An Arborescent Network Formulation and Dual Ascent Based Procedure for the Two-Stage Multi-Item Dynamic Demand Lotsize Problem

ABSTRACT Traditional approaches for modeling and solving dynamic demand lotsize problems are based on Zangwill's single‐source network and dynamic programming algorithms. In this paper, we propose an arborescent fixed‐charge network (ARBNET) programming model and dual ascent based branch‐and‐bo...

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Bibliographic Details
Published inDecision sciences Vol. 25; no. 1; pp. 103 - 121
Main Authors Gao, Li-Lian, Robinson Jr, E. Powell
Format Journal Article
LanguageEnglish
Published Oxford, UK Blackwell Publishing Ltd 01.01.1994
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Subject Areas: Inventory Management and Mathematical Programming
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Summary:ABSTRACT Traditional approaches for modeling and solving dynamic demand lotsize problems are based on Zangwill's single‐source network and dynamic programming algorithms. In this paper, we propose an arborescent fixed‐charge network (ARBNET) programming model and dual ascent based branch‐and‐bound procedure for the two‐stage multi‐item dynamic demand lotsize problem. Computational results show that the new approach is significantly more efficient than earlier solution strategies. The largest set of problems that could be solved using dynamic programming contained 4 end items and 12 time periods, and required 475.38 CPU seconds per problem. The dual ascent algorithms averaged .06 CPU seconds for this problem set, and problems with 30 end items and 24 time periods were solved in 85.65 CPU seconds. Similar results verify the superiority of the new approach for handling backlogged demand. An additional advantage of the algorithm is the availability of a feasible solution, with a known worst‐case optimality gap, throughout the problem‐solving process.
Bibliography:ArticleID:DECI103
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Li‐Lian Gao is Assistant Professor of Operations Management at the School of Business at Hofstra University. He received his Ph.D. from Indiana University in Bloomington. His publications include articles in Naval Research Logistics, Annals of the Society of Logistics Engineers, and Interfaces. He conducts research in the areas of distribution system design, distributed data networks, and inventory control. He is a member of the Decision Sciences Institute, The Institute of Management Sciences, and the Operations Research Society of America.
E. Powell Robinson, Jr., is Assistant Professor of Operations Management at the College of Business, Texas A & M University. He received his Ph.D. from the University of Texas at Austin, and was a member of the faculty at Indiana University prior to joining Texas A & M University. His primary research and consulting interests are in facility network strategy, systems acquisition, and multi‐echelon inventory control. He has published in Decision Sciences, Journal of Business Logistics, Naval Research Logistics, Physical Distribution & Logistics Management, and Interfaces. Dr. Robinson is a member of the Decision Sciences Institute, The Institute of Management Sciences, and the Operations Research ociety of America.
ISSN:0011-7315
1540-5915
DOI:10.1111/j.1540-5915.1994.tb00518.x