Inventory Costs and Replenishment Decisions Considering the Time Value of Money

Yıl 2020, , 1499 - 1518, 31.12.2020

Mustafa Çimen Gözdem Dural Selçuk Şule Tarım

https://doi.org/10.17482/uumfd.537729

Öz

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. 

Anahtar Kelimeler

Inventory Systems, Economic Order Quantity, Net Present Value

PARANIN ZAMAN DEĞERİ ÇERÇEVESİNDE STOK MALİYETLERİ VE SİPARİŞ KARARLARI

Öz

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. 

Anahtar Kelimeler

Envanter Sistemleri, Ekonomik Sipariş Miktarı, Net Bugünkü Değer

Kaynakça

• Beullens, P., & Janssens, G. K. (2014). Adapting inventory models for handling various payment structures using net present value equivalence analysis. International Journal of Production Economics, 157, 190-200. doi:10.1016/j.ijpe.2013.09.013
• Bogataj, D., & Bogataj, M. (2019). NPV approach to material requirements planning theory–a 50-year review of these research achievements. International Journal of Production Research, 57(15-16), 5137-5153. doi:10.1080/00207543.2018.1524167
• Chen, C.K. ve diğerleri (2007) A net present value approach in developing optimal replenishment policies for a product life cycle, Applied Mathematics and Computation, 184, 360–373. doi:10.1016/j.amc.2006.05.164
• Çalışkan, C. (2020a). A note about ‘on replenishment schedule for deteriorating items with time-proportional demand’. Production Planning & Control, 1-4. doi:10.1080/09537287.2020.1782500
• Çalışkan, C. (2020b). A derivation of the optimal solution for exponentially deteriorating items without derivatives. Computers & Industrial Engineering, 148, 106675. doi:10.1016/j.cie.2020.106675
• Çalışkan, C. (2020). The economic order quantity model with compounding. Omega, 102307. doi:10.1016/j.omega.2020.102307
• Dye, C.Y. ve diğerleri (2007). Inventory and pricing strategies for deteriorating items with shortages: A discounted cash flow approach, Computers and Industrial Engineering, 52, 29–40. doi:10.1016/j.cie.2006.10.009
• Followill, R. A. ve Dave, D.S. (1998) Financial cost inclusive reformulations of inventory lot size models, Computers and Industrial Engineering, 34 (3), 589–597. doi:10.1016/S0360-8352(97)00316-1
• Goyal, P. R. (1976). The inclusion of inspection costs in the determination of economic order quantity (Yayımlanmamış yüksek lisans tezi, Lehigh University, Bethlehem USA). Erişim adresi: https://preserve.lehigh.edu/etd/2050/
• Grubbstr¨om, R.W. (1998) A net present value approach to safety stocks in planned production, International Journal of Production Economics, 56-57, 213–229. doi:10.1016/S0925-5273(97)00094-7
• Grubbstr¨om, R.W. (1999) A net present value approach to safety stocks in a multi-level MRP system, International Journal of Production Economics, 59, 361–375. doi:10.1016/S0925-5273(98)00016-4
• Grubbstr¨om, R.W. (2010) The Newsboy problem when customer demand is a compound renewal process, International Journal of Production Economics, 203, 134–142. doi:10.1016/j.ejor.2009.06.032
• Grubbstr¨om, R.W. ve Thorstenson A. (1986) Evaluation of capital costs in a multi-level inventory system by means of the annuity stream principle, European Journal of Operational Research, 24 (1), 136–145. doi:10.1016/0377-2217(86)90019-6
• Gurnani, C. (1985) Economic Analysis Of Inventory Systems: A Reply, International Journal of Production Research, 23, 771–772. doi:10.1080/00207548508904745
• Hadley, G. (1964) A Comparison of Order Quantities Computed Using the Average Annual Cost and the Discounted Cost, Management Science, 10 (3), 472–476. doi:10.1287/mnsc.10.3.472
• Hadley, G. ve Whitin T.M. (1963) Analysis of Inventory Systems, Prentice Hall, NJ.
• Haneveld, W.K.K. ve Teunter R.H. (1998) Effects of discounting and demand rate variability on the EOQ, International Journal of Production Economics, 54, 173–192. doi: 10.1016/S0925-5273(97)00142-4
• Harris, FW. (1913) How many parts to make at once, The Magazine of Management 10 (2), 135–136.
• Hill, R.M. ve Pakkala T.P.M. (2005) A discounted cash flow approach to the base stock inventory model, International Journal of Production Economics, 93-94, 439–445. doi: 10.1016/j.ijpe.2004.06.040
• Hofmann, C. (1998) Investments in modern production technology and the cash flow-oriented EPQ- model, International Journal of Production Economics, 54, 193–206. doi: 10.1016/S0925-5273(97)00143-6
• Hsieh, T.P. ve diğerleri (2008) Determining optimal lot size for a two warehouse system with deterioration and shortages using net present value, European Journal of Operational Research, 191, 182–192. doi: 10.1016/j.ejor.2007.08.020
• Kim, Y. H. ve Chung, V. (1985) Economic Analysis Of Inventory Systems: A Clarifying Analysis, International Journal of Production Research, 23, 761–767. Doi: 10.1080/00207548508904743
• Kim, Y. H. ve diğerleri (1986) Evaluating Investment in Inventory Policy: A Net Present Value Framework, The Engineering Economist, 31 (2), 119–136. doi: 10.1080/00137918608902931
• Luciano, E. ve Lorenzo, P. (1999) Some basic problems in inventory theory: The financial perspective, European Journal of Operational Research, 114, 294–303. doi: 10.1016/S0377-2217(98)00257-4
• Mahajan, S., & Diatha, K. S. (2018). Minimizing the Discounted Average Cost Under Continuous Compounding in the EOQ Models with a Regular Product and a Perishable Product. American Journal of Operations Management and Information Systems, 3(2), 52-60. doi: 10.11648/j.ajomis.20180302.13
• Thompson, H.E. (1975) Inventory Management and Capital Budgeting: A Pedagogical Note, Decision Sciences, 6 (2), 383–398. doi:10.1111/j.1540-5915.1975.tb01029.x
• Trippi, R. R. ve Lewin, D. E. (1974) A present value formulation of the classical EOQ problem, Decision Sciences, 5, 30–35. doi:10.1111/j.1540-5915.1974.tb00592.x
• Van der Laan, E. (2003) An NPV and AC analysis of a stochastic inventory system with joint manufacturing and remanufacturing, International journal of Production Economics, 81-82, 317–331. doi:10.1016/S0925-5273(02)00297-9