Single and Multi-Period Inventory Control Models

Öz

Nowadays, companies have to provide the most suitable product to the customer's demands in the fastest way with minimum cost in order to be able to stand competitive conditions and to be placed in the market. All of these factors have encouraged firms to focus on the design and planning of well-organized inventory systems that allow the right amount of product to be distributed right at the right price. Numerous studies have been carried out in the literature, especially on inventory control problems in recent years. In this study, inventory control problems are collected in two main topics; single and multi period. The studies are summarized and categorized by considering the components such as demand type (deterministic or stochastic), number of products (single or multi product), system structure (single or multi stage), product life (unlimited shelf life or deteriorating products), number of objective function (single or multi objective), warehouse management policy. Also; other details such as constraints, modeling method, and solution approach are also mentioned. With this study, it is aimed to present the works done on single and multi period inventory problems to the reader in tabular form and to present the information to the researchers who will work on this subject.

Anahtar Kelimeler

• Single period,Multi-period,Inventory control model

Tek ve Çok Dönemli Envanter Kontrol Modelleri

Öz

Günümüzde firmalar rekabet şartlarına dayanabilmek ve pazarda yer edinebilmek için müşteri taleplerine en uygun ürünü, en az maliyetle en hızlı biçimde sağlamak zorundadırlar. Bütün bu faktörler firmaları, doğru kaynaktan doğru miktarda ürünün, doğru fiyat ile doğru yere dağıtılmasını sağlayan iyi organize olmuş envanter sistemlerinin tasarımı ve planlaması üzerine odaklanmaya teşvik etmiştir. Literatürde, özellikle son yıllarda envanter kontrol problemleri üzerine çok sayıda çalışma yapılmıştır. Bu çalışmada, envanter kontrol problemleri tek ve çok dönemli olmak üzere iki ana başlıkta toplanmıştır. Çalışmalar, talep türü (deterministik veya stokastik), ürün sayısı (tek veya çok ürünlü), sistem yapısı (tek veya çok aşamalı), ürün ömrü (sınırsız raf ömürlü veya bozulabilen ürünler), amaç fonksiyonu sayısı (tek amaçlı veya çok amaçlı), depo yönetim politikası gibi bileşenler dikkate alınarak özetlenmiş ve sınıflandırılmıştır. Ayrıca; kısıtlamalar, modelleme metodu ve çözüm yaklaşımı gibi diğer ayrıntılar da belirtilmiştir. Bu çalışma ile tek ve çok dönemli envanter problemleri ile ilgili yapılan çalışmaların tablolar halinde okuyucuya sunulması ve bu konuda çalışma yapacak araştırmacılara önbilgi sunulması amaçlanmıştır.

Anahtar Kelimeler

• Tek dönem,Çok dönem,Envanter kontrol modeli

Kaynakça

1. Alikar N., Mousavi S.M, Raja Ghazilla R.A., Tavana M., Olugu E.U., 2017. Application of the NSGA-II Algorithm to a Multi-Period Inventory-Redundancy Allocation Problem in A Series-Parallel System, Reliability Engineering & System Safety, 160, 1-10.
2. Axsater S., Nuttle H. L.W., 1987. Combining Items for Lot Sizing in Multi-Level Assembly Systems. International Journal of Production Research, 25, 795–807.
3. Aydemir E., 2015. Inventory Management and Extensions: A review of Economic Production Models. Anadolu University Journal of Social Sciences, 15 (3), 97-112.
4. Aydemir E., Bedir F., Ozdemir G., Eroglu A., 2014. An EPQ Model with Imperfect Items Using Interval Grey Numbers. An International Journal of Optimization and Control: Theories & Applications, 5(1), 21-32.
5. Aydemir, E., Bedir, F., Ozdemir, G., 2015. Degree of Greyness Approach for an EPQ Model with Imperfect Items in Copper Wire Industry. The Journal of Grey System, 27 No. 2, 13-26.
6. Bai Q.-G., Zhang Y.-Z., Dong G.-L., 2010. A Note on an Economic Lot-Sizing Problem with Perishable Inventory and Economies of Scale Costs: Approximation Solutions and Worst Case Analysis. International Journal of Automation and Computing, 7, 132–136.
7. Bakker M., Riezebos J., Teunter R.H. 2012. Review of Inventory Systems with Deterioration Since 2001. European Journal of Operational Research, 221(2), 275-284.
8. Cárdenas-Barrón L.E., González-Velarde J.L., Treviño-Garza G., 2015. A New Approach to Solve the Multi Product Multi-Period Inventory Lot Sizing with Supplier Selection Problem. Computers & Operations Research, 64, 225-232.

