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Polynomial dynamic programming algorithms for lot sizing models with bounded inventory and stockout and/or backlogging

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Abstract

This paper addresses a dynamic lot sizing problem with bounded inventory and stockout where both no backlogging and backlogging allowed cases are considered. The stockout option means that there is outsourcing in a period only when the inventory level at that period is non-positive. The production capacity is unlimited and production cost functions are linear but with fixed charges. The problem is that of satisfying all demands in the planning horizon at minimal total cost. We show that the no backlogging case can be solved in ) O(T 2) time with general concave inventory holding and outsourcing cost functions where T is the length of the planning horizon. The complexity can be reduced to O(T) when the inventory holding cost functions are also linear and have some realistic properties, even if the outsourcing cost functions remain general concave functions. When the inventory holding and outsourcing cost functions are linear, the backlogging case can be solved in O(T 3logT) time whether the outsourcing level at each period is bounded by the sum of the demand of that period and backlogging level from previous periods, or only by the demand of that period.

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Correspondence to Jinhong Zhong.

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Jinhong Zhong is currently associated professor of information management and information system at the School of Management, Hefei University of Technology, China. He received his M.S. degree in control theory and control engineering and PhD. degree in computer science from Hefei University of Technology in 1998 and 2001, respectively. He has published 6 Chinese books as co-author, over 60 articles in Chinese, and 12 papers in English. He has led or participated in more than twenty research and industrial projects. He has received three awards of provincial and ministerial level. His research interests include the modeling, simulation and optimization of logistic and supply chain systems.

Feng Chu received the B.S. degree in electrical engineering from Hefei University of Technology, Hefei, China, in 1986; the M.S. degree in metrology, automatic control, and electrical engineering from National Polytechnic Institute of Lorraine, Lorraine, France, in 1991; and the Ph.D. degree in automatic control, computer science, and production management from the University of Metz, Metz, France, in 1995. She is currently a full professor with the Computing, Integrative Biology and Complex Systems Laboratory, University of Evry-Val d’Essonne, Evry, France. She is the author of more than 60 papers in international journals. She has led or participated in ten research and industrial projects. Her research interests include the modeling, analysis, and optimization of complex systems, such as intelligent transportation systems and logistic and production systems based on combinatorial optimization, operations research, and Petri nets.

Dr. Chu served as an associate editor for the IEEE Transactions on Systems, Man, and Cybernetics – Part C: Applications and Review from 2010-2013. She is currently serving as an associate editor for the IEEE Transactions on Intelligent Transportation Systems and has served on program committees for nearly 30 international conferences.

Chengbin Chu received the B.Sc. degree in electrical engineering from Hefei University of Technology, Hefei, China, in 1985 and the Ph.D. degree in computer science from Metz University, Metz, France, in 1990. He was with the National Research Institute in Computer Science and Automation (INRIA), France, from 1987 to 1996. He was a professor with the University of Technology of Troyes, France, from 1996 to 2008, where he was also the Founding Director of the Industrial Systems Optimization Laboratory. He is currently a Chair Professor of supply chain management at Ecole Centrale Paris, France. He is interested in research areas related to operations research and modeling, analysis, and optimization of supply chain and production systems. He is author or co-author of three books and more than 140 articles in international journals such as Operations Research, SIAM Journal of Computing, IEEE Transactions on Robotics and Automation, IEEE Transactions on Automation Science and Engineering, IEEE Transactions on Systems, Man and Cybernetics, Parts A and C, International Journal of Production Research, Naval Research Logistics, and so on. He has also published many papers in conference proceedings. For his research and application activities, he received the First Prize of Robert Faure Award in 1996. He also received the “1998 Best Transactions Paper Award” from the IEEE Robotics and Automation Society.

Dr. Chu was named “Chang Jiang Scholars Programme” Chair Professor by the Chinese Ministry of Education in 2005. He was an overseas visiting professor and overseas director of the Department of Industrial Engineering at Xi’an Jiaotong University from 2006 to 2010. He is currently a visiting Chair Professor at Tongji University, Shanghai, China. He served as an associate editor of the IEEE Transactions on Robotics and Automation from 2001 to 2004. He is currently a member of the editorial board of Computers & Engineering, and an associate editor of the IEEE Transactions on Automation Science and Engineering and the IEEE Transactions on Industrial Informatics.

Shanlin Yang received the Master degree in computer science from Hefei University of Technology, Hefei, China, in 1985. He is currently a professor of management science and engineering at Hefei University of Technology, Hefei, China. He is also a member of Chinese Academy of Engineering. He is recognized as one of the leading researchers in decision science and technology, management information systems, and project management. He has published 47 academic papers indexed by SCI in the last five years and received many rewards, including two times of the second prize of National Scientific and Technological Progress Award, six times of the first-class scientific and technological progress award of Anhui province, etc. Currently, his research interests include management information system, decision science, big data, and social network.

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Zhong, J., Chu, F., Chu, C. et al. Polynomial dynamic programming algorithms for lot sizing models with bounded inventory and stockout and/or backlogging. J. Syst. Sci. Syst. Eng. 25, 370–397 (2016). https://doi.org/10.1007/s11518-015-5277-x

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