基于熵函数的流水车间小批生产信息量测度

An Entropy-based Approach for Measuring the Information Quantity of Small Lots Production in a Flow Shop

流水车间生产中,批量及批次的信息量测度意味着对描述不同批量及批次在工作站的状态所需信息量的度量,即求解批量及批次的信息熵表达.现有批量及批次信息控制研究主要集中在批量调度问题上,鲜有针对生产中的批量及批次与管理生产所需信息量关系的研究,造成研究结论很难为决策者从信息管理角度选择生产方式提供理论依据.针对上述问题,在分析信息熵度量特性基础上,理论上首次建立流水车间生产线不同批次相同加工时间条件下的批量及批次的信息熵函数,作为度量生产系统状态所需信息量的基础,并由此提出生产批次与熵函数变化关系两个定理,即:生产批次的信息熵函数单调递减;批次趋于无穷大时,系统信息熵趋于零.采用求导法与极值法分别对所提定理给予充分证明,从而理论上证明了流水车间的加工批次增加(或批量减小),则系统的信息熵降低.分别取工作站数量为10和20进行实证研究,以图示表达的结果再次验证了所提定理的正确性.批量与批次的信息量测度理论研究,对实际流水车间生产批量与批次的作业安排及最终生产方式的选择,都具有重要的理论支撑和现实指导意义.

In the production of the flow shop, the measurement of information quantity on the number and size of lots means a measure of the information quantity required to describe the status of different numbers and sizes of lots at the workstations, i.e., to solve the information entropy representation of the number and size of lots. The existing information control research on the number and size of lots mainly focuses on the batch scheduling problem of the flow shop. There are few research on the relationship between the number and size of lots and the amount of information required to manage production, so its research conclusions are difficult to provide a theoretical basis for decision makers to choose production methods from the perspective of information management. Based on the analysis of the information entropy measurement characteristics, the entropy functions of the processing lots of a production line of a flow shop are first established theoretically for the first time, as the basis for measuring the states of production systems needed the amount of information. According to the established entropy functions, two theorems on the relationship between production lots and the entropy functions are proposed, namely: the entropy function of production lots decreases monotonically;the systematic entropy tends to zero when the number of lots approach to infinity. The derivation and the extremum methods are used to fully prove the theorems, respectively. As a result, it is theoretically demonstrated for the first time that the move toward larger number(or smaller size) of lots implies less information needs. In the empirical study, the number of workstations was taken as 10 and 20, respectively. The correctness of the theorem was verified again by the calculation results of the graphic representation. The theory research on the measurement of information quantity of the number and size of lots has important theoretical support and practical guiding significance for the actual flow shop batch and batch scheduling arrangement and final production mode selection.