Reducing inventory costs is among the essential strategies for survival and profitability in today’s competitive environment. Classical inventory models have been developed to minimize inventory costs. However, they have several limiting assumptions. In this study, a three-level logistic chain consisting of a manufacturer, a distributor, and a retailer is considered. The problem of optimizing the inventory model for the distributor is examined. The distributor orders the products from the manufacturer. However, the manufacturer does not simultaneously deliver the total order and sends them in several discrete instances. In other words, it employs the multi-delivery strategy. Furthermore, the retailer’s demand is discrete and equal to a fixed amount at each equal interval of time. The distributor aims to determine the optimal order quantity and the optimal plan of receiving orders to minimize the total costs. Finally, the proposed problem is analyzed in a numerical example, and the results are compared with the classical inventory model. The results show that the proposed model has better performance with increasing holding and fixed ordering costs.
Arrow, K.J., T. Harris, & Marschak, J. (1951). Optimal inventory policy. Econometrica: Journal of the Econometric Society,19(3), 250-272.
Cárdenas-Barrón, L.E., Treviño-Garza, G., & Wee, H.M. (2012).A simple and better algorithm to solve the vendor managed inventory control system of multi-product multi-constraint economic order quantity model. Expert Systems with Applications, 39(3), 3888-3895.
Cheng, Y., Wang, W., Wei, C., & Lee, K. (2018). An integrated lot-sizing model for imperfect production with multiple disposals of defective items. Scientia Iranica. Transaction E, Industrial Engineering, 25(2), 852-867.
Fallahi, A., Azimi-Dastgerdi, M., & Mokhtari, H. (2021). A Sustainable Production-Inventory Model Joint with Preventive Maintenance and Multiple Shipments for Imperfect Quality Items. Scientia Iranica,Articles in Press.
García-Laguna, J., San-José, L.A., Cárdenas-Barrón, L.E., & Sicilia, J. (2010).The integrality of the lot size in the basic EOQ and EPQ models: applications to other production-inventory models. Applied Mathematics and Computation, 216(5), 1660-1672.
Harris, F.W. (1990). How many parts to make at once. Operations research. 38(6), 947-950.
Hasanpour, J., Hasani, A., & Ghodoosi, M. (2018). Delayed Payment Policy in the Inventory Model of Deteriorating Goods with Quadratic Demand in Order to Backlogging Shortage. Journal of Industrial Management Perspective, 7(4) 199-230. (In Persian)
Kalantari, S.S., & Taleizadeh, A.A. (2020). Mathematical modelling for determining the replenishment policy for deteriorating items in an EPQ model with multiple shipments. International Journal of Systems Science: Operations & Logistics, 7(2), 164-171.
Karthick, B., & Uthayakumar, R. (2021). A Multi-Item Sustainable Manufacturing Model with Discrete Setup Cost and Carbon Emission Reduction Under Deterministic and Trapezoidal Fuzzy Demand. Process Integration and Optimization for Sustainability, 16(5), 505–543..
Lagodimos, A., Skouri K., Christou, I., & Chountalas, P. (2018). The discrete-time EOQ model: Solution and implications. European Journal of Operational Research, 266(1), 112-121.
Ouyang, L.-Y., Wu, K.-S., & Ho, C.-H. (2004). Integrated vendor–buyer cooperative models with stochastic demand in controllable lead time. International Journal of Production Economics, 92(3), 255-266.
Pasandideh, S.H.R., & Niaki, S.T.A. (2008). A genetic algorithm approach to optimize a multi-products EPQ model with discrete delivery orders and constrained space. Applied Mathematics and Computation, 195(2), 506-514.
Pasandideh, S.H.R., Niaki, S.T.A., & Nia, A.R. (2011). A genetic algorithm for vendor managed inventory control system of multi-product multi-constraint economic order quantity model. Expert Systems with Applications, 38(3), 2708-2716.
Pasandideh, S.H.R., Niaki, S.T.A., & Yeganeh, J.A. (2010). A parameter-tuned genetic algorithm for multi-product economic production quantity model with space constraint, discrete delivery orders and shortages. Advances in Engineering Software, 41(2), 306-314.
