Minimizing Maximum Tardiness On A Single Machine With Family Setup Times And Machine Disruption

Due to the complexity of manufacturing processes, many industries today try to group their production components into families and use a common setup time to process every family. Also, the failure of machinery has an important impact on the planning of production systems. This paper deals with the problem of single machine scheduling with family setup times and randomly machine breakdown. It is assumed that there is disruption along the planning horizon with uncertain start and duration times based on a specific probability distribution function. The goal is to minimize the maximum expected tardiness. For this problem, a hill climbing based heuristic (HCO) and a novel hybrid variable neighborhood search metaheuristic (HVNS) have been developed. A branch and bound (BB) procedure is also proposed to optimally solve this problem using HCO and HVNS algorithms to derive upper bounds. Comparison of the solutions obtained from the presented algorithms with the mathematical programming model of the problem in small-scale instances shows that the solutions obtained from the proposed algorithms have a good quality in terms of the expected value of the objective function and the solving time. The computational results for executing the proposed algorithms on 36 series of various instances show that the BB procedure is able to solve 97.76% of the instances within the specified time frame and HVNS metaheuristic is capable to solve 41.07% of them, optimally. Also, the maximum mean deviation of HVNS solutions from the optimal solution is reported below 5% for hard instances and below 15% for instances with medium complexity. After performing a non-parametric hypothesis test, it is found that at a confidence level 99.9%, the deviation index for HVNS is less than 1.5% for difficult problems and less than 9% for semi-difficult ones. Finally, the results of solving large scale instances, demonstrate the efficiency of proposed metaheuristic. (C) 2021 Elsevier Ltd. All rights reserved.