A simulation of vendor managed inventory dynamics using fuzzy arithmetic operations with genetic algorithms

This paper develops a new simulation method for vendor managed inventory (VMI) model based on fuzzy arithmetic in the supply chain (SC). The traditional VMI model has been successfully used to reduce the ‘‘Bullwhip Effect” in the SC. Thus, in real industry the VMI model can be observed that some variables/ parameters may belong to the uncertain factors. Therefore, the traditional VMI model may need to be extended to treat the vague variables or parameters. This study develops a fuzzy system dynamic to simulate vendor managed inventory, automatic pipeline, inventory and order based production control system (VMI-APIOBPCS) model based on fuzzy difference equations, and these operators of difference equations adopt the weakest t-norm ðTW Þ operators. Based on the weakest t-norm operators we can get the approximate result using sup-min convolution for simulating fuzzy VMI model, and the fuzzy VMI model can be easier simulated under uncertain environment Moreover, the results of fuzzy VMI-APIOBPCS model can provide the whole extended information regarding the system behavior uncertainties for the decision-makers with fuzzy interval. Furthermore, the study uses genetic algorithms (GA) to search optimal parameters of fuzzy VMI-APIOBPCS model. The performance of Bullwhip measures shows that fuzzy VMI-APIOBPCS model also can reduce the ‘‘Bullwhip Effect” as crisp VMI model which can be evidenced by analysis of variance (ANOVA), and the performance of integral of time absolute error (ITAE) shows that the fuzzy VMI model outperforms previous method with fixing customer service level. Crown Copyright 2009 Published by Elsevier Ltd. All rights reserved.