Abstract
Scheduling began to be taken seriously in manufacturing at beginning of this century. Most of the real world scheduling problems are difficult to solve and named as NP-hard. This topic is concerned with allocating limited resources to optimize the objective function for the assigned tasks. Due to the concept of optimization, scheduling plays an important role in the manufacturing system. In this research, we consider two-stage multi-family flowshop scheduling problems with batching operations. These family jobs will be processed by a given sequence operation on both stages. Each family requires a setup time and removal time on both stages. Moreover, we also consider two-stage multi-family flowshop scheduling problems with processing identical jobs on each family and each stage may have a number of parallel processors. In this research, the objective is to find a sequence of families and sequence of jobs in each family such that the makespan is minimized. We consider the following scheduling problems:1. A two-stage multi-family flowshop scheduling problems with a batch processor at stage 1 and a discrete processor at stage 2.2. A two-stage multi-family flowshop scheduling problems with a discrete processor on each stage.3. A two-stage multi-family flowshop scheduling problems with a batch processor on each stage.4. A two-stage multi-family flowshop scheduling problems with processing identical jobs in the same family and each stage may have a number of parallel processors.We show that some of the proposed problems are NP-hard and we also design polynomial algorithms for the other problems in the polynomial time.