Model EPQ Multi Item yang Dimodifikasi untuk Dua Permintaan secara Simultan

Main Article Content

Taufiq Rahman
Jonrinaldi Jonrinaldi

Henmaidi Henmaidi



Inventory is one of many factors of the business operation that need to be controlled by industries in order to improve efficiency, enhance productivity, and decrease the holding cost. The holding cost of inventories in supply chain contribute to 20% - 40% of the product value. It can be controlled by applying appropriate inventory model, such as EPQ/Economic Production Quantity and EOQ/Economic Order Quantity. EPQ is an inventory model that used to determine the optimum production lot size with balanced the production setup cost and holding cost. Even the classic EPQ has applied widely in industries, the assumption used by this model differed between the researchers whether it is continuous or discrete demand, because the multi delivery or discrete demand is mostly used by industries. Even so, there are industries that used both continuous and discrete demand simultaneously. Based on previous research, there was an advanced EPQ model that synchronizing both assumptions simultaneously, but it still addressed single item problem. Since almost the industries produced multi item, this model has lack of applicability. Therefore, this research proposed a multi item EPQ Model that synchronizing continuous and discrete demand simultaneously. The solution procedure that used in this proposed model are classical calculus method/differential calculus and simultaneous approach. A numerical example is given to show the effectiveness of the proposed approach based on the data from the literature.


Download data is not yet available.


[1]       R.H. Ballou. Business Logistics Management: Planning, Organizing, and Controlling the Supply Chain. (Ed. 4). New Jersey: Prentice Hall, 1998.

[2]       D. Waters. Inventory Control and Management. London: John Wiley & Sons Ltd., 2003.

[3]       J. Garcia-Laguna, L.A. San-Jose, L.E. Cardenas-Barron, dan J. Sicilia. The Integrality of The Lot Size in The basic EOQ and EPQ Models: Applications to Other Production-Inventory Models. Applied Mathematics and Computation, 216, pp 1660-72, 2010.

[4]       A.A. Taleizadeh, S.S. Kalantari, dan L.E. Cardenas-Barron. Determining Optimal Price, Replenishment Lot Size and Number of Shipments for an EPQ Model with Rework and Multiple Shipments. Journal of Industrial and Management Optimization, 11 (4), pp 1059-71, 2015.

[5]       Y.S.P. Chiu, S.W. Chiu, C.Y. Li, dan C.K. Ting. Incorporating Multi-Delivery Policy and Quality Assurance into Economic Production Lot Size Problem. Journal of Scientific and Industrial Research, 68, pp 505-12, 2009.

[6]       K.K. Chen dan S.W. Chiu. Replenishment Lot Size and Number of Shipments for Model Derived without Derivates. Mathematichal and Computational Applications, 16 (3), pp 753-60, 2011.

[7]       L.E. Cardenas-Barron, G. Trevino-Garza, A. Widyadana, dan H.M. Wee. A Constrained Multi-Products EPQ Inventory Model with Discrete Delivery Order and Lot Size. Applied Mathematics and Computation, 230, pp 359-70, 2014.

[8]       Y.S.P. Chiu, M.F. Wu, S.W. Chiu, dan H.H. Chang. A Simplified Approach to The Multi-Item Economic Production Quantity Model with Scrap, Rework, and Multi-Delivery. Journal of Applied Research and Technology, 13, pp 472-76, 2015.

[9]       N. Oktavia, Henmaidi, dan Jonrinaldi. Pengembangan Model Economic Production Quantity (EPQ) dengan Sinkronisasi Demand Kontinu dan Diskrit secara Simlutan. Jurnal Optimasi Sistem Industri, 15 (1), pp 78-86, 2016.

[10]    B. Pal, S.S. Sana, dan K. Chaudhuri. A Mathematical Model on EPQ for Stochastic Demand in An Imperfect Production System. Journal of Manufacturing System, 32, pp 260-70, 2013.

[11]    R.J. Tersine. Principles of Inventory and Materials Management. (Ed. 4). New Jersey: Prentice Hall, 1994.

[12]    S.H.R. Pasandideh dan S.T.A. Niaki. A Genetic Algorithm Approach to Optimize A Multi Products EPQ Model with Discrete Delivery Orders and Constrained Space. Applied Mathematical and Computation, 195, pp 506-14, 2008.

[13]    K.N.F. Leung. A Generalized Geometric-Programming Solution to “An Economic Production Quantity Model with Flexibility and Reliability Considerations”. European Journal of Operational Research, 176, pp 240-51, 2007.

[14]    B. Sarkar, L.E. Cardenas-Barron, M. Sarkar, dan M.L. Singgih. An Economic Production Quantity Model with Random Defective Rate, Rework Process and Backorders for Single Stage Production System. Journal of Manufacturing Systems, 33, pp 423-35, 2014.

[15]    P.T. Chang dan C.H. Chang. An Elaborative Unit Cost Structure-Based Fuzzy Economic Production Quantity Model. Mathematical and Computer Modelling, 43, pp 1337-56, 2006.

[16]    H.G. Daellenbach. Systems and Decision Making: A Management Sciance Approach. England:  John Wiley & Sons Ltd., 1995.

[17]    H.G. Daellenbach dan D.C. McNickle. Management Science: Decision Making Through Systems Thinking. Hampshire: Palgrave Macmillan, 2005.