that are transported. This is the point at which quantity discounts are implemented. A segmented pricing structure is frequently established by suppliers to encourage the purchase of larger quantities by offering reduced per-unit costs. Traditional methods are unable to effectively address the distinctive challenge of incorporating quantity reductions, despite the extensive research conducted on the transportation problem. Our research explores this exact problem, acknowledging the constraints of current approaches to managing the complexities of quantity reductions. In response, we suggest a novel methodology that functions as a potent alternative. This method exceeds simply making use of a fixed cost per unit. Rather, it represents the fluctuating character of costs in relation to the volume of shipments. Image a staircase, with each step representing a distinct cost division that is initiated by a specific quantity range. This divided structure is easily incorporated into the optimization process by our methodology.

 The transportation problem, a fundamental optimization problem, aims to optimize profits or reduce costs by transporting products from suppliers to destinations. Nevertheless, a new level of complexity is introduced when the cost per unit of transportation is based on the quantity of goods that are transported. This is the point at which quantity discounts are implemented. A segmented pricing structure is frequently established by suppliers to encourage the purchase of larger quantities by offering reduced per-unit costs. Traditional methods are unable to effectively address the distinctive challenge of incorporating quantity reductions, despite the extensive research conducted on the transportation problem. Our research explores this exact problem, acknowledging the constraints of current approaches to managing the complexities of quantity reductions. In response, we suggest a novel methodology that functions as a potent alternative. This method exceeds simply making use of a fixed cost per unit. Rather, it represents the fluctuating character of costs in relation to the volume of shipments. Image a staircase, with each step representing a distinct cost division that is initiated by a specific quantity range. This divided structure is easily incorporated into the optimization process by our methodology.

 The transportation problem, a fundamental optimization problem, aims to optimize profits or reduce costs by transporting products from suppliers to destinations. Nevertheless, a new level of complexity is introduced when the cost per unit of transportation is based on the quantity of goods that are transported. This is the point at which quantity discounts are implemented. A segmented pricing structure is frequently established by suppliers to encourage the purchase of larger quantities by offering reduced per-unit costs. Traditional methods are unable to effectively address the distinctive challenge of incorporating quantity reductions, despite the extensive research conducted on the transportation problem. Our research explores this exact problem, acknowledging the constraints of current approaches to managing the complexities of quantity reductions. In response, we suggest a novel methodology that functions as a potent alternative. This method exceeds simply making use of a fixed cost per unit. Rather, it represents the fluctuating character of costs in relation to the volume of shipments. Image a staircase, with each step representing a distinct cost division that is initiated by a specific quantity range. This divided structure is easily incorporated into the optimization process by our methodology.

 Taşıma problemi, tedarikçilerden alıcı noktalara ürünlerin taşınmasıyla kar elini optimize etmeyi veya maliyetleri azaltmayı amaçlayan temel bir optimizasyon problemidir. Ancak, taşıma birimi başına maliyetin taşınan mal miktarına bağlı olduğu durumlarda yeni bir karmaşıklık seviyesi ortaya çıkar. İşte bu noktada miktar indirimleri ortaya çıkar. Tedarikçiler, daha büyük miktarların satın alınmasını teşvik etmek için birim başına maliyetleri düşürerek segmente edilmiş bir fiyatlandırma yapısı oluştururlar. Taşıma problemi üzerine yapılan kapsamlı araştırmalara rağmen, geleneksel yöntemler miktar indirimlerini etkin bir şekilde ele almada zorlanmaktadır. Araştırmamız, miktar indirimlerinin karmaşıklıklarını yönetme konusundaki yaklaşımların sınırlarını göz önünde bulundurarak bu özel problemi ele alır. Buna karşılık olarak, etkili bir alternatif olarak işlev gören yeni bir metodoloji öneriyoruz. Bu yöntem, sadece sabit bir birim maliyet kullanımını aşmanın yanısıra, maliyetlerin sevkiyat hacmiyle ilişkili dalgalanan karakterini temsil etmektedir. Her bir adımın belirli bir miktar aralığı tarafından tetiklenen farklı bir maliyet bölümünü temsil ettiği bir merdiven şeklindeki bölünmüş yapı, metodolojimiz tarafından optimizasyon sürecine kolayca entegre edilir.

Article Details

A Novel Perspective on Resolving the Discounted Transportation Problem

Authors:

Nurdan Kara

Publisher:

Afyon Kocatepe University

Main Topics:

Matematikte Optimizasyon

Journal:

Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi Vol.25 Issue 4, pp.798-803

Document Type:

Article

Publication Date:

4/2025

Document Language:

English

Document ID (Org No.):

2001354988

pISSN:

2149-3367

Transportation problem

Separable Programming

Piecewise cost function

Weighting.Taşıma problemi

Ayrılabilir programlama

Parçalı maliyet fonksiyonları

Ağırlıklandırma

Issues

Article Details

Authors: Nurdan Kara

Publisher: Afyon Kocatepe University

Main Topics: Matematikte Optimizasyon

Journal: Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi Vol.25 Issue 4, pp.798-803

Document Type: Article

Publication Date: 4/2025

Document Language: English

Document ID (Org No.): 2001354988

pISSN: 2149-3367

Issues

Authors:

Nurdan Kara

Publisher:

Afyon Kocatepe University

Main Topics:

Matematikte Optimizasyon

Journal:

Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi Vol.25 Issue 4, pp.798-803

Document Type:

Article

Publication Date:

4/2025

Document Language:

English

Document ID (Org No.):

2001354988

pISSN:

2149-3367