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Ruiz and Allahverdi [12] minimized the bi-criteria of makespan and maximum tardiness with an upper bound on maximum tardiness of the flowshop scheduling problem.
Since the old jobs have a common due date that must not be violated, our problem is a rescheduling problem with the objective of minimising the makespan of the new jobs (thus obtaining the tightest possible due date for the new jobs) and a constraint since the maximum tardiness of the old jobs must be equal to zero.
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Extensive computational experiments carried out on various criteria (makespan, total weighted flow time, total weighted tardiness, weighted sum of tardy jobs, maximum tardiness) show the efficiency of the proposed approach.
Also recently, Kanagasabapathi et al. (2009) by defining performance measures and considering maximum tardiness and mean tardiness of projects studied the MPRCSP in a static environment.
During this process, the algorithm keeps track of the maximum tardiness within each block (Θ i tardiness ).
Their model minimizes the expected total cost including maximum tardiness cost among all parts, the cost of sub-contracting for exceptional elements, and the cost of resource underutilization.
The first problem seeks to minimize the maximum tardiness, and the second problem is to minimize the number of tardy jobs.
In the present paper, the problems of minimizing costs associated with maximum tardiness, due date assignment and delivery for a single machine are considered.
To minimize the maximum tardiness, we propose a dynamic programming algorithm that optimally solves the problem in polynomial time.
Other operators such as if, min, max are also commonly used to evolve heuristics and have shown to be particularly useful when dealing with difficult scheduling objectives such as maximum tardiness and total weighted tardiness.
The single-objective problems are to minimize the makespan while the multi-objective scheduling problems are to minimize the makespan and the maximum tardiness.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com