Some new efficient methods to solve the n/1/ri/ϵTi scheduling problem

Chen, Chu; Portmann, Marie-Claude

doi:10.1016/0377-2217(92)90071-g

Cited by 35 publications

(31 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the 1|r i | T i problem, Chu and Portmann [17] and Chu [15] introduced dominance rules, heuristics, a lower bound and branch-and-bound procedures. Baptiste et al…”

Section: Introductionmentioning

confidence: 99%

Dominance rules for the parallel machine total weighted tardiness scheduling problem with release dates

Jouglet

Savourey²

2011

Computers & Operations Research

View full text Add to dashboard Cite

We address the parallel machine total weighted tardiness scheduling problem with release dates. We describe dominance rules and filtering methods for this problem. Most of them are adaptations of dominance rules based on solution methods for the single-machine problem. We show how it is possible to deduce whether or not certain jobs can be processed by a particular machine in a particular context and we describe techniques that use this information to improve the dominance rules. On the basis of these techniques we describe an enumeration procedure and we provide experimental results to determine the effectiveness of the dominance rules.Keywords: scheduling, parallel machines, total weighted tardiness, dominance rules, possible machines. * corresponding author 1 IntroductionIn this paper we consider the situation where a set of n jobs J = {1, . . . , n} has to be processed on a set of m identical parallel machines M = {1, . . . , m} and where the objective is to minimize the total weighted tardiness. Associated with each job i is a release date r i , a processing time p i , a due date d i and a weight w i . A job cannot start before its release date and preemption is not allowed. Machines cannot execute more than one job simultaneously. The tardiness of job i is defined as, where C i is the completion time of job i. The problem is to find a feasible schedule with minimum total weighted tardiness. This problem, denoted as P m|r i | w i T i , is strongly NP-Hard [25].The single machine problem has been intensively addressed over the last two decades. For the 1|r i | T i problem, Chu and Portmann [17] and Chu [15] introduced dominance rules, heuristics, a lower bound and branch-and-bound procedures. Baptiste et al.[7] also proposed a lower bound and a branch-andbound method using efficient dominance rules. For the 1|r i | w i T i problem, Akturk and Ozdemir [2] proposed dominance rules used in a branch-andbound algorithm [1,2]. Finally, Jouglet et al.[22] studied these two criteria and generalized and improved the above dominance rules which were used in a branch-and-bound method. More recently Jouglet et al.[23] described dominance-based heuristic methods for these problems.As regards parallel machine problems, several exact methods have been described. Yalaoui and Chu [32,33] described dominance rules, lower bounds and branch-and-bound methods for the general P m|r i | C i problem. More recently Nessah, Yalaoui and Chu [28] described dominance rules and a branch-and-bound method for the weighted case P m|r i | w i C i . Less attention has been given to the tardiness criteria. Nevertheless, Azizoglu and Kirca [3], Yalaoui et Chu [32] and Shim and Kim [30] solved the problem with equal release dates P m|| T i using a branch-and-bound algorithm and dominance rules. Moreover, Liaw et al.[26] also proposed a branch-and-bound algorithm using dominance properties for the weighted case considering unrelated parallel machines. Finally, Baptiste [6] showed that the special case P m|p i = p, r i | T i of the total ...

show abstract

“…For the 1|r i | T i problem, Chu and Portmann [17] and Chu [15] introduced dominance rules, heuristics, a lower bound and branch-and-bound procedures. Baptiste et al…”

Section: Introductionmentioning

confidence: 99%

Dominance rules for the parallel machine total weighted tardiness scheduling problem with release dates

Jouglet

Savourey²

2011

Computers & Operations Research

View full text Add to dashboard Cite

show abstract

“…Bianco and Ricciardelli's theorems for establishing dominance properties between adjacent jobs for 1|r j | w j C j may have a possible counterpart for 1|d j | w j E j . In a similar vein, the work of Chu and Portmann (1992) on establishing dominance properties for 1|r j | T j might be extendible to other related problems. An obvious ÿrst step might be the 1|r j | j T j problem.…”

Section: Research Opportunitiesmentioning

confidence: 94%

“…The descriptive work of Kanet (1981) has shown that the set of active schedules, although dominant over the set of nondelay schedules, is signiÿcantly larger. This is where contributions like those of Bianco and Ricciardelli (1992), Carlier (1982), Erschler et al (1983) and Chu and Portmann (1992) play a role. In each case the results serve to reduce the required search space within active schedules for a speciÿc scheduling objective.…”

Section: A Taxonomy For Iit Scheduling Problemsmentioning

confidence: 99%

Scheduling with Inserted Idle Time: Problem Taxonomy and Literature Review

Kanet

Sridharan

2000

Operations Research

127

View full text Add to dashboard Cite

In the context of production scheduling, inserted idle time (IIT) occurs whenever a resource is deliberately kept idle in the face of waiting jobs. IIT schedules are particularly relevant in multimachine industrial situations where earliness costs and=or dynamically arriving jobs with due dates come into play. We provide a taxonomy of environments in which IIT scheduling is relevant, review the extant literature on IIT scheduling, and identify areas of opportunity for future research.

show abstract

“…A lot of heuristics use dominance rules to improve the quality of the solutions built (see for example [43,44,45]). Dominances between instances of problems or between problems are particularly useful for the development of bounds (see Sections 6.2 and 6.3).…”

Section: Dominance Rules In Evaluation Methodsmentioning

confidence: 99%

Dominance rules in combinatorial optimization problems

Jouglet

Carlier

2011

European Journal of Operational Research

View full text Add to dashboard Cite

The aim of this paper is to study the concept of a "dominance rule" in the context of combinatorial optimization. A dominance rule is established in order to reduce the solution space of a problem by adding new constraints to it, either in a procedure that aims to reduce the domains of variables, or directly in building interesting solutions. Dominance rules have been extensively used over the last fifty years. Surprisingly, to our knowledge, no detailed description of them can be found in the literature other than a few short formal descriptions in the context of enumerative methods. We are therefore proposing an investigation into what dominance rules are. We first provide a definition of a dominance rule with its different nuances. Next, we analyze how dominance rules are generally formulated and what are the consequences of such formulations. Finally, we enumerate the common characteristics of dominance rules encountered in the literature and in the usual process of solving combinatorial optimization problems.

show abstract

Some new efficient methods to solve the n/1/ri/ϵTi scheduling problem

Cited by 35 publications

References 15 publications

Dominance rules for the parallel machine total weighted tardiness scheduling problem with release dates

Dominance rules for the parallel machine total weighted tardiness scheduling problem with release dates

Scheduling with Inserted Idle Time: Problem Taxonomy and Literature Review

Dominance rules in combinatorial optimization problems

Contact Info

Product

Resources

About