A revised method for allocating the optimum number of similar machines to operators

Purpose – The purpose of this paper is to propose a method to determine the optimal number of operators to be assigned to a given number of machines, as well as the number of machines that will be run by each operator (a numerical partition). This determination should be made with the objective of minimizing production costs or maximizing profits. Design/methodology/approach – The method calculates the machines interference rate via the binomial distribution function. The optimal assignment is calculated by transformation of a partition problem into a problem of finding the shortest path on a directed acyclic graph. Findings – The method enables the authors to calculate the adjusted cycle time, the workload of the operators, and the utility of the machines, as well as the production yield, the total cost per unit, and the hourly profit for each potential assignment of operators to machines. In a case study, the deviation of the output per hour of the proposed method from the actual value was about 2 percent. Practical implications – The paper provides formulas and tables that give machine interference rates through the application of binomial distribution. The practicability of the proposed method is demonstrated by a real-life case study. Originality/value – The method can be applied in a wide variety of manufacturing systems that use many identical machines. This includes tire presses in tire manufacturing operations, ovens in pastry manufacturing systems, textile machines, and so on.