9. Chen L., Chen Y., 2010. A Multiple-item Budget-Constraint Newsboy Problem with a Reservation Policy. OMEGA, 38(6), 431-439.
10. Chen S.-P., Ho Y.-H, 2013. Optimal Inventory Policy for the Fuzzy Newsboy Problem with Quantity Discounts, Information Sciences, 228, 75-89.
11. Choudhary D., Shankar R., 2011. Modeling and Analysis of Single Item Multi-Period Procurement Lot-Sizing Problem Considering Rejections and Late Deliveries. Computers & Industrial Engineering, 61, 1318–1323.
12. Clark A.J., Scarf H., 1960. Optimal Policies for a Multi-Echelon Inventory Problem, Management Science, 5(4), 475-490.
13. Çekiç B., 2015. Tedarik Zincirlerinde Durağan Olmayan Talep Altında Çok Kademeli Stok Kontrol Yönetimi için bir Stokastik Programlama Yaklaşımı, Hacettepe Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 33(1), 2015, 45-77.
14. Das B., Maiti M., 2007. An Application of Bi-Level Newsboy Problem in Two Substitutable Items Under Capital Cost, Applied Mathematics and Computation, 190 (1), 410–422.
15. Dem H., Singh S., Kumar J., 2014. An EPQ Model with Trapezoidal Demand Under Volume Flexibility. International Journal of Industrial Engineering Computations, 5(1), 127-138.
16. Ding S., 2013. Uncertain Multi-Product Newsboy Problem with Chance Constraint, Applied Mathematics and Computation, 223 (2013), 139–146.
17. Efendioğlu D., Bulkan S., 2017. Capacity Management in Hotel Industry for Turkey. Handbook of Research on Holistic Optimization Techniques in the Hospitality, Tourism, and Travel Industry, 286-304.
18. Eroğlu A., 2002. Deterministik Envanter Modelleri, Fakülte Kitabevi.
19. Gaiduk A. R., Vershinin Y. A., West M. J., 2002. Neural Networks and Optimization Problems, Proceedings of the IEEE International Conference on Control Applications, 1, 37–41, September 2002.
20. Gen M., Syarif A., 2005. Hybrid Genetic Algorithm for Multi-Time Period Production/Distribution Planning. Computers & Industrial Engineering, 48, 799–809.
21. Goyal S., Giri B., 2001. Recent Trends in Modeling of Deteriorating. European Journal of Operational Research, 134 (1), 1-16.
22. Gürler Ü., Özkaya B.Y., 2008. Analysis of the (s, S) Policy for Perishables with a Random Shelf Life. IIE Transactions, 40, 759–781.
23. Hadley G., Whitin T.M., 1963. Analysis of Inventory Systems, Prentice Hall, Englewood Cliffs, NJ.
24. Harris, F.W., 1913. How Many Parts to Make at Once. Factory The Magazine of Management, 10, 135–136.
25. Helber S., Sahling F., 2013. Dynamic Capacitated Lot Sizing with Random Demand and Dynamic Safety Stocks. OR Spectrum 35, 75–105.
26. Hnaien F., Dolgui A., Wu D.D. , 2016. Single-period Inventory Model for One-level Assembly System with Stochastic Lead times and Demand. International Journal of Production Research, 54, 186–203.
27. Hopp W.J., Spearman M.L., Zhang R.Q., 1997. Easily Implementable Inventory Control Policies. Operations Research, 45, 327–340.
28. Hosseini S.V., Moghadasi H., Noori A.H., Royani M.B., 2009. Newsboy Problem with Two Objectives, Fuzzy Costs and Total Discount Strategy. Journal of Applied Sciences, 9, 1880-1888.
29. Hsu V., 2003. An Economic Lot Size Model for Perishable Products with Age-Dependent Inventory and Backorder Costs. IIE Transactions, 35(8), 775–780.
30. Huang M. G., 2015. Optimal Ordering Policy for Perishable Items in an Advanced Booking System with Stochastic Reservation Cancellations. International Journal of Information and Management Sciences, 26(3), 271-290.
