## Theory and Methodology (1998)

### BibTeX

@MISC{Akturk98theoryand,

author = {M. Selim Akturk and Deniz Ozdemir},

title = {Theory and Methodology},

year = {1998}

}

### OpenURL

### Abstract

A new dominance rule to minimize total weighted tardiness with unequal release dates

### Citations

518 | Greedy randomized adaptive search procedures
- Feo, Resende
- 1995
(Show Context)
Citation Context ...et of problems. We now demonstrate how the proposed dominance rule can be implemented in a local search algorithm, namely on the greedy randomized adaptive search procedure �GRASP) by Feo and Resende =-=[11]-=- and the problem space genetic algorithm �PSGA) by Storer et al. [22]. The GRASP is an iterative process that provides a solution to the problem at the end of each iteration and the ®nal solution is t... |

77 |
Heuristic Scheduling Systems with Applications to Production Systems and Project Management
- Morton, Pentico
- 1993
(Show Context)
Citation Context ...job priorities do not change over time while priorities might change over time for the dynamic dispatching rules. A more detailed discussion on heuristic approaches can be found in Morton and Pentico =-=[16]-=-. Table 1 A set of competing algorithms Rule De®nition Rank and priority index MODD Earliest modi®ed due date minfmaxfdj; t ‡ pjgg ATC Apparent tardiness cost max pj ˆ wj X-RM X-dispatch ATC max pj 1 ... |

67 |
New search spaces for sequencing problems with application to job shop scheduling
- Storer, Wu, et al.
- 1992
(Show Context)
Citation Context ...n be implemented in a local search algorithm, namely on the greedy randomized adaptive search procedure �GRASP) by Feo and Resende [11] and the problem space genetic algorithm �PSGA) by Storer et al. =-=[22]-=-. The GRASP is an iterative process that provides a solution to the problem at the end of each iteration and the ®nal solution is the best one that is obtained during the search as discussed in [11]. ... |

49 |
A “pseudopolynomial” algorithm for sequencing jobs to minimize total tardiness
- Lawler
- 1977
(Show Context)
Citation Context ... wi > wj or di ˆ dj and pi ˆ pj and wi ˆ wj then ri 6 rj for all i and j such that i < j. Rinnooy Kan [20] shows that total tardiness problem with unequal release dates, 1jrjj P Tj is NP-hard. Lawler =-=[15]-=- shows that the total weighted tardiness problem, 1j j P wjTj, is strongly NP-hard, hence unequal release dates problem, 1jrjj P wjTj, is also strongly NP-hard because at least two of its sub problems... |

41 |
Priority rules for job shops with weighted tardiness costs
- Vepsalainen, Morton
- 1987
(Show Context)
Citation Context ...ing index is then selected to be processed next. The ranking index is a function of the time t at which the machine became free as well as pj, wj, and dj of the remaining jobs. Vepsalainen and Morton =-=[25]-=- have shown that the ATC rule is superior to other sequencing heuristics for the 1jj P wjTj problem. It trades o€ job's urgency �slack) against machine utilization, but due to the more complex weighte... |

20 |
Algorithms for scheduling a single machine to minimize the weighted number of late jobs
- Potts, Wassenhove
- 1988
(Show Context)
Citation Context ...ithms to minimize total ¯ow time, 1jrjj P Fj, whereas Bianco and Ricciardelli [3] and Hariri and Potts [12] consider the total weighted completion time problem, 1jrjj P wjCj. Potts and Van Wassenhove =-=[18]-=- propose a B&B algorithm to minimize the weighted number of late jobs. Erschler et al. [10] establish a dominance relationship within the set of possible sequences for 1 j rj problem independent of th... |

17 |
An algorithm for single machine sequencing with release times to minimize total weighted completion time
- Hariri, Potts
- 1983
(Show Context)
Citation Context ... other optimality criteria. Chu [5] and Dessouky and Deogun [8] give branch and bound �B&B) algorithms to minimize total ¯ow time, 1jrjj P Fj, whereas Bianco and Ricciardelli [3] and Hariri and Potts =-=[12]-=- consider the total weighted completion time problem, 1jrjj P wjCj. Potts and Van Wassenhove [18] propose a B&B algorithm to minimize the weighted number of late jobs. Erschler et al. [10] establish a... |

