Integrated Supply Chain for a Single Vendor and Multiple Buyers and Products with Crashing Lead Time

In this study, an integrated inventory model was developed among one vendor, multi buyers, and multi products. The total inventory cost to be minimized in this model is a combination of the vendor’s and the buyers’ total inventory costs. The total vendor inventory costs consist of setup costs and holding costs and the total inventory cost of the buyer consists of ordering costs, holding costs, stockout costs, and crashing lead time costs where the crashing lead time cost is approximated with an exponential function. Three decision variables will be calculated: the number of buyer orders, the lead time of each buyer, and the frequency of vendor shipments to all buyers in one production cycle. In this study, the optimal solution of each decision variable has been developed and applied to a case to show the use of models for finding optimal solutions. The sensitivity has also been performed to show the effects of some factors on the decision variables.

Crashing lead time; Integrated inventory model; Inventory management; Multi products; Multi buyers

In the supply chain, the increased competition and customer demands make a company continue to improve the efficiency of its operational activities to reduce the costs. This requires a good coordination or integration in its supply chain. In an integrated inventory model, the total cost to be minimized is the combined total cost of several parties involved. Pan and Yang (2002) developed an integrated inventory model between one vendor and one buyer that considered the crashing lead time. Ouyang et al. (2004) developed Pan and Yang’s research by considering the stockout (fully backorder). Yang and Pan (2004) again developed an integrated inventory model between one vendor and one buyer that considered crashing lead time and the investment cost for quality improvement.

   Jha and Shanker (2009) developed an inventory model that integrates one vendor and one buyer. In the model, there is one additional decision variable that must be determined: the number or frequency of delivery from vendor to buyer in one production cycle. They assumed that the vendor uses a batch production system, while the buyer uses a continuous review policy or inventory system of method Q. Jha and Shanker (2013) further developed an inventory model that integrates one vendor and several buyers, considering the possibility of reducing lead times accompanied by the service level limits. However, this model has never been developed into a multi-product inventory model. Zhu and Xu (2012) developed the optimized design of a closed-loop supply chain on an uncertain environment where dynamic state of location, facility extension, and capacity improvement were considered. Vijayashree and Uthayakumar (2016) also developed a model of inventory with the possibility to reduce the lead time. The model did not consider the stockout costs and assumed that the cost of crashing lead time is approximated by an exponential function with the maximum value of LE and can be reduced to a minimum value of LS. By reducing the lead time, a company can reduce the amount of safety stock, reduce the possibility of stockouts, and increase the service levels. Then, they improved the model by considering three lead time crashing cost functions (2017). An integrated inventory model finds the optimal solutions of order quantity, lead time, total cost for the buyer, total cost for the vendor, and the total number of deliveries. These two papers present an integrated single vendor and single buyer inventory model to minimize the sum of the cost of ordering, setup, holding, and crashing by simultaneously optimizing the optimal order quantity, lead time, and number of deliveries. The main contribution of these two proposed models is to find and minimize the integrated total cost for the single vendor and single buyer. The study of a single vendor–buyer model with stochastic demand and transportation cost was also investigated by Ivan and Hui (2018). In this study, the transportation cost was a function of shipping weight, distance, and transportation modes. A heuristic model was developed to minimize the integrated total relevant cost, and the decision variables were the buyer’s order quantity and the vendor’s production quantity per cycle. They then considered defective items and error in inspection (2019). The results showed that lead-time can be shortened with smaller production lot sizes. Mofokeng and Chinomona (2019) found that partnership, collaboration, and integration can generally influence the performance of supply chain, particularly within the small and medium enterprise (SME). The research explained some general factors that affect the supply chain performance.

        No single study takes into full consideration the factors of one vendor, multi buyers, multi products, crashing lead-time, and stockout. In this study, the continuation of an integrated inventory model has been carried out by considering all these factors. The total inventory cost, as the supply chain performance and to be minimized in this model, is a combination of the vendor’s and the buyer’s total inventory costs.

The following are the conclusions of the study: (1) The equation of the total inventory cost between a vendor and many buyers and products, the existence of a stock out, and the possibility for buyers to reduce the lead time has been modeled; (2) The total order of all buyers that can minimize the total inventory cost between vendor and buyers has been derived; (3) Lead time that can minimize the total inventory cost between vendor and buyers by considering the possibility for buyers to reduce their lead time was derived; (4) The frequency of shipping in a production cycle that can minimize the total inventory cost between vendors and buyers has also been derived costly, and it does not affect the interior spaces. Also, this method can be applied to existing buildings which reduces the need for mechanical heating or cooling systems and associated costs. Last, considering the quality of materials and their associated infiltration rates, designers can draft intelligent façades to increase the energy efficiency of new and existing buildings by adapting the geometries to account for wind pressure and direction.

