Integrated Inventory Model for Single Vendor Multi-Buyer with a Single Item by Considering Warehouse and Capital Constraint


  • Agustiandi Agustiandi Department of Industrial Technology, Parahyangan Catholic University, Bandung, Indonesia
  • Yoon Mac Kinley Aritonang Department of Industrial Technology, Parahyangan Catholic University, Bandung, Indonesia
  • Cherish Rikardo Department of Industrial Technology, Parahyangan Catholic University, Bandung, Indonesia



Capital Constraint, Warehouse Constraint, Lagrange Multipliers, Vendor-Buyer, inventory


Integrated inventory management coordinates all party's replenishment policies to provide optimal benefits. Many models have been developed, but none of them have considered capital and warehouse constraints comprehensively. It may cause the model which cannot be applied, since it has exceeded the capacity. This study developed an integrated inventory model that consisted of one vendor, multi-buyer, and one type of item. The main objective was to minimize the joint total expected cost by considering warehouse, capital, and service level constraint. The optimal formula was constructed by using the Lagrange multipliers method.  The results showed that with an increment in holding cost, the vendor tends to reduce lot size to minimize joint total expected cost. It is vice versa to the increment in set up cost. An increment in buyer service level can increase lot size and reduce order frequency. The buyer capacity is essential to determine its capability to apply the optimal replenishment policy.


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I. Mas'udin and M. S. Kamara, "Electronic Data Interchange and Demand Forecasting Implications on Supply Chain Management Collaboration: A Customer Service Perspective," Jurnal Teknik Industri, vol. 18, pp. 138-148, 2017.

M. Mofokeng Teboho and R. Chinomona, "Supply chain partnership, supply chain collaboration and supply chain integration as the antecedents of supply chain performance," South African Journal of Business Management, vol. 50, pp. 1-10, 2019.

L. Yang, H. Li, and J. F. Campbell, "Improving Order Fulfillment Performance through Integrated Inventory Management in a Multi-Item Finished Goods System," Journal of Business Logistics, vol. 41, pp. 54-66, 2020.

G. Hadley and T. M. Whitin, Analysis of inventory systems. Biblioteca Central: Englewood Cliffs, N. J. : Prentice-Hall, 1963.

R. J. Tersine, Principles of inventory and materials management. New Jersey: Prentice Hall, 1994.

J. K. Jha and K. Shanker, "Single-vendor multi-buyer integrated production-inventory model with controllable lead time and service level constraints," Applied Mathematical Modelling, vol. 37, pp. 1753-1767, 2013.

S. K. Goyal, "An integrated inventory model for a single supplier-single customer problem," International Journal of Production Research, vol. 15, pp. 107-111, 1977.

S. Lee, Y. J. Kim, T. Cheong, and S. H. Yoo, "Effects of Yield and Lead-Time Uncertainty on Retailer-Managed and Vendor-Managed Inventory Management," IEEE Access, vol. 7, pp. 176051-176064, 2019.

K. Aritonang, M. Nainggolan, and A. V. Djunaidi, "Integrated Supply Chain for a Single Vendor and Multiple Buyers and Products with Crashing Lead Time," International Journal of Technology, vol. 11, pp. 642-651, 2020.

S.-P. Huang, "Using simple and efficient algorithm involving ordering cost reduction and backorder price discount on inventory system under variable lead time," Information Technology Journal, vol. 9, pp. 804-810, 2010.

S.-L. Hsu and C. C. Lee, "Replenishment and lead time decisions in manufacturer–retailer chains," Transportation Research Part E: Logistics and Transportation Review, vol. 45, pp. 398-408, 2009.

N. A. Kurdhi, A. Jamaluddin, W. A. Jauhari, and D. R. S. Saputro, "A periodic review integrated inventory model with controllable safety stock and setup cost under service level constraint and distribution-free demand," in Journal of Physics: Conference Series, 2017, p. 012022.

Q. Mou, Y. Cheng, and H. Liao, "A note on “lead time reduction strategies in a single-vendor-single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand”," International Journal of Production Economics, vol. 193, pp. 827-831, 2017.

