Document Type : Research Paper

Authors

1 Department of Operation Research and Business informatics, Wroclaw University of Science and Technology, Wroclaw, Poland.

2 King Fahd University of Petroleum and Minerals, Dhahran, Saudi-Arabia.

Abstract

Consignment stocks agreement had been very useful in inventory control. The benefit ranges from improved cash flow, reduced risk level, savings on investment, reduced ownership cost, low inventory carrying cost and regular restocking to mention few. Also, small batch delivery is an effective strategy for launching a product since it enables a business to assess the market and validate the product before committing to a large production run. In this paper, we combined small batch delivery and consignment stock policy by considering a supply chain setting where a vendor fulfilled the shipment requirement of each buyer sequentially in a single production set up. To achieve this, and as against the equal size shipments policy assumed in literature for different buyers, the vendor sends a smaller shipment first as early entry, followed by n equal shipments. These n shipments are proportionately increased according to the vendor rate of production to each buyer’s demand rate. A mathematical cost function is developed to reduce the overall cost of the integrated supply chain system through the optimal cycle time and the optimal numbers of shipments to be delivered to each buyer. Numerical example is given using data from an existing literature, results were compared, and the new distribution policy gives better financial savings in terms of cost over the equal shipment policy assumed in literature. Sensitivity analyses were performed on key parameters to evaluate the robustness of the model.