31. Janssen L., Claus T., Sauer J., 2016. Literature Review of Deteriorating Inventory Models by Key Topics From 2012 to 2015, International Journal of Production Economics, 182, 86-112.
32. Kahraman C., Öztayşi B., 2014. Supply Chain Management under Fuzziness, Series: Studies in Fuzziness and Soft Computing: Recent Developments and Techniques, 313, Springer Verlag.
33. Kahraman C., Yavuz M., 2010. Production Engineering and Management under Fuzziness, Springer-Verlag, Series: Studies in Fuzziness and Soft Computing.
34. Karaesmen I.Z., Scheller-Wolf A., Deniz B., 2011. Managing Perishable and Aging Inventories: Review and Future Research Directions. International Series in Operations Research & Management Science, 151, 393-436.
35. Karahan M., Aslan Ş., 2016. Bir Çimento Fabrikasında Hammadde Stok Kontrolü Uygulaması. Süleyman Demirel Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 21(3), 773-783.
36. Karimi M., Niknamfar A.H., Pasandideh S.H.R., 2016. Two-stage Single Period Inventory Management for A Manufacturing Vendor under Green-Supplier Supply Chain. International Journal of Systems Assurance Engineering and Management, 1-15.
37. Kasap N., Biçer İ., Yüksel Özkaya B., 2010. Stokastik Envanter Model Kullanılarak İş Makinelerinin Onarımında Kullanılanılan Kritik Yedek Parçalar için Envanter Yönetim Sistemi Oluşturulması. İstanbul Üniversitesi İşletme Fakültesi Dergisi, 39(2), 310-334.
38. Khouja M.J., 1999. The Single-period (News-vendor) Problem: Literature Review and Suggestions for Future Research. Omega, 27(5), 537-553.
39. Kim G., Wu K., Huang E., 2015. Optimal Inventory Control in A Multi-Period Newsvendor Problem with Non-Stationary Demand. Advanced Engineering Informatics, 29(1), 139-145.
40. Lee A.H.I., Kang H.Y., 2008. A Mixed 0–1 Integer Programming for Inventory Model: A Case Study of TFT-LCD Manufacturing Company in Taiwan. Kybernetes, 37 (1), 66–82.
41. Mahapatra N.K., Maiti M., 2005. Multi-objective Inventory Models of Multi-items with Quality and Stock-Dependent Demand and Stochastic Deterioration. Advanced Modeling and Optimization, 7 (1), 69–84.
42. Mandal N.K., Roy T.K., Maiti M., 2005. Multi-objective Fuzzy Inventory Model with Three Constraints: A Geometric Programming Approach. Fuzzy Sets and Systems, 150, 87–106.
43. Mousavi S.M., Hajipour V., Niaki S.T.A., Alikar N., 2013. Optimizing Multi-item Multi-Period Inventory Control System With Discounted Cash Flow And Inflation: Two Calibrated Meta-Heuristic Algorithms. Applied Mathematical Modelling, 37, 2241–2256.
44. Mousavi S.M., Niaki S.T.A., Bahreininejad A., Musa S.N., 2014. Multi-item Multi-periodic Inventory Control Problem with Variable Demand and Discounts: A Particle Swarm Optimization Algorithm. The Scientific World Journal, 1–16.
45. Mousavi S.M., Pasandideh S.H., 2011. A Multi-Periodic Multi-Product Inventory Control Problem with Discount: GA Optimization Algorithm. Journal of Optimization in Industrial Engineering, 4(7), 37–44.
46. Mousavi S.M., Sadeghi J., Niaki S.T.A., Tavana M., 2016. A Bi-Objective Inventory Optimization Model Under Inflation and Discount Using Tuned Pareto-Based Algorithms: NSGA-II, NRGA, and MOPSO. Applied Soft Computing, 43, 57–72.
47. Murray C.C., Gosavi A., Talukdar D., 2012. The Multi-Product Price-Setting Newsvendor with Resource Capacity Constraints. International Journal of Production Economics, 138 (1), 148–158.