M. Vijayashree and R. Uthayakumar, "A single-vendor and a single-buyer integrated inventory model with ordering cost reduction dependent on lead time," Journal of Industrial Engineering International, vol. 13, pp. 393-416, 2017.

M. AlDurgam, K. Adegbola, and C. H. Glock, "A single-vendor single-manufacturer integrated inventory model with stochastic demand and variable production rate," International Journal of Production Economics, vol. 191, pp. 335-350, 2017.

M. A. Hoque and A. Bhattacharya, "A manufacturer-buyers integrated inventory model with generic distribution of lead times to deliver equal and/or unequal batch sizes," Computers & Operations Research, vol. 124, p. 105047, 2020.

J.-J. Liao, K.-J. Chung, and K.-N. Huang, "A deterministic inventory model for deteriorating items with two warehouses and trade credit in a supply chain system," International Journal of Production Economics, vol. 146, pp. 557-565, 2013.

L.-Y. Ouyang, C.-H. Ho, C.-H. Su, and C.-T. Yang, "An integrated inventory model with capacity constraint and order-size dependent trade credit," Computers & Industrial Engineering, vol. 84, pp. 133-143, 2015.

H. Tarhini, M. Karam, and M. Y. Jaber, "An integrated single-vendor multi-buyer production inventory model with transshipments between buyers," International Journal of Production Economics, vol. 225, p. 107568, 2020.

D. M. Utama, "Model Penentuan Lot Pemesanan Dengan Mempertimbangkan Unit Diskon dan Batasan Kapasitas Gudang dengan Program Dinamis," Jurnal Teknik Industri, vol. 18, pp. 94-102, 2017.

I. Bendavid, Y. T. Herer, and E. Yücesan, "Inventory management under working capital constraints," Journal of Simulation, vol. 11, pp. 62-74, 2017.

S. K. D. B. Maulana, D. M. Utama, M. S. Asrofi, I. S. Ningrum, N. Alba, H. A. Ahfa, et al., "The Capacitated Sustainable EOQ Models: Models Considering Tax Emissions," Jurnal Teknik Industri, vol. 21, pp. 12-21, 2019.

B. Sarkar, W. Ahmed, S.-B. Choi, and M. Tayyab, "Sustainable Inventory Management for Environmental Impact through Partial Backordering and Multi-Trade-Credit-Period," Sustainability, vol. 10, 2018.

S. Tiwari, W. Ahmed, and B. Sarkar, "Multi-item sustainable green production system under trade-credit and partial backordering," Journal of Cleaner Production, vol. 204, pp. 82-95, 2018.

A. K. Agrawal and S. Yadav, "Price and profit structuring for single manufacturer multi-buyer integrated inventory supply chain under price-sensitive demand condition," Computers & Industrial Engineering, vol. 139, p. 106208, 2020.

Y.-C. Tsao, Q. Zhang, H.-P. Fang, and P.-L. Lee, "Two-tiered pricing and ordering for non-instantaneous deteriorating items under trade credit," Operational Research, vol. 19, pp. 833-852, 2019.

A. Banu and S. K. Mondal, "Analyzing an inventory model with two-level trade credit period including the effect of customers’ credit on the demand function using q-fuzzy number," Operational Research, vol. 20, pp. 1559-1587, 2020.

B. C. Giri and S. Sharma, "Optimal ordering policy for an inventory system with linearly increasing demand and allowable shortages under two levels trade credit financing," Operational Research, vol. 16, pp. 25-50, 2016.

W. L. Winston and J. B. Goldberg, Operations research: applications and algorithms vol. 3: Thomson/Brooks/Cole Belmont eCalif Calif, 2004.

M. A. Hoque, "Synchronization in the single-manufacturer multi-buyer integrated inventory supply chain," European Journal of Operational Research, vol. 188, pp. 811-825, 2008.




How to Cite

Agustiandi, A., Aritonang, Y. M. K., & Rikardo, C. (2021). Integrated Inventory Model for Single Vendor Multi-Buyer with a Single Item by Considering Warehouse and Capital Constraint. Jurnal Teknik Industri, 22(1), 71-84.