12 |
Wassenhove, Local Search Heuristics for the Single machine Total Weighted Tardiness Scheduling Problem
- Crauwels, Potts, et al.
- 1998
(Show Context)
Citation Context ... rule. The obvious disadvantage of dispatching rules is that the solutions generated by these methods may be far from the optimum. This problem can be tackled by local search methods. Crauwels et al. =-=[7]-=- present several local search heuristics for the 1jj P wjTj problem. They introduce a new binary encoding scheme to represent solutions, together with a heuristic to decode the binary representations ... |

11 |
Scheduling of a single machine to minimize total weighted completion time subject to release dates
- Bianco, Ricciardelli
- 1982
(Show Context)
Citation Context ...e has been considered for other optimality criteria. Chu [5] and Dessouky and Deogun [8] give branch and bound �B&B) algorithms to minimize total ¯ow time, 1jrjj P Fj, whereas Bianco and Ricciardelli =-=[3]-=- and Hariri and Potts [12] consider the total weighted completion time problem, 1jrjj P wjCj. Potts and Van Wassenhove [18] propose a B&B algorithm to minimize the weighted number of late jobs. Erschl... |

10 |
Sequencing jobs with unequal ready times to minimize mean flow time
- Dessouky, Deogun
- 1981
(Show Context)
Citation Context ...approaches discussed above assume that the jobs have equal release dates, even though the unequal release dates case has been considered for other optimality criteria. Chu [5] and Dessouky and Deogun =-=[8]-=- give branch and bound �B&B) algorithms to minimize total ¯ow time, 1jrjj P Fj, whereas Bianco and Ricciardelli [3] and Hariri and Potts [12] consider the total weighted completion time problem, 1jrjj... |

9 |
A Branch-and-Bound algorithm to minimize total tardiness with different release dates, Naval Research Logistic 39
- Chu
- 1992
(Show Context)
Citation Context ...jobs. Erschler et al. [10] establish a dominance relationship within the set of possible sequences for 1 j rj problem independent of the optimality criterion to ®nd a restricted set of schedules. Chu =-=[4]-=- proves some dominance properties and provides a lower bound for 1jrjj P Tj problem. A B&B algorithm is then constructed using the previous results of Chu and Portmann [6] and problems with up to 30 j... |

9 |
Minimizing total cost in one-machine scheduling
- Kan, Lageweg, et al.
- 1975
(Show Context)
Citation Context ... cases when all jobs are initially available. Emmons [9] derives several dominance rules for 1jj P Tj problem that restrict the search for an optimal solution. Rachamadugu [19] and Rinnooy Kan et al. =-=[21]-=- extended these results to 1j j P wjTj. Szwarc and Liu [24] present a two-stage decomposition mechanism to 1jj P wjTj problem when tardiness penalties are proportional to the processing times. Recentl... |

8 |
A new dominance concept in scheduling n jobs on a single machine with ready times and due dates
- Erschler, Fontan, et al.
- 1983
(Show Context)
Citation Context ...i and Potts [12] consider the total weighted completion time problem, 1jrjj P wjCj. Potts and Van Wassenhove [18] propose a B&B algorithm to minimize the weighted number of late jobs. Erschler et al. =-=[10]-=- establish a dominance relationship within the set of possible sequences for 1 j rj problem independent of the optimality criterion to ®nd a restricted set of schedules. Chu [4] proves some dominance ... |

7 |
One machine sequencing to Minimize Certain Functions of Job Tardiness
- Emmons
- 1969
(Show Context)
Citation Context ... two of its sub problems are already known to be strongly NP-hard. Enumerative solution methods have been proposed for both weighted and unweighted cases when all jobs are initially available. Emmons =-=[9]-=- derives several dominance rules for 1jj P Tj problem that restrict the search for an optimal solution. Rachamadugu [19] and Rinnooy Kan et al. [21] extended these results to 1j j P wjTj. Szwarc and L... |