The authors would like to thank to Department of Industrial Engineering, Faculty of Industrial Technology - Universitas Katolik Parahyangan, Bandung for all supports. 

Ashari, H., Yusoff, Y.M., Zamani, S.N.M., Talib, A.N.A., 2018. A Study of the Effect of Market Orientation on Malaysian Automotive Industry Supply Chain Performance. International Journal of Technology, Volume 9(8), pp. 1651–1657

Ben-Daya, M., Raouf, A., 1994. Inventory Models Involving Lead Time as a Decision Variable. Journal of the Operational Research Society, Volume 45(5), pp. 579–582

Chang, C.T., Chang, S.C., 2001. On the Inventory Model with Variable Lead Time and Price-Quantity Discount. Journal of the Operational Research Society, Volume 52(10), pp. 1151–1158

Chen, K. K., Chang, C. T., 2007. A Seasonal Demand Inventory Model with Variable Lead Time and Resource Constraints. Applied Mathematical Modelling, Volume 31(11), pp. 2433–2445

Ivan, D.W., Hui, M.W., 2018. An Integrated Vendor Buyer Inventory Model with Transportation Cost and Stochastic Demand. International Journal of Systems Science: Operation & Logistics, Volume 5(4), pp. 295–309

Jha, J.K., Shanker, K., 2013. Single-Vendor Multi-Buyer Integrated Production-Inventory Model with Controllable Lead Time and Service Level Constraints. Applied Mathematical Modelling, Volume 37, pp. 1753–1767

Jha, J., Shanker, K., 2009. Two-echelon Supply Chain Inventory Model with Controllable Lead Time and Service Level Constraint. Computers & Industrial Engineering, Volume 57, pp. 1096–1104

Liao, C.J., Shyu, C.H., 1991. An Analytical Determination of Lead Time with Normal Demand. International Journal of Operations & Production Management, Volume 11(9), pp. 72–78

Miro, E.D., Martin, J.L., Lopez, L., Sescon, J., Oracion, C., Loanzon, J., 2018. A Supply Chain Profile of a School-based Feeding Program using the Centralized Kitchen Model. International Journal of Technology, Volume 9(7), pp. 1394–1404

Mofokeng, T.M., Chinomona, R., 2019. Supply Chain Partnership, Supply Chain Collaboration, and Supply Chain Integration as the Antecedents of Supply Chain Performance. South African Journal of Business Management, Volume 50(1), pp. 1–10

Moon, I., Choi, S., 1998. A Note on Lead Time and Distributional Assumptions in Continuous Review Inventory Models. Computers & Operations Research, Volume 92(11), pp. 1007–1012

Ouyang, L.Y., Wu, K.S., 2004. Integrated Vendor-Buyer Cooperative Models with Stochastic Demand in Controllable Lead Time. International Journal Production Economics, Volume 92, pp. 255–266

Ouyang, L.Y., Yeh, N.C., Wu, K.S., 1996. Mixture Inventory Model with Backorders and Lost Sales for Variable Lead Time. Journal of the Operational Research Society, Volume 47(6), pp. 829–832

Pan, J.C., Yang, J.S., 2002. A Study of Integrated Inventory with Controllable Lead Time. International Journal of Production Research, Volume 40(5), pp. 1263–1273

Riazi, S.R.M., Nawi, M.N.M., 2018. Project Delays in the Malaysian Public Sector: Causes, Pathogens and the Supply Chain Management Approach. International Journal of Technology, Volume 9(8), pp. 1668–1680

Tersine, R., 1994. Principles of Inventory and Materials Management. New Jersey: Prentice Hall, Inc.

Vijayashree, M., Uthayakumar, R., 2016. Inventory Models Involving Lead Time Crashing Cost as an Exponential Function. International Journal of Managing Value and Supply Chains, Volume 7(2), pp. 29–39

Yang, J.S., Pan, J.C., 2004. Just-in-time Purchasing: An Integrated Inventory Model Involving Deterministic Variable Lead Time and Quality Improvement Investment. International Journal of Production Research, Volume 42(5), pp. 853–863

Zhu, X.X., Xu, X., 2012. An Integrated Optimization Model of a Closed Loop Supply Chain under Uncertainty. Journal of System and Management Science, Volume 2(3), pp. 9–17