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### Single Machine Scheduling Model for Total Weighted Tardiness

#### Affiliations

• Department of Mathematics, Graphic Era University, Dehradun – 248002, Uttarakhand, India
• Department of Mathematics, Meerut College, Meerut – 250001, Uttar Pradesh, India

#### Abstract

Objectives: We proposed two heuristic algorithms for Total Weighted Due Date Tardiness Scheduling (TWDDTS). The main aim of this paper is to optimize the weighted tardiness based criteria. Methods/Statistical Analysis: The first one heuristic algorithm for 'TWDDTS' is based on dispatching rule (EDD-Earliest Due Date) and the second one heuristic algorithm for Modified Total Weighted Due Date Tardiness Scheduling (MTWDDTS) is based on modified weighed due dates. We equated the effectiveness of both the proposed heuristic algorithms with the help of numerical illustrations. Findings: The main aim to propose these heuristic algorithms is to obtain the optimal solution of the problem related to weighted tardiness scheduling based criteria, when processing times of the jobs are also associated with probabilities. These heuristic algorithms are justified by numerical illustrations and comparative study of both the heuristic algorithms (with the help of numerical example) show that an improved heuristic algorithm for MTWDDTS is outperform and give better results than a TWDDTS heuristic algorithm. We also found that when we measure the mean completion time of jobs by both the heuristic algorithms then we observed that the MTWDDTS heuristic algorithm gives the best result as compared to a TWDDTS heuristic algorithm. So we find that MTWDDTS gives the best result for minimization the weighted tardiness based criteria as well as makespan. Application/Improvements: The proposed MTWDDTS algorithm is more useful than the EDD dispatching rule for weighted tardiness based scheduling problems. It is easy to understand and provide an important tool for decision makers.

#### Keywords

EDD Dispatching Rule, Modified Weighted Due Dates (MWDD), Single Machine Scheduling, Stochastic Processing Time, Weighted Tardiness.

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#### References

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