Abstract
Problem statement: In this research, we addressed the problem of minimizing the earliness-tardiness penalties and manufacturing costs of a single machine with a stochastic controllable processing and tooling cost. Approach: We developed a mathematical non-linear integer programming model and its linearised version to find the optimal solution. We introduced a new genome representation in single machine scheduling literature that evolved by a genetic algorithm to solve the problem. The genome representation includes two genes per job, one represents the job starting time and other corresponds to the job processing time. The algorithms were compared based on the solution quality, CPU time and memory consumption in bytes on a set of randomly generated test problems. Results: The results showed that developed algorithms could define the global optimal solution of most scheduling problems with n ≤ 20 jobs. For larger n, the developed genetic algorithm outperforms the math models in terms of solution quality and less CPU seconds while consumes moderate memory kilobytes of 3295 compared with 5058 and 1685 of linear and nonlinear models on the average. Conclusion: The GA's average performance achieves 6.013 related to the lower bound of math linear program whereas nonlinear model achieves an average of 1.034. The GA's performance increases by increasing n compared with other techniques. We hope to expand the developed algorithms for different configurations as parallel and job shops.
Highlights
In this article, we examine the single machine scheduling problem with controllable processing time
In various real-life systems, the job processing time. These paradigms working on the optimal resource allocations in order to minimize the manufacturing cost that can be reflected in an increase in profit by cost reduction rather than the may be controlled by allocating extra resources such as conventional approach of increasing the profit by money, manpower, energy, catalysts, spindle speed, price increase
Kaspi and Shabtay (2004) considered the single machine scheduling problem with controllable processing time for identical and non-identical job release times restricted by a common limited convex decreasing resource consumption function for minimizing makespan
Summary
Producing jobs according to the just-in-time principle. In this article, we examine the single machine scheduling problem with controllable processing time. Processing cost as the work done by Alidaee and Hoogeveen and Woeginger (2002) considered a Ahmadian (1993); Cheng et al (1996a; 1996b ); Jansen controllable processing single machine scheduling problem to minimize the multi-criteria of the total weighted job processing times plus the linear compression cost function of the processing times and showed that the problem was NP-complete. Kaspi and Shabtay (2004) considered the single machine scheduling problem with controllable processing time for identical and non-identical job release times restricted by a common limited convex decreasing resource consumption function for minimizing makespan. We develop a genome representation that can be considered as a new addition to the single machine scheduling and Cheng (2005) to minimize the makespan plus total problem with controllable processing and investigate its resource consumption cost. The big M is taken to equal to the sum of upper processing times for all jobs
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