Keywords

Main Subjects

[1]     Zavanella, L., & Zanoni, S. (2009). A one-vendor multi-buyer integrated production-inventory model: The ‘Consignment Stock’case. International journal of production economics, 118(1), 225–232.
[2]     Goyal, S. K. (1977). An integrated inventory model for a single supplier-single customer problem. The international journal of production research, 15(1), 107–111.
[3]     Goyal, S. K. (1977). Determination of optimum production quantity for a two-stage production system. Journal of the operational research society, 28(4), 865–870.
[4]     Banerjee, A. (1986). Note—On “A Quantity Discount Pricing Model to Increase Vendor Profits.” Management science, 32(11), 1513–1517.
[5]     Banerjee, A. (1986). A joint economic-lot-size model for purchaser and vendor. Management science, 32(11), 1513–1517.
[6]     Goyal, S. K. (1988). “A joint economic-lot-size model for purchaser and vendor”: A comment. Decision sciences, 19(1), 236–241.
[7]     Goyal, S. K., & Gupta, Y. P. (1989). Integrated inventory models: the buyer-vendor coordination. European journal of operational research, 41(3), 261–269.
[8]     Lu, L. (1995). A one-vendor multi-buyer integrated inventory model. European journal of operational research, 81(2), 312–323.
[9]     Hill, R. M. (1997). The single-vendor single-buyer integrated production-inventory model with a generalised policy. European journal of operational research, 97(3), 493–499.
[10]   Hill, R. M. (1999). The optimal production and shipment policy for the single-vendor singlebuyer integrated production-inventory problem. International journal of production research, 37(11), 2463–2475.
[11]   Goyal, S. K. (2000). On improving the single-vendor single-buyer integrated production inventory model with a generalized policy. European journal of operational research, 125(2), 429–430.
[12]   Valentini, G., & Zavanella, L. (2003). The consignment stock of inventories: industrial case and performance analysis. International journal of production economics, 81, 215–224.
[13]   Braglia, M., & Zavanella, L. (2003). Modelling an industrial strategy for inventory management in supply chains: The’Consignment Stock’case. International journal of production research, 41(16), 3793–3808.
[14]   Zanoni, S., & Grubbstrom*, R. W. (2004). A note on an industrial strategy for stock management in supply chains: modelling and performance evaluation. International journal of production research, 42(20), 4421–4426.
[15]   Ben-Daya, M., & Hariga, M. (2004). Integrated single vendor single buyer model with stochastic demand and variable lead time. International journal of production economics, 92(1), 75–80.
[16]   Hoque, M. A., & Goyal, S. K. (2006). A heuristic solution procedure for an integrated inventory system under controllable lead-time with equal or unequal sized batch shipments between a vendor and a buyer. International journal of production economics, 102(2), 217–225.
[17]   Hill, R. M., & Omar, M. (2006). Another look at the single-vendor single-buyer integrated production-inventory problem. International journal of production research, 44(4), 791–800.
[18]   Sarmah, S. P., Acharya, D., & Goyal, S. K. (2006). Buyer vendor coordination models in supply chain management. European journal of operational research, 175(1), 1–15.
[19]   Zhou, Y. W., & Wang, S. D. (2007). Optimal production and shipment models for a single-vendor--single-buyer integrated system. European journal of operational research, 180(1), 309–328.
[20]   Islam, S. M. S. (2014). Single-vendor single-buyer optimal consignment policy for a seasonal product. Journal of science and technology, 12, 59–66.
[21]   Jaber, M. Y., Zanoni, S., & Zavanella, L. E. (2014). A consignment stock coordination scheme for the production, remanufacturing and waste disposal problem. International journal of production research, 52(1), 50–65.
[22]   Zanoni, S., Mazzoldi, L., & Jaber, M. Y. (2014). Vendor-managed inventory with consignment stock agreement for single vendor--single buyer under the emission-trading scheme. International journal of production research, 52(1), 20–31.
[23]   Giri, B. C., & Bardhan, S. (2015). A vendor--buyer JELS model with stock-dependent demand and consigned inventory under buyer’s space constraint. Operational research, 15, 79–93.
[24]   Zahran, S. K., Jaber, M. Y., & Zanoni, S. (2016). The consignment stock case for a vendor and a buyer with delay-in-payments. Computers & industrial engineering, 98, 333–349.
[25]   Khan, M., Jaber, M. Y., Zanoni, S., & Zavanella, L. (2016). Vendor managed inventory with consignment stock agreement for a supply chain with defective items. Applied mathematical modelling, 40(15–16), 7102–7114.
[26]   Giri, B. C., Chakraborty, A., & Maiti, T. (2017). Consignment stock policy with unequal shipments and process unreliability for a two-level supply chain. International journal of production research, 55(9), 2489–2505.
[27]   AlDurgam, M., Adegbola, K., & Glock, C. H. (2017). A single-vendor single-manufacturer integrated inventory model with stochastic demand and variable production rate. International journal of production economics, 191, 335–350.
[28]   Islam, S. M. S., & Hoque, M. A. (2018). Single-vendor single-buyer optimal consignment policy with generic demand distribution by considering some realistic factors. International journal of operational research, 31(2), 141–163.
[29]   Hariga, M., Babekian, S., & Bahroun, Z. (2019). Operational and environmental decisions for a two-stage supply chain under vendor managed consignment inventory partnership. International journal of production research, 57(11), 3642–3662.
[30]   Zavanella, L. E., Marchi, B., Zanoni, S., & Ferretti, I. (2019). Energy considerations for the economic production quantity and the joint economic lot sizing. Journal of business economics, 89(7), 845–865.
[31]   Gharaei, A., Karimi, M., & Shekarabi, S. A. H. (2019). An integrated multi-product, multi-buyer supply chain under penalty, green, and quality control polices and a vendor managed inventory with consignment stock agreement: The outer approximation with equality relaxation and augmented penalty algorithm. Applied mathematical modelling, 69, 223–254.
[32]   Giri, B. C., & Masanta, M. (2022). A closed-loop supply chain model with uncertain return and learning-forgetting effect in production under consignment stock policy. Operational research, 1–29.
[33]   Çömez-Dolgan, N., Moussawi-Haidar, L., & Jaber, M. Y. (2021). A buyer-vendor system with untimely delivery costs: Traditional coordination vs. VMI with consignment stock. Computers & industrial engineering, 154, 107009. https://www.sciencedirect.com/science/article/pii/S0360835220306793
[34]   Hemmati, M., Al-e-Hashem, S. M. J. M., & Ghomi, S. M. T. F. (2021). Heuristic analyses of separate and bundling sales for complimentary products under consignment stock policy. Computers \& industrial engineering, 157, 107297. https://www.sciencedirect.com/science/article/pii/S0360835221002011
