Balancing straight and U-shaped assembly lines with resource dependent task times

The basic assumption of assembly line balancing is that every task's time is fixed. However, in practice, different processing alternatives may be available to process a task with different times. The problem in this case is to assign tasks and resources to work stations that minimise total cost and so-called resource dependent assembly line balancing (RDALB) in the literature. This study proposes a new integer programming formulation for RDALB. This formulation is then modified to develop a formulation for RDULB problem in U-shaped assembly lines. To the best knowledge of the authors, this study is the first RDULB study and the developed formulation is the first RDULB formulation. The proposed formulations are illustrated and validated using several examples. An experimental analysis is also conducted to examine the percent improvement in total cost when the line layout is switched into the U-shaped from the straight line shape. Experimental results show that an improvement in total operating cost is obtained when the straight line is switched into the U-shaped line configuration. Results also show that percentage improvement in total operating cost is significantly greater for problem instances having a large number of tasks and having greater values for the strength of the precedence relationships among tasks.