A simple approach to an integrated single-vendor single-buyer inventory system with shortage

Tsu-Pang Hsieha*Tsu-Pang Hsieh is an assistant professor in the Graduate School of Management Sciences at Aletheia University in Taiwan. He earned his PhD and MS degrees from the Graduate Institute of Management Sciences at Tamkang University, and a BS degree in Management Science from National Chiao Tung University. His research interest lies in the field of the analysis of inventory system. He has publications in The Engineering Economist, European Journal of Operational Research, Computers & Industrial Engineering and Journal of the Operational Research Society., Horng-Jinh ChangbcHorng-Jinh Chang is a professor of Asia University and Tamkang University in Taiwan. He received his PhD from the Graduate Institute of Management Sciences at Tamkang University. His research interests are in the fields of sampling theory, statistical theory and management sciences. He has publications in numerous journals and articles, including the Journal of the Operational Research Society, Operations Research Letters, Asia-Pacific Journal of Operational Research, European Journal of Operational Research, Journal of Applied Statistics, Metrika, Statistical Papers and Journal of Communications in Statistics: Theory and Methods., Ming-Wei WengcMing-Wei Weng is currently a PhD student at Tamkang University in Taiwan. He received his MS degree from the Graduate Institute of Man- agement Sciences at Tamkang University and a BS degree in Department of Industrial Engineering and Systems Management from Feng-Chia University. His research interest lies in the field of the analysis of inventory system, probability and statistics. & Chung-Yuan DyedChung-Yuan Dye is a professor in the Department of Business Management at Shu-Te University in Taiwan. His research interest lies in the field of the analysis of inventory system. He has publications in Omega, Operations Research Letters and Journal of the Operational Research Society. a Graduate School of Management Sciences, Aletheia University , Tamsui, Taipei, Taiwan, Republic of China b Asia University , Wufeng, Taichung, Taiwan, Republic of China c Graduate Institute of Management Sciences, Tamkang University , Tamsui, Taipei, Taiwan, Republic of China d Department of Business Management , Shu-Te University , Yen Chao, Kaohsiung, Taiwan, Republic of China * E-mail: tsupang@gmail.com In this article, a simple approach with two basic inequalities (Cauchy–Schwarz inequality and arithmetic–geometric mean inequality) is used to solve the integrated single-vendor single-buyer inventory problem developed by Wu and Ouyang (Wu, K.-S. and Ouyang, L.-Y., 2003. An integrated single-vendor single-buyer inventory system with shortage derived algebraically. Production Planning & Control, 14 (6), 555–561). Without the method of completing perfect square, the proposed approach yields the global minimum of the integrated total cost per year more easily than the algebraic approach used by Wu and Ouyang (2003). In addition, for people without the background of calculus, it is more useful to determine the buyer's economic order quantity and the vendor's optimal number of deliveries.