Using simple methods to derive EOQ and EPQ models with shortage and imperfect quality

Abstract

Huang [ Journal of Statistics and Management Systems, Vol. 6 (2003), No. 2, pp. 171– 180 ] studied the EOQ (Economic Order Quantity) and EPQ (Economic Production Quantity) models with backlogging and defective items using the algebraic approach. He assumed 100% inspection policy and the known proportion of defective items was removed prior to storage or use after the screening process. In this paper, we will off er both basic inequalities, arithmetic-geometric mean inequality (AGM) and Cauchy-Bunyakovsky-Schwarz inequality (CBS), to derive both the optimal lot size and backorder level under the total relevant cost per unit time minimized. Without the method of completing perfect square, the proposed methods derive the global minimum of the total relevant cost per unit time more easily than the algebraic approach used by Huang (2003)

Keywords:

• Arithmetic-geometric mean inequality
• Cauchy-Bunyakovsky-Schwarz inequality
• EOQ
• EPQ
• Shortage
• Defective item