Assessing network reliability in a hybrid flow shop with rush order insertion

Rush order (RO) insertion is a common problem in industrial plants and represents immediate customer demand characterized by early delivery requirements. Consequently, capacity prioritizes handling RO over processing general orders (GO). In a manufacturing system, the number of machines in a workstation can be influenced by factors, such as failure and maintenance, resulting in the stochastic capacity of each workstation. Considering the stochastic nature of the capacity state in a manufacturing system, this study models it as a stochastic hybrid flow shop (SHFS) network. Algorithms are proposed to generate the lowest capacity vectors (LCVs) that satisfy both the GO and RO. In particular, the proposed algorithms can be applied to an arbitrary capacity probability distribution of a workstation. To assess the system performance of the SHFS network, we employed network reliability as a performance metric to evaluate the possibility of meeting the demand within the specified time constraints in terms of LCVs. We consider GO and RO, each with different time constraints for completion. Numerical examples show that the network reliability indicates the capability of an SHFS to handle both GO and RO. Therefore, decision-makers can ensure that the capacity of the SHFS is sufficient to meet customer demand.