Stok kontrolü ve ekonomik sipariş miktarı modellerinde yeni açılımlar: ödemelerde gecikmeye izin verilmesi durumu ve bir model önerisi

Stok kontrol modelleri, talebin kesin olarak bilinip bilinememesine göre deterministik ve olasılıklı modeller olarak ikiye ayrılmaktadır. Deterministik stok kontrol modelleri arasında en yaygın kullanılan modeller Klasik Ekonomik Sipariş ve Üretim Miktarı Modelleridir. Bu modellerde ele alınan varsayımların çoğu, gerçek hayatta geçerli olabilen değişik durumları veya içinde bulunulan ekonomik koşulları dikkate almamaktadır. Dolayısıyla, sözü edilen varsayımların gevşetilmesi veya ek yeni varsayımlar yardımıyla, gerçek yaşamla daha tutarlı ve geçerli ekonomik koşulları dikkate alan yeni modeller üretilmiştir. Örneğin, stoksuzluk, öğrenme, enflasyon ve paranın zaman değeri etkileri, stoktaki ürünlerin zamanla bozulması, kusurlu ürün, ödemelerde gecikmeye izin verilmesi gibi yeni açılımlar, bu alanda geniş bir çalışma yelpazesi oluşmasını sağlamıştır. Bu çalışmada, klasik ekonomik sipariş miktarı modellerinde geçerli olan varsayımlardan bazıları gevşetilerek gelen siparişlerin belli bir oranda kusurlu ürün içerdiği, stoksuzluğa ve ödemelerde belli bir süre gecikmeye izin verildiği durum için yeni bir ekonomik sipariş miktarı modeli elde edilmektedir. Modelde, ödemelerde izin verilen gecikme süresinin iki farklı durumu için optimal değerler ile izin verilen gecikme süresi ve kusurlu ürün oranı arasındaki ilişkiler belirlenmektedir. Ayrıca, geliştirilen model için sayısal örnekler verilmekte ve izin verilen gecikme süresi ve kusurlu ürün oranındaki değişimlerin etkileri duyarlılık analizi ile incelenmektedir. Yapılan analizler sonucu ödemelerde izin verilen gecikme süresi arttıkça sipariş miktarının azaldığı toplam karın ise azaldığı görülmektedir. Anahtar Kelimeler: Ekonomik Sipariş Miktarı, Kusurlu Ürün, Ödemelerde Gecikmeye İzin Verilmesi, Stoksuzluk.\ud Inventory control models are classified as deterministic and stochastic models upon the condition that the demand is definitely known, or not. Economic Order and Production Quantity models are among the most widely used techniques in deterministic inventory control models. As a result of many unrealistic assumptions embedded in these models, some real life situations and current economic circumstances are not considered. Therefore, by loosening these assumptions and introducing some extra hypotheses, many new models consistent with real life and consider current economic conditions were developed. A vast literature has occurred under these conditions which are known as new approaches such as shortage, effect of learning, inflation and time value of money, deterioration, defective items and permissible delay in payment. In this study, a new model is proposed in the case of defective items, permissible delay in payments and shortage by loosening some of the assumptions of classical Economic Order Quantity models. For two case of permissible delay in payments, the relationships between permissible delay time, rate of defective item and optimal values are determined. Furthermore, numerical examples are given and analyzed for the developed model. Changes in the optimal values with respect to the rate of defective item and permissible delay in payments are analyzed with sensitivity analysis. Result of the analysis show that while permissible delay of payment increases order quantity decreases and total profit increases. However when rate of defective items increases order quantity increases and total profit decreases. Keywords: Economic Order Quantity, Defective Items, Permissible Delay in Payments, Shortag

