Batch sizing control of a flow shop based on the entropy-function theorems

Abstract

It is a crucial decision-making issue to determine the batch size in production for manufacturing enterprises which implement multi-variety and small batch production. Regarding the current limitations, little research has been done on the relationship between batch sizing and the amount of information needed for production management. This paper first constructs the functional expression between the number of batches and the system entropy according to the measured property of entropy itself. Then, the two theorems on the relationship between the number of batches and the system entropy are theoretically put forward for the first time, i.e., an increase in the number of batches will reduce the system entropy, thus reducing the information required to manage production. Also, the two theorems are fully proved based on the proposed functions. In an empirical study, the variations between the system entropy functions and the number of batches are comparatively analyzed by designating two cases of 10 and 20 machining units. Consequently, the results of graphical representation once again illustrate the validity of the developed two theorems. The conclusions of this study not only provide a crucial information-theoretic basis for the feasible arrangement of batch size with an expert decision support system but contribute to guiding practical production for assembly line managers.