[35]   Sen, N., Bardhan, S., & Giri, B. C. (2021). Effectiveness of consignment stock policy under space limitations and deterioration. International journal of production research, 59(6), 1834–1851.
[36]   Marchi, B., Zanoni, S., & Jaber, M. Y. (2021). Credit-dependent demand in a vendor-buyer model with a two-level delay-in-payments contract under a consignment-stock policy agreement. Applied mathematical modelling, 99, 585–605.
[37]   den Bogaert, J., & Van Jaarsveld, W. (2022). Vendor-managed inventory in practice: understanding and mitigating the impact of supplier heterogeneity. International journal of production research, 60(20), 6087–6103.
[38]   Zhang, T., Hao, Y., & Zhu, X. (2022). Consignment inventory management in a closed-loop supply chain for deteriorating items under a carbon cap-and-trade regulation. Computers \& industrial engineering, 171, 108410. https://www.sciencedirect.com/science/article/pii/S0360835222004491
[39]   Asadkhani, J., Fallahi, A., & Mokhtari, H. (2022). A sustainable supply chain under VMI-CS agreement with withdrawal policies for imperfect items. Journal of cleaner production, 376, 134098. https://www.sciencedirect.com/science/article/pii/S0959652622036708
[40]   Keshavarz-Ghorbani, F., & Pasandideh, S. H. R. (2022). Incorporating a choice-based diffusion model into a bi-objective multi-generation product optimization problem under consignment stock policy. Journal of cleaner production, 381, 135175. https://www.sciencedirect.com/science/article/pii/S0959652622047497
[41]   Hemmati, M., Fatemi Ghomi, S. M. T., & Sajadieh, M. S. (2023). A multi-echelon supply chain of deteriorating items with stock-and price-sensitive demand under consignment stock policy. Engineering optimization, 55(3), 476–493.
[42]   Ambroszkiewicz, S., & Bylka, S. (2023). Relatively optimal policies for stock management in a supply chain with option for inventory space limitation. Applied mathematical modelling, 114, 291–317.
[43]   Lal, R., & Staelin, R. (1984). An approach for developing an optimal discount pricing policy. Management science, 30(12), 1524–1539.
[44]   Joglekar, P. N. (1988). Note—Comments on “A quantity discount pricing model to increase vendor profits.” Management science, 34(11), 1391–1398.
[45]   Banerjee, A., & Banerjee, S. (1994). A coordinated order-up-to inventory control policy for a single supplier and multiple buyers using electronic data interchange. International journal of production economics, 35(1–3), 85–91.
[46]   Viswanathan, S., & Piplani, R. (2001). Coordinating supply chain inventories through common replenishment epochs. European journal of operational research, 129(2), 277–286.
[47]   Woo, Y. Y., Hsu, S.-L., & Wu, S. (2001). An integrated inventory model for a single vendor and multiple buyers with ordering cost reduction. International journal of production economics, 73(3), 203–215.
[48]   Boyac\i, T., & Gallego, G. (2002). Coordinating pricing and inventory replenishment policies for one wholesaler and one or more geographically dispersed retailers. International journal of production economics, 77(2), 95–111.
[49]   Siajadi, H., Ibrahim, R. N., & Lochert, P. B. (2006). Joint economic lot size in distribution system with multiple shipment policy. International journal of production economics, 102(2), 302–316.
[50]   Kim, T., Hong, Y., & Chang, S. Y. (2006). Joint economic procurement—production--delivery policy for multiple items in a single-manufacturer, multiple-retailer system. International journal of production economics, 103(1), 199–208.
[51]   Srinivas, C., & Rao, C. S. P. (2010). Optimization of supply chains for single-vendor--multibuyer consignment stock policy with genetic algorithm. The international journal of advanced manufacturing technology, 48, 407–420.
[52]   Hariga, M., Gumus, M., Ben-Daya, M., & Hassini, E. (2013). Scheduling and lot sizing models for the single-vendor multi-buyer problem under consignment stock partnership. Journal of the operational research society, 64(7), 995–1009.
[53]   Ben-Daya, M., Hassini, E., Hariga, M., & AlDurgam, M. M. (2013). Consignment and vendor managed inventory in single-vendor multiple buyers supply chains. International journal of production research, 51(5), 1347–1365.
[54]   Mandal, P., & Giri, B. C. (2015). A single-vendor multi-buyer integrated model with controllable lead time and quality improvement through reduction in defective items. International journal of systems science: operations & logistics, 2(1), 1–14.
[55]   Fauza, G., Amer, Y., Lee, S.-H., & Prasetyo, H. (2016). An integrated single-vendor multi-buyer production-inventory policy for food products incorporating quality degradation. International journal of production economics, 182, 409–417.
[56]   Sarkar, B., Majumder, A., Sarkar, M., Kim, N., & Ullah, M. (2018). Effects of variable production rate on quality of products in a single-vendor multi-buyer supply chain management. The international journal of advanced manufacturing technology, 99, 567–581.
[57]   Omar, M., & Zulkipli, H. (2018). A single-vendor multi-buyer integrated production-inventory system with stock-dependent demand. International journal of systems science: operations & logistics, 5(3), 204–210.
[58]   Guchhait, R., Sarkar, M., Sarkar, B., & Pareek, S. (2017). Single-vendor multi-buyer game theoretic model under multi-factor dependent demand. International journal of inventory research, 4(4), 303–332.
[59]   Chan, C. K., Fang, F., & Langevin, A. (2018). Single-vendor multi-buyer supply chain coordination with stochastic demand. International journal of production economics, 206, 110–133.
[60]   Ben-Daya, M., As’ ad, R., & Nabi, K. A. (2019). A single-vendor multi-buyer production remanufacturing inventory system under a centralized consignment arrangement. Computers & industrial engineering, 135, 10–27.
[61]   Castellano, D., Gallo, M., Grassi, A., & Santillo, L. C. (2019). The effect of GHG emissions on production, inventory replenishment and routing decisions in a single vendor-multiple buyers supply chain. International journal of production economics, 218, 30–42.
[62]   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. Journal tecknik industry, 22(1), 71–84.
[63]   Castellano, D., Gallo, M., & Santillo, L. C. (2021). A periodic review policy for a coordinated single vendor-multiple buyers supply chain with controllable lead time and distribution-free approach. 4OR, 19, 347–388.
[64]   Chakraborty, A., Verma, N. K., & Chatterjee, A. K. (2022). A single supplier multi buyer supply chain coordination under vendor-managed inventory: Ensuring Buyers’ interests in a decentralized setting. IIM kozhikode society & management review, 22779752211072936. https://journals.sagepub.com/doi/abs/10.1177/22779752211072934
[65]   Adegbola, K. (2023). A simulation study of single-vendor, single and multiple-manufacturers supply chain system, with stochastic demand and two distribution policies. Journal of decision analytics and intelligent computing, 3(1), 62–79.