Applying The Cauchy Bunyakovsky Schwarz Inequality (CBS) and Arithmetic Geometric Mean (AGM) on The Model of Economic Order Quantity (EOQ) with Backorder

Muhammad Trynadi Zanuar, Muhammad Yusuf Fajar, Faridh A Badruzzaman


The ability of the company to ensure the production system or business activity runs smoothly determined by the inventory control. Too much inventory procurement will cause some major costs for the company, including maintenance cost, rental fees, etc. On the other hand, too little inventory procurement will cause major loss to companies, including the increasing message cost, cessation of production process due to raw materials shortage, which leads to potential loss of income, and loss of consumer confidence whom switch to other company. One of the steps taken to solve the problem on inventory system is developing a matematical model of Economic Order Quantity (EOQ) with backorder. The model is developed by applying Arithmetic Geometric Mean (AGM) and Cauchy-Bunyakovsky-Schwarz (CBS) to the basic EOQ model. The mathematical model for the total cost is . The model is then solved by applying AGM:      , and CBS: . From the model, we discovered the backorder  , optimal lot size  and the optimum total cost .


Economic Order Quantity, Backorder, Arithmetic Geometric Mean, Cauchy Bunyakovsky Schwarz


L. E. Cárdenas-Barrón, “An easy method to derive EOQ and EPQ inventory models with backordered,”

Computers and Mathematics with Applications, vol. 59, pp. 948-952, 2010.

Miller Steven j., “proofs of the Arithmetic Mean - Geometric Mean Inequality”., Eitan Sayag, and the students of Math 487 (Ohio State, Autumn 2003).

Wu Hui-Hua and Wu Shanhe. “Proofs of the Cauchy-Schwarz inequality” Department of Mathematics and Computer Science, Longyan University, Longyan, Fujian 364012, P. R. China.

Heizer j and Render B. 2015 .Manajemen keberlangsungan dan rantai pasokan. Diterjemahkan oleh: Ariyato, Kresnohadi. Jakarta. Salemba Empat.

Ristono A. 2009. Manajemen Persediaan. Yogyakarta. Graha Ilmu

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