Single Machine Scheduling With a Generalized Total Tardiness Objective Function (original) (raw)
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A note on a single machine scheduling problem with generalized total tardiness objective function
Information Processing Letters, Vol. 112, No. 3, 2012, 72 - 76, 2012
In this note, we consider a single machine scheduling problem with generalized total tardiness objective function. A pseudo-polynomial time solution algorithm is proposed for a special case of this problem. Moreover, we present a new graphical algorithm for another special case, which corresponds to the classical problem of minimizing the weighted number of tardy jobs on a single machine. The latter algorithm improves the complexity of an existing pseudo-polynomial algorithm by Lawler. Computational results are presented for both special cases considered.
Single machine total tardiness maximization problems: complexity and algorithms
Annals of Operations Research, 2013
In this paper, we consider some scheduling problems on a single machine, where weighted or unweighted total tardiness has to be maximized in contrast to usual minimization problems. These problems are theoretically important and have also practical interpretations. For the total weighted tardiness maximization problem, we present an NP-hardness proof and a pseudo-polynomial solution algorithm. For the unweighted total tardiness maximization problem with release dates, NP-hardness is proven. Complexity results for some other classical objective functions (e.g., the number of tardy jobs, total completion time) and various additional constraints (e.g., deadlines, weights and/or release dates of jobs may be given) are presented as well.
A New Algorithm for Solving the Single Machine Total Tardiness Scheduling Problem
We are analyzing a multifunctional machine and the set of tasks to be performed by the machine. Each task has to be finished before a given due date. We are interested in finding a schedule of the tasks in such a way that the machine complies with the due dates. The problem is formulated as a minimum total tardiness scheduling problem. An heuristic algorithm for the problem is proposed. Finally, a comparative computational experience between this algorithm and other heuristic and exact algorithms is reported. Key-Words: scheduling, tardiness problem, single machine, exact and heuristic algorithms CSCC99, pp.2851-2858
Algorithms for Special Single Machine Total Tardiness Problems
The scheduling problem of minimizing total tardiness on a single machine is known to be NP -hard in the ordinary sense. In this pa- per, we consider the special case of the problem when the processing times pj and the due dates dj of the jobs j, j ∈ N = {1,2 ,...,n }, are oppositely ordered: p1 ≥ p2 ≥ ... ≥ pn and d1 ≤ d2 ≤ ... ≤ dn. It is shown that already this special case is NP -hard in the ordinary sense, too. The set of jobs N is partitioned into k,1 ≤ k ≤ n, subsets M1, M2 ,..., Mk, Mν � Mμ = ∅ for ν �= μ, N = M1 � M2 � ... � Mk, such that maxi,j∈Mν |di − dj |≤ minj∈Mν pj for each ν =1 ,2 ,..., k. We propose algorithms which solve the prob- lem: in O(knpj )t ime if 1≤ k <n ;i nO(n2 )t ime ifk = n ;a nd in O(n2 )t ime if max i,j∈N |di − dj |≤ 1. The polynomial algorithms do neither require the conditions p1 ≥ p2 ≥ ... ≥ pn mentioned above nor integer processing times to construct an optimal schedule. Finally, we apply the idea of the presented algorithm for the case k = 1 t...
2007
This paper deals with a common due date parallel machines scheduling problem in which each job has a different tardiness penalty. The objective is to minimize the total weighted tardiness. The scheduling problem of minimizing the total weighted tardiness with a common due date on a single machine is known to be ordinary NP-hard. This is also the case for problem P m|d i = d| w i T i . A new dynamic programming algorithm is proposed to solve the 1|d i = d| w i T i scheduling problem and a fully polynomial time approximation scheme (FPTAS) is deduced from this algorithm. We show that the complexity of this FPTAS is better than existing one. These results are generalized to the parallel machines scheduling case.
Solution of the single machine total tardiness problem
Journal of Scheduling, 1999
The paper deals with the solution of the single machine total tardiness model. It improves and generalizes an important rule to decompose the model into two subproblems. It also provides a O(n) procedure to implement this rule and its generalization. Those two rules, along with some known results, are incorporated in a branch and bound algorithm that efficiently handles instances with up to 300 jobs and uses the original and maximally increased due dates to solve the original problem. Several properties that justify the modified due date version of our algorithm and produce an easy-to-implement new lower bound are established. The paper also provides an explanation why using the increased due dates may improve the efficiency of certain algorithms.