Improved Algorithms for Economic Lot Size Problems

Many problems in inventory control, production planning, and capacity planning can be formulated in terms of a simple economic lot size model proposed independently by A. S. Manne (1958) and by H. M. Wagner and T. M. Whitin (1958). The Manne-Wagner-Whitin model and its variants have been studied wid...

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Published in:	Operations research Vol. 41; no. 3; pp. 549 - 571
Main Authors:	Aggarwal, Alok, Park, James K
Format:	Journal Article
Language:	English
Published:	Linthicum, MD INFORMS 01.05.1993 Operations Research Society of America Institute for Operations Research and the Management Sciences
Subjects:	Algorithms analysis of algorithms: optimal and suboptimal algorithms Applied sciences Capital costs Commercial production computers/computer science: faster lot sizing using Monge arrays Cost functions Cost structure Dynamic programming Economic costs Economic models Exact sciences and technology Inventories Inventory control Inventory control, production control. Distribution inventory/production: faster algorithms for various Wagner-Whitin models Mathematical analysis Mathematical minima Operational research and scientific management Operational research. Management science Operations research Production costs Production planning Inventory control Lot sizing Dynamic programming Fast algorithm Time complexity Production control
ISSN:	0030-364X, 1526-5463
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Abstract	Many problems in inventory control, production planning, and capacity planning can be formulated in terms of a simple economic lot size model proposed independently by A. S. Manne (1958) and by H. M. Wagner and T. M. Whitin (1958). The Manne-Wagner-Whitin model and its variants have been studied widely in the operations research and management science communities, and a large number of algorithms have been proposed for solving various problems expressed in terms of this model, most of which assume concave costs and rely on dynamic programming. In this paper, we show that for many of these concave cost economic lot size problems, the dynamic programming formulation of the problem gives rise to a special kind of array, called a Monge array. We then show how the structure of Monge arrays can be exploited to obtain significantly faster algorithms for these economic lot size problems. We focus on uncapacitated problems, i.e., problems without bounds on production, inventory, or backlogging; capacitated problems are considered in a separate paper.
AbstractList	Many problems in inventory control, production planning, and capacity planning can be formulated in terms of a simple economic lot size model proposed independently by A. S. Manne (1958) and by H. M. Wagner and T. M. Whitin (1958). The Manne-Wagner-Whitin model and its variants have been studied widely in the operations research and management science communities, and a large number of algorithms have been proposed for solving various problems expressed in terms of this model, most of which assume concave costs and rely on dynamic programming. In this paper, we show that for many of these concave cost economic lot size problems, the dynamic programming formulation of the problem gives rise to a special kind of array, called a Monge array. We then show how the structure of Monge arrays can be exploited to obtain significantly faster algorithms for these economic lot size problems. We focus on uncapacitated problems, i.e., problems without bounds on production, inventory, or backlogging; capacitated problems are considered in a separate paper. Many problems in inventory control, production planning, and capacity planning can be formulated in terms of a simple economic lot size model proposed independently by A.S. Manne (1858) and by H.M. Wagner and T.M. Whitin (1958). The Manne-Wagner-Whitin model and its variants have been studied widely in the operations research and management science communities, and a large number of algorithms have been proposed for solving various problems expressed in terms of this model, most of which assume concave costs and rely on dynamic programming. It is shown that for many of these concave cost economic lot size problems, the dynamic programming formulation of the problem gives rise to a special kind of array, called a Monge array. It is then shown how the structure of Monge arrays can be exploited to obtain significantly faster algorithms for these economic lot size problems. The focus is on uncapacitated problems - problems without bounds on productivity, inventory, or backlogging.
Author	Aggarwal, Alok Park, James K
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Copyright	Copyright 1993 The Operations Research Society of America 1993 INIST-CNRS Copyright Institute for Operations Research and the Management Sciences May/Jun 1993
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Snippet	Many problems in inventory control, production planning, and capacity planning can be formulated in terms of a simple economic lot size model proposed...
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SubjectTerms	Algorithms analysis of algorithms: optimal and suboptimal algorithms Applied sciences Capital costs Commercial production computers/computer science: faster lot sizing using Monge arrays Cost functions Cost structure Dynamic programming Economic costs Economic models Exact sciences and technology Inventories Inventory control Inventory control, production control. Distribution inventory/production: faster algorithms for various Wagner-Whitin models Mathematical analysis Mathematical minima Operational research and scientific management Operational research. Management science Operations research Production costs Production planning
Title	Improved Algorithms for Economic Lot Size Problems
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