Priyan, S. & Uthayakumar, R. (2017). Setup cost reduction EMQ inventory system with probabilistic defective and rework in multiple shipments management. International Journal of System Assurance Engineering and Management, 8(2), 223-241.
Radfar, A., & Mohammaditabar, D. (2019). Bi-Objective Optimization of Vendor Managed Inventory Problem in a Mult Echelon Green Supply Chain. Journal of Industrial Management Perspective, 9(3), 109-134 (In Persian).
Rahman, T., Wirdianto, E., & Zhang. D. (2018). A Multiple Items EPQ/EOQ Model for a Vendor and Multiple Buyers System with Considering Continuous and Discrete Demand Simultaneously. in IOP Conference Series: Materials Science and Engineering. IOP Publishing.
Sadeghi, H. (2019). A forecasting system by considering product reliability, POQ policy, and periodic demand. Journal of Quality Engineering and Production Optimization, 4(2) 133-148.
Sadeghi, H., Golpîra, H., & Khan, S.A.R. (2021). Optimal integrated production-inventory system considering shortages and discrete delivery orders. Computers & Industrial Engineering, 156,
Sadeghi, H., Makui, A., & Heydari, M. (2016). Multilevel production systems with dependent demand with uncertainty of lead times. Mathematical Problems in Engineering,(2016), 1-12.
Sadeghi, H., Makui, A., Heydari, M., & Ghapanchi A.H., (2015). Proposing a model for optimising planned lead-times and periodicity in MRP systems under uncertainty. International Journal of Services and Operations Management, 21(3), 310-331.
Sajadi, S., Arianezhad, M.G., & Sadeghi, H.A. (2009). An Improved WAGNER-WHITIN Algorithm. International Journal of Industrial Engineering & Production Research, 20(3), 117-123.
Sarkar, B. (2013). A production-inventory model with probabilistic deterioration in two-echelon supply chain management. Applied Mathematical Modelling, 37(5), 3138-3151.
Taft, E. (1918). The most economical production lot. Iron Age, 101(18), 1410-1412.
Taheri, S.A., Mokhtari, H., & Fallahi, A. (2021). An imperfect economic production quantity model with probabilistic machine breakdown and multiple shipments policy. Journal of Industrial Management Perspective, In press. ( In Persian).
Taleizadeh, A.A., Kalantari, S.S., & Cárdenas-Barrón, L.E. (2015). Determining optimal price, replenishment lot size and number of shipments for an EPQ model with rework and multiple shipments. Journal of Industrial & Management Optimization, 11(4), 1059-1071
Widyadanaa, G.A., & Wee, H.M. (2009). A multi-product EPQ model with discrete delivery order: A Langrangean solution approach, in Global perspective for competitive enterprise, economy and ecology. Springer. 601-608.
Sadeghi, H., Mahmoodi, A., & Rajabi, Z. (2022). Economic Order Quantity with Discrete Demand and Delivery Orders. Journal of Industrial Management Perspective, 12(2), 113-133. doi: 10.52547/jimp.12.2.113
MLA
Heibatolah Sadeghi; Anwar Mahmoodi; Zahra Rajabi. "Economic Order Quantity with Discrete Demand and Delivery Orders". Journal of Industrial Management Perspective, 12, 2, 2022, 113-133. doi: 10.52547/jimp.12.2.113
HARVARD
Sadeghi, H., Mahmoodi, A., Rajabi, Z. (2022). 'Economic Order Quantity with Discrete Demand and Delivery Orders', Journal of Industrial Management Perspective, 12(2), pp. 113-133. doi: 10.52547/jimp.12.2.113
VANCOUVER
Sadeghi, H., Mahmoodi, A., Rajabi, Z. Economic Order Quantity with Discrete Demand and Delivery Orders. Journal of Industrial Management Perspective, 2022; 12(2): 113-133. doi: 10.52547/jimp.12.2.113