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## An Evolutionary Computation Approach to the Economic Lot Scheduling Problem (1996)

Citations: | 1 - 0 self |

### Citations

10040 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
Citation Context ...rial optimization. Genetic Algorithms (GA) are a class of machine-learning techniques that are so named due to their resemblance to natural evolution. They were pioneered by Holland [18] and Goldberg =-=[19]-=-, and have been applied to combinatorial problems by various authors (e.g., Biegel and Davern [20], Muhlenbein et al. [21]). These iterative solution techniques maintain a population of candidate solu... |

378 |
Modern Heuristic Techniques for Combinatorial Problems
- Reeves
- 1993
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Citation Context ...function. In SA, if a solution increases the cost function it is still accepted, but with a probability that is inversely related to the magnitude of the cost increase. A recent book edited by Reeves =-=[23]-=- is a very good reference for various applications of modern heuristic techniques such as the two mentioned above to combinatorial optimization 13 problems. The algorithm described in this paper is ba... |

163 |
Optimization by simulated annealing
- Vecchi
- 1983
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Citation Context ...Simulated Annealing (SA) is another stochastic search technique, that is derived from statistical mechanics, and is used to search for global minima in large optimization problems. Kirkpatrick et al. =-=[22]-=- were the first to introduce this technique and apply it to combinatorial optimization problems, primarily in response to the problems of applying traditional hill-climbing methods to global optimizat... |

98 |
O.: Evolution algorithms in combinatorial optimization
- Mühlenbein, Gorges-Schleuter, et al.
- 1988
(Show Context)
Citation Context ...blance to natural evolution. They were pioneered by Holland [18] and Goldberg [19], and have been applied to combinatorial problems by various authors (e.g., Biegel and Davern [20], Muhlenbein et al. =-=[21]-=-). These iterative solution techniques maintain a population of candidate solutions, and at each iteration improvements are made by using information from good solutions in the current candidate popul... |

40 |
The economic lot scheduling problem (ELSP): Review and extensions
- Elmaghraby
- 1978
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Citation Context ...rovide an exhaustive coverage of the literature; rather, we choose to briefly describe some of the better known heuristics in order to form a basis for comparison with the proposed method. Elmaghraby =-=[2]-=- was the first to provide a comprehensive overview of the heuristics for the ELSP that existed at that time; a more recent paper by Lopez and Kingsman [3] provides an overview and discusses later deve... |

21 |
A Dynamic Programming Approach to a Lot Size Scheduling Problem
- Bomberger
- 1966
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Citation Context ...any of the heuristics is to impose a condition that ensures the existence of a feasible schedule, and to then optimize individual cycle times. In the original Basic Period (BP) algorithm of Bomberger =-=[6]-=-, feasibility is ensured by choosing the basic period W such that it is long enough to accommodate the production of all items. This leads to a dynamic programming formulation where the item multiplie... |

19 |
On the General Feasibility Test of scheduling Lot Size for several Products on One Machine; Management science 29; 93-105. www.SID.ir Ar chi ve
- Hsu
- 1983
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Citation Context ...mechanisms for providing a final solution that is feasible, and all of these have their drawbacks. Checking for feasibility is a major problem when developing any solution technique for the ELSP. Hsu =-=[16]-=- has shown that the problem of finding a feasible schedule for the ELSP, or even proving that none exists, is NP-complete. Vemuganti [17] has shown that for the two product case, feasibility may be de... |

15 |
Genetic algorithms and job shop scheduling
- Biegal, Davern
- 1990
(Show Context)
Citation Context ...named due to their resemblance to natural evolution. They were pioneered by Holland [18] and Goldberg [19], and have been applied to combinatorial problems by various authors (e.g., Biegel and Davern =-=[20]-=-, Muhlenbein et al. [21]). These iterative solution techniques maintain a population of candidate solutions, and at each iteration improvements are made by using information from good solutions in the... |

9 |
An Iterative Procedure for the Single-Machine, MultiProduct Lot Scheduling Problem
- Doll, Whybark
- 1973
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Citation Context ...Madigan's solution can be significantly improved by computing the optimum duration of W once the multiplier vector n is known. A more efficient procedure for the ELSP is suggested by Doll and Whybark =-=[9]-=- (D&W) who use an iterative procedure to simultaneously determine item multipliers n and the basic period W. The starting solution is based on the independent solution, and the procedure iterates unti... |

8 |
An Improved Extended Basic Period Procedure for Solving the Economic Lot Scheduling Problem
- Haessler
- 1979
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Citation Context ...inal solution without resorting to any ad hoc steps. The earliest and best known of these is based on the extended basic period of Elmaghraby, and was proposed in Haessler and Hogue [12] and Haessler =-=[13]-=- (HAE). It is an iterative algorithm that successively determines n and W values until they converge, similar to the D&W algorithm. However, Haessler explicitly provides a method of testing the feasib... |

6 |
The economic lot scheduling problem: theory and practice
- Lopez, Kingsmans
- 1991
(Show Context)
Citation Context ...mparison with the proposed method. Elmaghraby [2] was the first to provide a comprehensive overview of the heuristics for the ELSP that existed at that time; a more recent paper by Lopez and Kingsman =-=[3]-=- provides an overview and discusses later developments. As pointed out in these papers, the heuristics that have been proposed for this problem cluster around two approaches: the ones that assume a ba... |

6 |
Lot sizing and sequencing for n products on one facility
- Delporte, Thomas
- 1978
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Citation Context ...is problem cluster around two approaches: the ones that assume a basic period W and represent the cycle times of all items as multiples of this W, and those which reject the concept of a basic period =-=[4,5]-=-. This study follows the first approach. A tactic commonly followed by many of the heuristics is to impose a condition that ensures the existence of a feasible schedule, and to then optimize individua... |