Responsible Inventory Models for Operation and Logistics Management

The industrialization and the subsequent economic development occurred in the last century have led industrialized societies to pursue increasingly higher economic and financial goals, laying temporarily aside the safeguard of the environment and the defense of human health. However, over the last decade, modern societies have begun to reconsider the importance of social and environmental issues nearby the economic and financial goals. In the real industrial environment as well as in today research activities, new concepts have been introduced, such as sustainable development (SD), green supply chain and ergonomics of the workplace. The notion of “triple bottom line” (3BL) accounting has become increasingly important in industrial management over the last few years (Norman and MacDonald, 2004). The main idea behind the 3BL paradigm is that companies’ ultimate success should not be measured only by the traditional financial results, but also by their ethical and environmental performances. Social and environmental responsibility is essential because a healthy society cannot be achieved and maintained if the population is in poor health. The increasing interest in sustainable development spurs companies and researchers to treat operations management and logistics decisions as a whole by integrating economic, environmental, and social goals (Bouchery et al., 2012). Because of the wideness of the field under consideration, this Ph.D. thesis focuses on a restricted selection of topics, that is Inventory Management and in particular the Lot Sizing problem. The lot sizing problem is undoubtedly one of the most traditional operations management interests, so much so that the first research about lot sizing has been faced more than one century ago (Harris, 1913). The main objectives of this thesis are listed below: 1) The study and the detailed analysis of the existing literature concerning Inventory Management and Lot Sizing, supporting the management of production and logistics activities. In particular, this thesis aims to highlight the different factors and decision-making approaches behind the existing models in the literature. Moreover, it develops a conceptual framework identifying the associated sub-problems, the decision variables and the sources of sustainable achievement in the logistics decisions. The last part of the literature analysis outlines the requirements for future researches. 2) The development of new computational models supporting the Inventory Management and Sustainable Lot Sizing. As a result, an integrated methodological procedure has been developed by making a complete mathematical modeling of the Sustainable Lot Sizing problem. Such a method has been properly validated with data derived from real cases. 3) Understanding and applying the multi-objective optimization techniques, in order to analyze the economic, environmental and social impacts derived from choices concerning the supply, transport and management of incoming materials to a production system. 4) The analysis of the feasibility and convenience of governmental systems of incentives to promote the reduction of emissions owing to the procurement and storage of purchasing materials. A new method based on the multi-objective theory is presented by applying the models developed and by conducting a sensitivity analysis. This method is able to quantify the effectiveness of carbon reduction incentives on varying the input parameters of the problem. 5) Extending the method developed in the first part of the research for the “Single-buyer” case in a "multi-buyer" optics, by introducing the possibility of Horizontal Cooperation. A kind of cooperation among companies in different stages of the purchasing and transportation of raw materials and components on a global scale is the Haulage Sharing approach which is here taken into consideration in depth. This research was supported by a fruitful collaboration with Prof. Robert W. Grubbström (University of Linkoping, Sweden) and its aim has been from the beginning to make a breakthrough both in the theoretical basis concerning sustainable Lot Sizing, and in the subsequent practical application in today industrial contexts

Estimating Costs in the EOQ Formula

[EN] The EOQ formula (Harris, Fact Mag Manage 10(2):135-6-152, 1913) provides a balance between setup costs and holding costs in the system. This formula has been widely developed in the literature. However in the industrial reality, it is often difficult to know the exact value of these setup and holding costs. In this paper, we develop a formula to estimate lot size from the values known in the company. It is verified that the behavior of these formulas meets expectations.The work described in this paper has been supported by Project “CORSARI MAGIC DPI2010-18243” from the Spanish Ministry of Science and Innovation.Vidal-Carreras, PI.; García Sabater, JP.; Valero-Herrero, M.; Santandreu Mascarell, C. (2014). Estimating costs in the EOQ formula. Lecture Notes in Management and Industrial Engineering. 4(1):175-182. https://doi.org/10.1007/978-3-319-04705-8_20S17518241Bomberger EE (1966) A dynamic programming approach to a lot size scheduling problem. Manage Sci 12(11):778Brander P, Segerstedt A (2009) Economic lot scheduling problems incorporating a cost of using the production facility. Int J Prod Res 47(13):3611–3624Goyal SK (1985) Economic order quantity under conditions of permissible delay in payments. J Oper Res Soc 44:785–795Harris FW (1913) How many parts to make an once. Fact Mag Manage 10(2):135-6-152Huang YF (2007) Economic order quantity under conditionally permissible delay in payments. Eur J Oper Res 176(2):911–924Jaggi CK, Goyal SK, Goel SK (2008) Retailer’s optimal replenishment decisions with credit-linked demand under permissible delay in payments. Eur J Oper Res 190(1):130–135Lee WJ (1993) Determining order quantity and selling price by geometric programming: optimal solution, bounds, and sensitivity. Decision Sci 24(1):76–87Meyer B (2004) Value-adding logistics for a world assembly line. Bonifatius Verlag, PaderbornMo J, Mi F, Zhou F, Pan H (2009) A note on an EOQ model with stock and price sensitive demand. Math Comput Model 49(9):2029–2036Sadjadi SJ, Oroujee M, Aryanezhad MB (2005) Optimal production and marketing planning. Comput Optim Appl 30(2):195–203Shirodkar S, Kempf K (2006) Supply chain collaboration through shared capacity models. Interfaces 36(5):420–432Taleizadeh AA, Pentico DW, Saeed Jabalameli M, Aryanezhad M (2013) An EOQ model with partial delayed payment and partial backordering. Omega 41(2):354–368Vidal-Carreras PI, Garcia-Sabater JP, Coronado-Hernandez JR (2012) Economic lot scheduling with deliberated and controlled coproduction. Eur J Oper Res 219(2):396–404Whitin TM (1955) Inventory control and price theory. Manage Sci 2(1):61–68You PS, Chen TC (2007) Dynamic pricing of seasonal goods with spot and forward purchase demands. Comput Math Appl 54(4):490–49