Kareye Tamamlama Yöntemi ve Aritmetik-Geometrik Ortalama Eşitsizliğiyle İki Aşamalı Tedarik Zinciri Modelinin Çözümü ve Analizi

Year 2023, Volume: 41 Issue: 4, 650 - 674, 24.12.2023

Harun Öztürk

https://doi.org/10.17065/huniibf.1281343

Abstract

Bu çalışmada, farklı ülkelerde bulunan tek bir üretici ve tek bir perakendeciden oluşan iki aşamalı tedarik zinciri problemi için bir bütünleşik stok kontrol modeli geliştirilmiştir. Bu çalışmanın amacı, bütünleşik toplam maliyeti minimum yapacak şekilde üreticinin parti sayısının ve perakendecinin parti büyüklüğünün, yani bütünleşik üretim-stok kontrol politikası parametrelerinin birlikte hesaplanmasıdır. Tek kalem ürünün siparişi, eşit büyüklükte partiler halinde teslim alınmaktadır. Perakendecinin teslim aldığı her parti iyi kaliteli ürünlerle birlikte kusurlu ürünler de içermektedir. Kusurlu ürünler, kalite kontrol işleminin ardından indirimli fiyattan satılmak üzere tek parti halinde stoktan çıkarılmaktadır; kusurlu ürün sayısı kadar iyi kaliteli fakat daha yüksek fiyatlı ürünler yerel bir tedarikçiden satın alınmaktadır. Üretici ve perakendecinin toplam stok maliyeti fonksiyonları elde edilmiş ve bütünleşik toplam stok maliyeti fonksiyonu türetilmiştir. Optimum çözüm diferensiyel hesabı kullanmadan aritmetik-geometrik ortalama eşitsizliği ve kareye tamamlama yöntemiyle elde edilmiştir. Sayısal bir örnek yardımıyla teorik sonuçlar elde edilmiş ve duyarlılık analizleri verilmiştir.

Keywords

Tedarik zinciri, Stok kontrolü, Matematik model, Kareye tamamlama tekniği, Aritmetik-geometirk ortalama eşitsizliği

The Complete Squares Method and the Arithmetic-Geometric Mean Inequality to Solve and Analyze A Two-Level Supply Chain Problem

Abstract

In this study, an integrated inventory model is developed for a two-level supply chain problem consisting of a single manufacturer and a single retailer located in different countries. The aim of this study is to jointly calculate the number of batches of the manufacturer and the batch size of the retailer, i.e. the parameters of the integrated production-inventory control policy, in a way that minimizes the integrated total cost. The order of a single type of product is delivered in batches of equal size. Each batch received by the retailer contains both good quality products and defective products. Defective products are removed from inventory as a single batch at a discounted price after a quality control process; good quality products, equal to the number of defective products, are purchased from a local supplier, but at a higher price. The total cost functions for the manufacturer and the retailer are obtained and the integrated total cost function is derived. The optimal solution is obtained by using the complete square method and the arithmetic-geometric mean inequality without using differential calculus. With the help of a numerical example, theoretical results were obtained and sensitivity analyses were given.

Keywords

Supply Chain, Inventory Control, Mathematical Model, Complete Squares Method, Arithmetic-Geometric Mean Inequality

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