A No-Wait Flowshop Scheduling Problem with Batch Delivery System

This study investigates the no-wait permutation flowshop scheduling problem (NWPFSP). This type of problem adds constraints to the permutation flow type scheduling problem in that jobs are prohibited from waiting between machines during processing. The NWFSP is a common problem type in industry. After processing jobs on machines, products are distributed to several customers. It is recommended that products be transferred immediately after they are finished on a production line to avoid delays. However, this approach may lead to high distribution costs. Consequently, a balance between distribution costs and delay must be considered when making operational decisions. Grouping products for delivery is an effective way to reduce the cost of distribution and is called batch delivery (BD) in literature. For this reason, the integration of the NWFSP with the batch delivery (BD) is addressed by minimizing the total delay and batch delivery costs. This problem is called the No-Wait Flowshop Scheduling Problem with Batch Delivery (NWFSPBD). For this integrated production and distribution problem, the Mixed-Integer Linear Programming Model (MILPM) and Constraint Programming Model (CPM) were developed. These two mathematical models were tested on the instance sets that were produced regarding the related literature. Since the problem is complex, both models have difficulty obtaining an optimal solution within the specified time limit. However, when the results of the CPM are compared with the results of the MILPM, it finds either the same or better results for each data set. Therefore, the CPM has high applicability as it can achieve better results.