Minimizing fuzzy makespan in a two-stage cross docking flow shop problem with considering fuzzy processing times

Nowadays Cross dock facilities have an important role in supply chain management that can decrease transportation and maintenance costs. In recent years, cross dock scheduling problems are widely studied and few of them have considered the uncertainty in their study. Practically, the time of loading and unloading trucks is not a crisp number. In this work, Cross dock is considered as a two stage flow shop that jobs in the second stage only can be processed when its precedence jobs in the first stage have been processed and inbound and outbound doors considered as machines that at least one stage has more than one machine. In literature a mixed integer programming model is presented that can only be used for small scale instances. Therefore, four heuristics for moderate and large scale instances are proposed. In this study, we consider the loading and unloading truck as jobs with a fuzzy processing time that has a trapezoidal membership function. We modify four proposed heuristics to accept these fuzzy processing times and calculate optimum fuzzy makespan. Numerical example is provided for illustration the use of modified heuristics.