| The complexity of production-inventory systems has challenged researchers and practitioners like for decades. In recent years, the ever-intensive competition in a global market and the advent of information technology have even elevated the needs of developing methods dealing with the dynamic situations in supply chain systems. Clearly mathematical models only based on average or steady state conditions are insufficient in such dynamic environment. Hence, the mathematical tools based on control theory to handle time-varying phenomena have been reinvigorated to accommodate these new needs.; This work addresses two main issues not mentioned in previous research. The first issue is the application of different model types at different levels of the supply chain (i.e., the factory level, the cell level, etc.). The purpose is to take advantage of similarity between functions at each level (i.e., order policy, forecast, etc.) to build a control theoretic modeling framework (CTMF). This CTMF has to be uniform because in that way it can be scalable among levels. The CTMF also has to be generic, so it can be applied to the existing configurations at each level.; The second issue is concerned with the lack of feasible means to estimate the parameters included in control theoretic models. For some control theoretic applications (i.e., electrical or mechanical engineering) these parameters usually represent time constants and can be easily calculated, but that is not the case for production-inventory applications.; A combination of discrete event simulation and analytical models is proposed to estimate the parameters. First, an analytical expression in the time domain is obtained by inverse Laplace transforms of the transfer function from the control theoretic model of a production center. The production center could be considered a Factory, a cell, or a machine. Then, a discrete simulation model of the same production center is built and an appropriate number of replications is made to collect information about the dynamic behavior of the system.; The information obtained from the discrete simulation (data collected) and from the control theoretic model (analytical expression) represent the same dynamic event. Therefore, parameters for the control theoretic model are determined in such a way that the dynamic response from the control model coincides with the response obtained from the discrete simulation. This problem is represented as a nonlinear least squares optimization. The parameters are the variables to be estimated and the data from the discrete simulation as well as the analytical expression in the time domain are the inputs. The problem is solved using the optimization software GAMS.; Finally, the methodology is illustrated by an industrial case in the automotive part manufacturing industry. Results showed viability of the approach and demonstrated promising potential for further analysis of dynamic events such as: Machine failures, setups, supply shortages, sudden demand variations, expedited batches (rush orders), order cancellations (customer changes), etc. |
