Optimal Control of Multi-Supplier Inventory Management with Lead Time

Darsih Idayani, Subchan Subchan

Abstract


In the current global competition, companies are required to save money in order to survive. One of the expenses that can be reduced is the cost of inventory control. To minimize these costs, we require a proper planning and management of the inventory. Ordering supplies should be performed at a certain time period, especially with uncertain demand. As such, the company must determine when to order at the suppliers and how many should be ordered. So there will be no excess inventory in the warehouse because of too much ordering or because of the inventory cannot meet demand due to late or too little order to suppliers. Consequently, in this research, a quadratic cost functional is used as the objective function in multi-supplier inventory management problem with different lead time. Optimal control theory, LQR (Linear Quadratic Regulator) is used to solve this problem. According to the simulation, we conclude that the smaller weight resulted in more optimal inventory cost.

Keywords


Optimal control; Linear quadratic regulator; Inventory control; Multi supplier; Lead time

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References


D. Bertsekas, “Dynamic programming and optimal control 4th edition, volume II,” Athena Scientific, 2015.

S. Sethi, Optimal Control Theory: Application to Management Science and Economics. Springer International Publishing, 2019.

H. Sarimveis, P. Patrinos, C. Tarantilis, and C. Kiranoudis, “Dynamic modeling and control of supply chain systems: A review,” Computers & Operations Research, vol. 35, no. 11, pp. 3530–3561, 2008.

P. Ignaciuk and A. Bartoszewicz, “Lq optimal and time-varying sliding modes for inventory management systems,” in IEEE Control Applications,(CCA) & Intelligent Control,(ISIC), 2009, pp. 279–284.

H. Xiao-Jun, F. Ai-Ming, and Z. Bao-Lin, “Approximate optimal inventory control of supply chain networks with lead time,” in The 27th Chinese Control and Decision Conference (2015 CCDC), 2015, pp. 4523–4528.

V. Smagin, G. Koshkin, and K. Kim, “Locally optimal inventory control with time delay in deliveries and incomplete information on demand,” in 2016 Second International Symposium on Stochastic Models in Reliability Engineering, Life Science and Operations Management (SMRLO), 2016, pp. 570–574.

Y. Akikuni, K. Okuhara, and Y. Fujisaki, “Optimal control of inventory systems with multiple suppliers,” in 56th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE), 2017, pp. 353–354.

S. Granin, A. Mandel, and M. Vilms, “Simulation of inventory control process for supply chain with several suppliers,” in Tenth International Conference Management of Large-Scale System Development (MLSD), 2017, pp. 1–4.

M. Luthfi, Sutrisno, and Widowati, “Stock control of single product inventory system with imperfect delivery by using robust linear quadratic regulator,” in 4th International Conference on Science and Technology (ICST), 2018, pp. 1–4.

D. Idayani, L. Sari, and Z. Munawwir, “Optimal control of procurement policy optimization with limited storage capacity,” in IOP Conference Series: Earth and Environmental Science, vol. 243, no. 1, 2019, p. 012044.

D. Nguyen, C. Haoxun, and W. Nengmin, “Modeling and optimization of biomass supply chain with two types of feedstock suppliers,” in Proceedings of the 7th International Conference on Industrial Engineering and Systems Management, 2017.

D. Nguyen and H. Chen, “Supplier selection and operation planning in biomass supply chains with supply uncertainty,” Computers & Chemical Engineering, vol. 118, pp. 103–117, 2018.

S. Hosseini, N. Morshedlou, D. Ivanov, M. Sarder, K. Barker, and A. Al Khaled, “Resilient supplier selection and optimal order allocation under disruption risks,” International Journal of Production Economics, vol. 213, pp. 124–137, 2019.

A. Memari, A. Dargi, M. Jokar, R. Ahmad, and A. Rahim, “Sustainable supplier selection: A multi-criteria intuitionistic fuzzy topsis method,” Journal of Manufacturing Systems, vol. 50, pp. 9–24, 2019.

P. Ignaciuk and A. Bartoszewicz, “Linear–quadratic optimal control strategy for periodic-review inventory systems,” Automatica, vol. 46, no. 12, pp. 1982–1993, 2010.

D. Naidu, Optimal control systems. CRC press, 2002.

S. Subchan and R. Zbikowski, Computational optimal control: Tools and practice. John Wiley & Sons, 2009.

V. Katsikis, MATLAB: A fundamental tool for scientific computing and engineering applications. BoD–Books on Demand, 2012, vol. 3.

D. Zwillinger, Handbook of differential equations. Gulf Professional Publishing, 1998, vol. 1.

Subiono, Optimal kontrol. Departemen Matematika-ITS, 2010.

P. Ignaciuk and A. Bartoszewicz, Congestion control in data transmission networks: sliding mode and other designs. Springer Science & Business Media, 2012.

B. Anderson and J. Moore, Optimal control: linear quadratic methods. Courier Corporation, 2007.

K. Ogata, Discrete-time control systems. Prentice Hall Englewood Cliffs, NJ, 1995, vol. 2.

Y. Prawoto, “Integrasi metode analytic hierarchy process (ahp) dan metode fuzzy multi objective untuk optimasi pemilihan pemasok multi supplier dan alokasi pengadaan (studi kasus: Perum bulog sub divre wilayah i surabaya utara),” 2011.

S. Chopra, P. Meindl, and D. Kalra, Supply chain management: strategy, planning, and operation. Pearson Boston, MA, 2013, vol. 232.




DOI: http://dx.doi.org/10.12962/j24775401.v6i1.5040

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International Journal of Computing Science and Applied Mathematics by Pusat Publikasi Ilmiah LPPM, Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/ijcsam.