Inventory Costs and Replenishment Decisions Considering the Time Value of Money

Abstract

In this study, we propose economic order quantity formulations considering the time value of money, using a net present value based approach. We address the optimal lot sizing problem with static-deterministic demand under fixed ordering cost, linear holding and penalty cost assumptions. This problem has been investigated in the literature by two articles. However, despite addressing the problem under the same assumptions, these two articles propose two different formulations. The writers of both of the studies have objected each other’s formulations claiming that their own study is correct. In our study we present the exact formulations for the aforementioned problem and point out the shortcomings of the previously presented net present value based economic order quantity formulations. Our numerical study demonstrates that both (i) not integrating cash flows analysis into classical economic order quantity model, and (ii) using the erroneous models presented by the two articles which make this integration incorrectly, may lead to sub-optimal solutions. 

Keywords

• Inventory Systems
• Economic Order Quantity
• Net Present Value

PARANIN ZAMAN DEĞERİ ÇERÇEVESİNDE STOK MALİYETLERİ VE SİPARİŞ KARARLARI

Abstract

Bu makalede; net bugünkü değer yaklaşımı uygulanarak elde edilen, paranın zaman değerini dikkate alan ekonomik sipariş miktarı formülasyonları sunulmaktadır. Makalede; sabit kurulum maliyeti, doğrusal elde bulundurma maliyeti ve ceza maliyeti varsayımları altında, statik-deterministik talepli optimal sipariş miktarı problemi ele alınmıştır. Söz konusu problem literatürde daha önce iki farklı makalede incelenmiştir. Ancak bu iki makalede, problem aynı varsayımlar altında incelendiği halde iki farklı formülasyon sunulmuştur. Her iki makalenin da yazarları birbirlerinin formüllerine itiraz ederek kendi formüllerinin doğru olduğunu iddia etmişlerdir. Bu çalışmada, bahsi geçen problem için ekonomik sipariş miktarının doğru formülasyonları sunulmakta ve daha önceki iki makalenin de hatalı olduğu gösterilmektedir. Yapılan nümerik analizler, (i) hem nakit akışı analizi ekonomik sipariş miktarı modeline entegre edilmediğinde, (ii) hem de bu entegrasyonu hatalı olarak yapan iki makalede önerilen hatalı formülasyonun kullanılması durumunda alt-optimal sonuçlar elde edilebileceğini göstermektedir. Nümerik sonuçlar bu makalede sunulan formülasyonun katma değerini ortaya koymaktadır. 

Keywords

• Envanter Sistemleri
• Ekonomik Sipariş Miktarı
• Net Bugünkü Değer

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