Computers Ops Res. Vol. 19, No. 6, pp. 495-504, 1992 0305-0548/92 $5.00 + 0.00 Printed in Great Britain. All rights reserved Copyright 0 1992 Pergamon Press Ltd zyxwvut AN EFFICIENT ALGORITHM FOR THE DYNAMIC ECONOMIC LOT SIZE PROBLEM-f B. GOLANY~, R. MAMAN& and M. YADIN~ Faculty of Industrial and Management Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel zyxwvutsrqponmlkjihgfedcbaZYXWVUTSR (Received May 1991; in revised form December 1991) Scope ad Purpose-The purpose of this paper is to introduce a simple decomposition technique which allows breaking up the problem of production quantities decision over a large number of (discrete) periods into a sequence of smaller problems, each dealing with a small set of consecutive periods. Thus, the computation burden involved in solving the original problem may be drastically reduced. Abstract-This paper addresses the question of production/procurement planning for finite horizon, deterministic, dynamic demand process, known as the “Dynamic Economic Lot size Problem”. A new algorithm is presented and compared to existing exact procedures. The algorithm first decomposes the problem into much smaller sequences (planning horizons). It then applies an exact method to schedule the production in each sequence (this stage is illustrated here with the “classical” dynamic programming algorithm of Zangwill [S]). Finally, it combines the partial solutions to an overall optimal solution. Computational results which demonstrate the effectiveness of the proposed algorithm are provided. 1. INTRODUCTION The Dynamic Economic Lot-Size Problem (DELSP) has been investigated extensively in the inventory literature during the last 30 years. The solution techniques offered for the DELSP include both exact and heuristic techniques. The former class are typically based on integer or dynamic programming models, see [2]. The two most famous techniques were given by Wagner and Within [7], and Zangwill [S], The heuristic techniques are usually myopic in nature, considering only partial information at any stage. A well-known algorithm in this class is the Silver and Meal algorithm [ 51. The drawback in the classical exact techniques is in their level of complexity, O(N’) for an N-period planning horizon. The heuristic algorithms overcome this problem by reducing the required computation but can only offer locally minimal solutions which may be significantly different from the optimal solutions in some cases. In this paper we develop a new exact algorithm which is characterized, in the average case, by a much smaller complexity than the classical algorithms. The algorithm is composed of three stages: Step zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 1. Step 2. Step 3. A decomposition stage: dividing the set of N periods into collectively exhaustive subsets of n n i, z, . zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK . . , n, periods where overlapping between the sets occur at their end periods. A combination stage: solving the sub-problems to optimality using known exact technique (e.g. a dynamic programming algorithm). A composition stage: deriving the optimal solution from the solutions of the sub-problems. t This research was partially supported by the Technion V.P.R. Fund-Y. Apter Research Fund. $ Boaz Golany is an assistant professor in the Industrial Engineering and Management department at The Technion-Israel Institute of Technology. His research areas are mainly in applications of Operations Research to Industrial Engineering, in particular, in efficiency evaluation, plant layout and production management. He holds a Ph.D. from the University of Texas in Austin and a B.Sc. from The Technion. 5 Rafi Maman is a researcher in the Koninklijke/Shell Laboratorium Amsterdam (Shell Research B.V.) in the department of Mathematics and System Engineering. He received his B.Sc. in Industrial Engineering and Management from the Technion in 1989. BMicha Yadin was the Gruenblat professor of Production Engineering in the faculty of Industrial Engineering and Management at The Technion. He received his B.Sc. (Mechanical Eng ), M.Sc. (Industrial Eng.) and Ph.D. (Operations Research) from The Technion. His research areas included Stochastic Modeling and Production and Operations Management. He was the Dean of the I.E. faculty and the President of the Israeli O.R. Society. Professor Yadin passed away in May 1991. 495