Optimization Based on Simulation Studies of the Number of Machinery on the Workshop Production Scheduling Under Uncertainty Conditions and Space and Budget Constraints

There is a direct relationship between the number of machinery in any industrial problem, their costs of purchase,  and the space they occupy. Accordingly, due considerations about the constraints are required in space and budget. Workshop production problems under uncertainty conditions including more than two pieces of machinery are regarded as NP-hard. Therefore, using common research in operation techniques, one cannot embark upon modelling and finding the optimal answer for such problems. Hence, this study aims to propose a conceptual mathematical model for the problem of industrial production. The research problem involves cost limitations while working out the solution through simulation studies.

Design/methodology/approach: 

First a mathematical model has been proposed for workshop production with cost and space constraints. Then by enlisting the help of Arena software, 14 simulation models have been designed for machine ‘m’ and work ‘n’ of different production sequences. Finally, by solving a numerical model example, the problem of nearing the optimal condition of the problem, considering minimizing the objective function of the tardiness and earliness costs, has been resolved. This measure has been adopted to determine the optimal number of machinery, considering work prioritization laws in work cells by executing the model and scatter search algorithm and designing relevant experiments.

Solving a numerical example considering the default number of machinery and the LPT optimization method resulted in the best answer when the total tardiness and earliness costs were intended. In contrast, in the case of increasing the number of machineries, both the LPT (longest process time) and CR (critical ratio) methods led to the best answers with the help of dispersed search algorithms in simulation studies. The results included the cost and space constraints.

Research implications:

 One of the prominent features of simulation is that with the minimum distance between the problem and the real world (not removing the limitations and complexities for solving the problem, which is usually done by removing the facts in other problem-solving methods, to reduce the complexity and the possibility of solving the problem) problem-solving and decision-making scenarios are applied. This helps managers in decision-making. Most of the time, the physical study of systems is very difficult and costly, or even impossible; therefore, an alternative model should be used to study the system.

Originality/value: 

A careful investigation of previous research and relevant literature reveals that none of the studies in the literature have simultaneously dealt with the problem of the number of machinery in conditions of cost and space limitations. Therefore, the present study incorporated the mentioned constraints in the scheduling problems and adopted simulation problem-solving methods. It resulted in delving and enriching the subject further.