7 |
A decision theory approach to priority dispatching for job shop scheduling
- Kanet, Zhou
- 1993
(Show Context)
Citation Context ...at X-RM I ˆ…1:6; p†, X-RM II ˆ…2; p†, X-RM III ˆ…1:6; pmin†, and X-RM IV ˆ…2; pmin†. The KZRM is a local search heuristic that combines the ATC rule and the decision theory approach of Kanet and Zhou =-=[14]-=-. The decision theory approach de®nes the alternative courses of action at each decision juncture, evaluate the consequences of each alternative according to a given criterion, and choose the best alt... |

6 |
A note on the weighted tardiness problem
- Rachamadugu
- 1987
(Show Context)
Citation Context ...both weighted and unweighted cases when all jobs are initially available. Emmons [9] derives several dominance rules for 1jj P Tj problem that restrict the search for an optimal solution. Rachamadugu =-=[19]-=- and Rinnooy Kan et al. [21] extended these results to 1j j P wjTj. Szwarc and Liu [24] present a two-stage decomposition mechanism to 1jj P wjTj problem when tardiness penalties are proportional to t... |

5 |
Local Search in Problem and Heuristic Space for Job Shop Scheduling
- Storer, Wu, et al.
- 1996
(Show Context)
Citation Context ...rch-based GRASP algorithm in terms of computational time requirements as well as total weighted tardiness. PSGA have been used successfully in the past on several scheduling problems by Storer et al. =-=[23]-=-. At the heart of a PSGA is a constructive heuristic which maps a problem instance to a sequence. We again use the X-RM IV augmented with the proposed local dominance rule as the constructive heuristi... |

4 |
A new lower bounding scheme for the total weighted tardiness problem
- Akturk, Yildirim
- 1998
(Show Context)
Citation Context ... to 1j j P wjTj. Szwarc and Liu [24] present a two-stage decomposition mechanism to 1jj P wjTj problem when tardiness penalties are proportional to the processing times. Recently, Akturk and Yildirim =-=[1]-=- proposed a new dominance rule and a lower bounding scheme for 1j j P wjTj problem that can be used in reducing the number of alternatives in any exact approach. All the optimizing approaches discusse... |

4 |
Weighted tardiness single machine scheduling with proportional weights
- Szwarc, Liu
- 1993
(Show Context)
Citation Context ...rives several dominance rules for 1jj P Tj problem that restrict the search for an optimal solution. Rachamadugu [19] and Rinnooy Kan et al. [21] extended these results to 1j j P wjTj. Szwarc and Liu =-=[24]-=- present a two-stage decomposition mechanism to 1jj P wjTj problem when tardiness penalties are proportional to the processing times. Recently, Akturk and Yildirim [1] proposed a new dominance rule an... |

3 | European - Birkelund, E |

3 |
Tactically delayed versus non-delay scheduling: an experimental investigation
- Kanet
- 1986
(Show Context)
Citation Context ...om overshadowing clusters of shorter jobs. We set the look-ahead parameter k at 2as suggested in [16], and p is the average processing time of remaining unscheduled jobs at time t. According to Kanet =-=[13]-=-, schedules with inserted idleness appear to have better best case behavior than non-delayed schedules as already shown in Fig. 1. He concluded that non-delay schedules may produce reasonably good per... |

2 | New dominance properties for 1jrjj P wjTj problem - Akturk, Ozdemir - 1998 |

2 |
Guide forward search in tardiness scheduling of large one machine problems, in: Intelligent Scheduling Systems
- Morton, Ramnath
- 1995
(Show Context)
Citation Context ...than non-delayed schedules as already shown in Fig. 1. He concluded that non-delay schedules may produce reasonably good performance but rarely provide a schedule which is optimal. Morton and Ramnath =-=[17]-=- modify the ATC rule to allow inserted idleness, which is named the X-RM rule. The X-RM rule can be de®ned as follows. Whenever a resource is idle, assign it a job which is either available at that ti... |

1 |
Some new e cient methods to solve the nj1 j rij P Ti scheduling problem
- Chu, Portmann
(Show Context)
Citation Context ... P wjTj problem. The problem may be stated as follows. There are n independent jobs each has an integer processing time pj, a release date rj, a due date dj, anda positive weight wj. Chu and Portmann =-=[6]-=- shown that the problem can be simpli®ed by using corrected due dates, i.e. if rj ‡ pj > dj then dj takes the value rj ‡ pj. Jobs will be processed without interruption on a single machine that can ha... |