scholarly journals An FPTAS for the Minimum Total Weighted Tardiness Problem with a Fixed Number of Distinct Due Dates

2009 ◽  
pp. 238-248 ◽  
Author(s):  
George Karakostas ◽  
Stavros G. Kolliopoulos ◽  
Jing Wang
Keyword(s):  
Fixed Number ◽  
Total Weighted Tardiness ◽  
Due Dates ◽  
Weighted Tardiness

scholarly journals An FPTAS for the minimum total weighted tardiness problem with a fixed number of distinct due dates

2012 ◽  
Vol 8 (4) ◽  
pp. 1-16 ◽  
Author(s):  
George Karakostas ◽  
Stavros G. Kolliopoulos ◽  
Jing Wang
Keyword(s):  
Fixed Number ◽  
Total Weighted Tardiness ◽  
Due Dates ◽  
Weighted Tardiness

scholarly journals Bi-criteria parallel batch machine scheduling to minimize total weighted tardiness and electricity cost

2020 ◽  
Vol 90 (9) ◽  
pp. 1345-1381
Author(s):  
Jens Rocholl ◽  
Lars Mönch ◽  
John Fowler
Keyword(s):  
Genetic Algorithms ◽  
Pareto Front ◽  
Total Weighted Tardiness ◽  
Mixed Integer ◽  
Due Dates ◽  
Semiconductor Wafer ◽  
Weighted Tardiness ◽  
Electricity Cost ◽  
Problem Instances ◽  
Special Case

Abstract A bi-criteria scheduling problem for parallel identical batch processing machines in semiconductor wafer fabrication facilities is studied. Only jobs belonging to the same family can be batched together. The performance measures are the total weighted tardiness and the electricity cost where a time-of-use (TOU) tariff is assumed. Unequal ready times of the jobs and non-identical job sizes are considered. A mixed integer linear program (MILP) is formulated. We analyze the special case where all jobs have the same size, all due dates are zero, and the jobs are available at time zero. Properties of Pareto-optimal schedules for this special case are stated. They lead to a more tractable MILP. We design three heuristics based on grouping genetic algorithms that are embedded into a non-dominated sorting genetic algorithm II framework. Three solution representations are studied that allow for choosing start times of the batches to take into account the energy consumption. We discuss a heuristic that improves a given near-to-optimal Pareto front. Computational experiments are conducted based on randomly generated problem instances. The $$ \varepsilon $$ ε -constraint method is used for both MILP formulations to determine the true Pareto front. For large-sized problem instances, we apply the genetic algorithms (GAs). Some of the GAs provide high-quality solutions.

Minimizing Total Weighted Tardiness on Parallel Batch-Processing Machine Scheduling Problems with Varying Machine Capacities

2011 ◽  
Vol 110-116 ◽  
pp. 3906-3913 ◽  
Author(s):  
Fuh Der Chou ◽  
Hui Mei Wang
Keyword(s):  
Heuristic Algorithms ◽  
Batch Processing ◽  
Total Weighted Tardiness ◽  
Mixed Integer ◽  
Due Dates ◽  
Weighted Tardiness ◽  
Processing Machine ◽  
Release Times ◽  
Mip Model ◽  
Batch Processing Machine

This paper extends the study of Mathirajan et al. (Minimizing total weighted tardiness on a batch-processing machine with non-agreeable release times and due dates. Int. J. Adv. Manuf. Technol., 2010, doi: 10.1007/s00170-009-2342-y) to parallel batch-processing machine problems because these have not been examined to date. For the problem concerning compatible product families, job release times, non-identical job sizes, and varying machine capacities, we propose a mixed integer programming (MIP) model, and a number of simple dispatch-based heuristic and simulated annealing (SA) algorithms. Computational results revealed that the proposed SA is capable of obtaining similar solutions acquired by MIP within a short time. The SA algorithms outperform other heuristic algorithms with respect to solution quality.

scholarly journals SORTING APPROACHES IN THE HEURISTIC BASED ON REMAINING AVAILABLE AND PROCESSING PERIODS TO MINIMIZE TOTAL WEIGHTED TARDINESS IN PROGRESSIVE IDLING-FREE 1-MACHINE PREEMPTIVE SCHEDULING

2021 ◽  
Author(s):  
Vadym V. Romanuke
Keyword(s):  
Computational Study ◽  
Computation Time ◽  
Combinatorial Problem ◽  
Total Weighted Tardiness ◽  
Release Dates ◽  
Preemptive Scheduling ◽  
Scheduling Problems ◽  
Due Dates ◽  
Weighted Tardiness ◽  
Priority Weights

Background. In preemptive job scheduling, total weighted tardiness minimization is commonly reduced to solving a combinatorial problem, which becomes practically intractable as the number of jobs and the numbers of their processing periods increase. To cope with this challenge, heuristics are used. A heuristic, in which the decisive ratio is the weighted reciprocal of the maximum of a pair of the remaining processing period and remaining available period, is closely the best one. However, the heuristic may produce schedules of a few jobs whose total weighted tardiness is enormously huge compared to the real minimum. Therefore, this heuristic needs further improvements, one of which already exists for jobs without priority weights with a sorting approach where remaining processing periods are minimized. Three other sorting approaches still can outperform it, but such exceptions are quite rare. Objective. The goal is to determine the influence of the four sorting approaches and try to select the best one in the case where jobs have their priority weights. The heuristic will be applied to tight-tardy progressive idling-free 1-machine preemptive scheduling, where the release dates are given in ascending order starting from 1 to the number of jobs, and the due dates are tightly set after the release dates. Methods. To achieve the said goal, a computational study is carried out with applying each of the four heuristic approaches to minimize total weighted tardiness. For this, two series of 4151500 scheduling problems are generated. In the solution of a scheduling problem, a sorting approach can “win” solely or “win” in a group of approaches, producing the heuristically minimal total weighted tardiness. In each series, the distributions of sole-and-group “wins” are ascertained. Results. The sole “wins” and non-whole-group “wins” are rare: the four sorting approaches produce schedules with the same total weighted tardiness in over 98.39 % of scheduling problems. Although the influence of these approaches is different, it is therefore not really significant. Each of the sorting approaches has heavy disadvantages leading sometimes to gigantic inaccuracies, although they occur rarely. When the inaccuracy occurs to be more than 30 %, this implies that 3 to 9 jobs are scheduled. Conclusions. Unlike the case when jobs do not have their priority weights, it is impossible to select the best sorting approach for the case with job priority weights. Instead, a hyper-heuristic comprising the sorting approaches (i. e., the whole group, where each sorting is applied) may be constructed. If a parallelization can be used to process two or even four sorting routines simultaneously, the computation time will not be significantly affected.

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