48. Nahmias S., Schmidt C.P., 1984. An Efficient Heuristic for the Multi-item Newsboy Problem with A Single Constraint. Naval Research Logistics, 31 (3), 463–474.
49. Önal M., Romeijn H.E., Sapra A., van den Heuvel W., 2015. The Economic Lot-Sizing Problem with Perishable Items and Consumption Order Preference. European Journal of Operational Research, 244(3), 881-891.
50. Pahl J., Voß S., 2010. Discrete Lot-Sizing and Scheduling Including Deterioration and Perishability Constraints. Advanced Manufacturing and Sustainable Logistics. Springer Berlin Heidelberg, Berlin, Heidelberg, 345–357.
51. Panda D., Kar S., Maity K., Maiti M., 2008. A Single Period Inventory Model with Imperfect Production And Stochastic Demand Under Chance and Imprecise Constraints. European Journal of Operational Research, 188 (1), 121-139.
52. Parlar M., Perry D., Stadje W., 2011. FIFO versus LIFO Issuing Policies for Stochastic Perishable Inventory Systems”, Methodology and Computing in Applied Probability, 13, 405-417.
53. Pasandideh S. H. R., Niaki S. T. A., Keshavarzi A.A., 2017. A Two-Echelon Single-Period Inventory Control Problem with Market Strategies and Customer Satisfaction. Journal of Uncertain Systems, 11(1), 18-34.
54. Pasandideh S.H., Niaki S.T.A., Rashidi R., 2011a. A Two-Echelon Single-Period Inventory Control Problem under Budget Constraint. The International Journal of Advanced Manufacturing Technology, 56, 1205-1214.
55. Pasandideh S.H.R., Niaki S. T. A., Tokhmehchi N., 2011b. A Parameter-Tuned Genetic Algorithm to Optimize Two-Echelon Continuous Review Inventory Systems. Expert Systems with Applications, 38, 11708–11714.
56. Pasandideh S.H.R., Niaki S.T.A., Mousavi S. M., 2013. Two Metaheuristics to Solve A Multi-item Multi-period Inventory Control Problem under Storage Constraint and Discounts. International Journal of Advanced Manufacturing Technology, 69, 1671–1684.
57. Rezaeian J., Shokoufi K., Haghayegh S., Mahdavi I., 2016. Designing an Integrated Production/Distribution and Inventory Planning Model of Fixed-Life Perishable Products. Journal of Optimization in Industrial Enginering, 19, 47–59.
58. Sadeghi J., Mousavi M.S., Niaki S.T.A., 2016. Optimizing an Inventory Model with Fuzzy Demand, Backordering, and Discount Using a Hybrid Imperialist Competitive Algorithm. Applied Mathematical Modelling, 40 (15–16), 7318-7335.
59. Saraçoglu I., Topaloglu S., Keskinturk, T. 2014. A Genetic Algorithm Approach for Multi-Product Multi-Period Continuous Review Inventory Models. Expert Systems with Applications, 41(18), 8189-8202.
60. Sazvar Z., SMirzapour Al-e-hashem.M.J., Govindan K., Bahli B., 2016. A Novel Mathematical Model for A Multi-Period, Multi-Product Optimal Ordering Problem Considering Expiry Dates in A FEFO System. Transportation Research Part E: Logistics and Transportation Review, 93, 232-261.
61. Sezen B., 2002. Tek Dönemli Envanter Problemine Yeni Yaklaşımlar. İstanbul Üniversitesi İşletme Fakültesi Dergisi, 31(2), 71-86.
62. Shao Z., Ji X., 2006. Fuzzy Multi-Product Constraint Newsboy Problem. Applied Mathematics and Computation, 180 (1), 7-15.
63. Sharma S., 2004. Optimal Production Policy with Shelf Life Including Shortages. The Journal of the Operational Research Society, 55(8), 902–909.