4 |
The Application of Marginal Analysis to the Economic Lot Scheduling Problem
- Fujita
- 1978
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Citation Context ...e problems Bom2, Bom3 and Bom4 respectively. Problem Bom4 in particular has been extensively used as a benchmark problem in the literature. Next, we consider the six test problems presented by Fujita =-=[26]-=-. Fujita's first example is actually Bomberger's original problem which we have already included here as Bom1. Fujita's problems are denoted as Fuj2, Fuj3, Fuj4, Fuj5 and Fuj6. It should be noted that... |

3 |
A Note on Bomberger's Approach to Lot Size Scheduling
- Stankard, Gupta
- 1969
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Citation Context ...ping the solution. While this approach could be generalized to loading more than two consecutive basic periods, the increase in modeling and computational complexity rule this out. Stankard and Gupta =-=[7]-=- (S&G) devised a heuristic where they group items based on their cycle times. They present a necessary and sufficient feasibility condition which is less restrictive than that of Bomberger and yields ... |

3 |
A note on the single-machine multi-product lot scheduling problem, Manage Sci 22
- Haessler, Hogue
- 1976
(Show Context)
Citation Context ...asibility of the final solution without resorting to any ad hoc steps. The earliest and best known of these is based on the extended basic period of Elmaghraby, and was proposed in Haessler and Hogue =-=[12]-=- and Haessler [13] (HAE). It is an iterative algorithm that successively determines n and W values until they converge, similar to the D&W algorithm. However, Haessler explicitly provides a method of ... |

2 |
Two Heuristics for the Economic Lot Scheduling Problem: An Experimental Study
- Geng, Vickson
- 1988
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Citation Context ... is fixed during the course of the search for feasibility, so that the feasible solution obtained may not be a good solution anymore. A more recent and simpler algorithm suggested by Geng and Vickson =-=[14]-=- (G&V) is very similar to Haessler's algorithm in the way it restores feasibility, although it is also more likely to have higher costs. This method has drawbacks that are similar to those of HAE. Las... |

1 |
A Computational Approach to the Lot Scheduling Problem
- Rogers
- 1958
(Show Context)
Citation Context ...is problem cluster around two approaches: the ones that assume a basic period W and represent the cycle times of all items as multiples of this W, and those which reject the concept of a basic period =-=[4,5]-=-. This study follows the first approach. A tactic commonly followed by many of the heuristics is to impose a condition that ensures the existence of a feasible schedule, and to then optimize individua... |

1 |
Scheduling a Multi-Product Single-Machine System for an Infinite Planning Period
- Madigan
- 1968
(Show Context)
Citation Context ...er of possible groupings could in general, be very large. An alternative to requiring feasibility at the start is to try and attain feasibility when a desirable solution becomes infeasible. Madigan's =-=[8]-=- approach (MDG) is based on the independent solution and the common cycle approach. It starts with the CC solution and modifies the item multipliers so as to minimize the deviations of the costs of in... |

1 |
Scheduling a Multi-Product Single-Machine System
- Goyal
- 1973
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Citation Context ...any algorithmic procedure for this. Furthermore, if one develops a heuristic procedure to restore feasibility and links it to this method, it is possible that convergence may never be achieved. Goyal =-=[10]-=-,[11] (GOY) developed 7 a very similar iterative procedure with a slight difference in how the item multipliers are determined. The same drawbacks of D&W also apply to Goyal's procedure. Finally, we c... |

1 |
The Economic Lot-Scheduling Problem: A Simple Approach
- Larraneta, Onieva
- 1988
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Citation Context ...n the way it restores feasibility, although it is also more likely to have higher costs. This method has drawbacks that are similar to those of HAE. Lastly, we have the method of Larraneta and Onieva =-=[15]-=- (L&O) which presupposes that a reference subset of the products with relatively small independent cycle times have multipliers of one, while the frequencies of the others are related to their cycle t... |

1 |
On the Feasibility of Scheduling Lot Sizes for Two Products on One Machine
- Vemuganti
- 1978
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Citation Context ...oblem when developing any solution technique for the ELSP. Hsu [16] has shown that the problem of finding a feasible schedule for the ELSP, or even proving that none exists, is NP-complete. Vemuganti =-=[17]-=- has shown that for the two product case, feasibility may be determined through a fairly simple necessary and sufficient condition. However, this is mostly of theoretical interest since it does not ap... |

1 |
A Local Expansion Search Heuristic with an Application to an Assembly System
- Tunasar, Rajgopal
(Show Context)
Citation Context ... the quality of the solution as well as the solution time. This particular technique has also been applied successfully by the authors to other areas, such as lotsizing in multistage assembly systems =-=[24]-=-. The algorithm (LES) is an iterative search technique and similar to GA, the search proceeds with an evolving population of solutions. The evolutionary mechanism employs information from the current ... |

1 |
A Note on Scheduling a Multi-Product Single-Machine System for an Infinite Planning Period
- Haessler
- 1971
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Citation Context ... integer vectors. The vector n is sufficient to represent a solution since the duration of the basic period W that is optimum for a given vector n can be determined from the following equation (e.g., =-=[25]) ( ) W -=-A n h r b n i i i i i i i i = - �� �� ( ) ( ) 1 2 . (9) The individual item cycle times can then be computed as T i =n i W. Unfortunately, this solution is not necessarily feasible for any n. ... |