Efficient algorithms for machine scheduling problems with earliness and tardiness penalties (original) (raw)
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Expert Systems With Applications, 2009
The single-machine tardiness problem with sequence dependent setup times is a core topic for scheduling studies. Tardiness is actually a difficult criterion to deal with, even in a relatively simple manufacturing system, such as a single-machine is strongly NP-hard. Motivated by the computational complexity of this problem, a simple iterated greedy (IG) heuristic is proposed to solve it. To validate and verify the proposed IG heuristic, computational experiments were conducted on three benchmark problem sets that included weighted and un-weighted tardiness problems. The experiment results clearly indicate that the proposed IG heuristic is highly effective as compared to the state-of-the-art meta-heuristics on the same benchmark instances. In terms of both solution quality and computational expense, this study successfully develops an effective and efficient approach for single-machine total tardiness problems with sequence dependent setup times.
Computers & Operations Research, 2004
The single-machine early/tardy (E/T) scheduling problem is addressed in this research. The objective of this problem is to minimize the total amount of earliness and tardiness. Earliness and tardiness are weighted equally and the due date is common and large (unrestricted) for all jobs. Machine setup time is included and is considered sequence-dependent. When sequence-dependent setup times are included, the complexity of the problem increases signiÿcantly and the problem becomes NP-hard. In the literature, only mixed integer programming formulation is available to optimally solve the problem at hand. In this paper, a branch-and-bound algorithm (B&B) is developed to obtain optimal solutions for the problem. As it will be shown, the B&B solved problems three times larger than what has been reported in the literature. ?
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...
Single-machine scheduling with sequence dependent setup to minimize total weighted squared tardiness
Iie Transactions, 1999
This paper addresses the NP-hard problem of scheduling N independent jobs on a single machine with release dates, due dates, sequence dependent setup times, and no preemption where the objective is to minimize the weighted sum of squared tardiness. A Lagrangian relaxation based approach is developed for single-machine scheduling with sequence dependent setup times that is based on a list scheduling concept in conjunction with Lagrangian relaxation. Sequence dependent setup times are formulated as capacity constraints, and then are relaxed using Lagrangian multipliers. The primal problem is decomposed into job-level subproblems which are solved optimally and an approximate dual problem is then solved using a sub-gradient technique. The result of the relaxation is a list of jobs sequenced by beginning times that is then improved via a three-way swap. Experimental results are compared with EDD (Earliest Due Date) and ATCS (Apparent Tardiness Cost with Setups) dispatching rules, a four-way swap local search, tabu search, and simulated annealing. The adopted approach results in superior solution quality with respect to EED, ATCS, four-way swap, and tabu search results. It has comparable solution quality to the simulated annealing results, but is substantially more computationally efficient. Overall, the approach is capable of dealing with realistically sized single machine scheduling problems with release dates, due dates, and sequence dependent setup times.
The International Journal of Advanced Manufacturing Technology, 2011
The unrelated parallel machine scheduling problem with sequence-and machine-dependent setup times in the presence of due date constraints represents an important but relatively less-studied scheduling problem in the literature. In this study, a simple iterated greedy (IG) heuristic is presented to minimize the total tardiness of this scheduling problem. The effectiveness and efficiency of the proposed IG heuristic are compared with existing algorithms on a benchmark problem dataset used in earlier studies. Extensive computational results indicate that the proposed IG heuristic is capable of obtaining significantly better solutions than the state-of-the-art algorithms on the same benchmark problem dataset with similar computational resources.
Algorithms for single machine total tardiness scheduling with sequence dependent setups
European Journal of Operational Research, 2006
We consider the problem of scheduling a single machine to minimize total tardiness with sequence dependent setup times. We present two algorithms, a problem space-based local search heuristic and a Greedy Randomized Adaptive Search Procedure (GRASP) for this problem. With respect to GRASP, our main contributions area new cost function in the construction phase, a new variation of Variable Neighborhood Search in the improvement phase, and Path Relinking using three different search neighborhoods. The problem space-based local search heuristic incorporates local search with respect to both the problem space and the solution space. We compare our algorithms with Simulated Annealing, Genetic Search, Pairwise Interchange, Branch and Bound and Ant Colony Search on a set of test problems from literature, showing that the algorithms perform very competitively.
Improved heuristics for the early/tardy scheduling problem with no idle time
2005
In this paper we consider the single machine earliness/tardiness scheduling problem with no idle time. We present two new heuristics, a dispatch rule and a greedy procedure, and also consider the best of the existing dispatch rules. Both dispatch rules use a lookahead parameter that had previously been set at a fixed value. We develop functions that map some instance statistics into appropriate values for that parameter. We also consider the use of dominance rules to improve the solutions obtained by the heuristics. The computational results show that the function-based versions of the heuristics outperform their fixed value counterparts and that the use of the dominance rules can indeed improve solution quality with little additional computational effort.
Single machine scheduling with early and quadratic tardy penalties
Computers & Industrial Engineering, 2004
This paper considers the problem of scheduling a single machine when the objective uses a penalty for each job that is equal to the earliness of the job plus the squared tardiness of the job. A timetabling algorithm is presented that inserts idle time into a sequence in order to minimize the objective considered. Optimal branch and bound algorithms are presented as well as efficient heuristic algorithms. The procedures are tested on randomly generated problems of varying numbers of jobs and due date tightness parameters. The results show that a branch and bound procedure can solve small and medium sized problems in a reasonable amount of time and that a simple descent procedure can quickly generate solutions that are close to optimal.