64. Silver E.A., 2008. Inventory Management: An Overview, Canadian Publications, Practical Applications and Suggestions for Future Research. Information Systems and Operational Research (INFOR), 46(1), 15–28.
65. Silver E.A., Pyke D.F., Peterson R.P., 1998. Inventory Management and Production Planning and Scheduling, Third edition, John Wiley, New York.
66. Silver, E.A., 1979. Coordinated Replenishments of Items Under Time-Varying Demand: Dynamic Programming Formulation. Naval Research Logistics Quarterly, 26, 141–151.
67. Srivastav A., Agrawal S., 2015. Multi-Objective Optimization of A Mixture Inventory System using a MOPSO–TOPSIS Hybrid Approach. Transactions of the Institute of Measurement and Control, 39(4) 555–566.
68. Srivastav A., Agrawal S., 2017. Multi-Objective Optimization of Slow Moving Inventory System Using Cuckoo Search. Intelligent Automation & Soft Computing, 1-7.
69. Sulak H., Eroğlu A., 2009. Ekonomik Sipariş ve Üretim Miktarı Modellerinde Yeni Açılımlar. Süleyman Demirel Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 14(3), 383-406.
70. Taleizadeh A.A., Niaki S.T.A., 2009. A Hybrid Meta-Heuristic Method to Optimize Bi-Objective Single Period Newsboy Problem with Fuzzy Cost and Incremental Discount, Journal of Industrial Engineering, 3, 1-13.
71. Taleizadeh A.A., Niaki S.T.A., Hoseini V., 2009. Optimizing Multi-Product Multi-Constraint Bi-Objective Newsboy Problem Constrained with Discount by A Hybrid Method of Goal Programming and Genetic Algorithm. Engineering Optimization, 41, 437–457.
72. Toledo C.F.M., de Oliveira, R.R.R., Morelato França, P., 2013. A Hybrid Multi-Population Genetic Algorithm Applied to Solve the Multi-Level Capacitated Lot Sizing Problem with Backlogging. A Hybrid Multi-Population Genetic Algorithm Applied to Solve the Multi-Level Capacitated Lot Sizing, 40, 910–919.
73. Tsou C.S., 2008. Multi-objective Inventory Planning using MOPSO and TOPSIS. Expert Systems with Applications, 35 (1-2), 136–142.
74. Uzunoğlu Koçer U., Yalçın B., 2013. Bir Stokastik Model Olarak Bozulabilir Envanter Problemi: Literatür Araştırması. Dokuz Eylül Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi 28(1), 119-144.
75. Vairaktarakis G.L. 2000. Robust Multi-item Newsboy Models with A Budget Constraint. International Journal of Production Economics, 66, 213-226.
76. Wagner H.M., Whitin T.M., 1958. Dynamic Version of the Economic Lot Size Model. Management Science, 5, 89–96.
77. Walker J., 1993. The Single-Period Inventory Problem with Triangular Demand Distribution. Journal of Operations Research Society, 44 (7), 725–731.
78. Wang D., Qin Z., Kar S., 2015. A Novel Single-Period Inventory Problem with Uncertain Random Demand and Its Application, Applied Mathematics and Computation, 269, 133-145.
79. Zhang G., 2010. The Multi-Product Newsboy Problem with Supplier Quantity Discounts and a Budget Constraint, European Journal of Operational Research, 206(2), 350-360.
80. Zhao X., Qiu M., Xie J., He Q., 2012. Computing (r, Q) Policy for an Inventory System with Limited Sharable Resource. Computers and Operations Research, 39, 2368- 2379.
81. Zhou W.-Q., Chen L., Ge H.-M., 2013. A Multi-Product Multi-Echelon Inventory Control Model with Joint Replenishment Strategy, Applied Mathematical Modelling, 37(4), 2039-2050.
82. Ziukov S., 2015. A Literature Review on Models of Inventory Management Under Uncertainty, Business Systems and Economics, 5(1), 26-35.