Workforce size problem in manufacturing with dynamic programming approach

Abstract

Workforce size problem is a common issue in manufacturing, which is to determine the optimal number of workers required such that the productivity of a product is ensured. As such, the situation of understaffing and overstaffing in the manufacturing could be handled properly, in turn, to save the labour cost and to fulfil the economic supply and demand. In this paper, the workforce size problem in manufacturing is described, and the dynamic programming approach is applied to solve the workforce size problem. In the discussion, the return function of the workforce size problem and the state transition equation are identified. Then, the backward recursion equation of dynamic programming is formulated. According to each stage considered, the possible states are determined, and the related value of the return functions are calculated. It is followed by establishing the optimal decision policy for having the optimal number of workers. For illustration, an example of the workforce size problem in manufacturing, which is on a weekly basis, is studied. The result obtained showed that the minimum recruitment cost is RM33, where the optimal number of workers for the respective weeks is four workers, eight workers, eight workers, six workers, and six workers. In conclusion, the efficiency of the dynamic programming method in solving the workforce size problem in manufacturing is highly demonstrated.