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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Vydáno v:Operations research Ročník 41; číslo 3; s. 549 - 571
Hlavní autoři: Aggarwal, Alok, Park, James K
Médium: Journal Article
Jazyk:angličtina
Vydáno: Linthicum, MD INFORMS 01.05.1993
Operations Research Society of America
Institute for Operations Research and the Management Sciences
Témata:
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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Popis
Shrnutí: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.
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ISSN:0030-364X
1526-5463
DOI:10.1287/opre.41.3.549