Separate and carousel type allocations of workers in a U-shaped production line

In this paper, we consider a U-shaped production line with multiple multi-function workers. Each multi-function worker takes charge of multiple machines. The processing, operation, and walking times are assumed to be stochastic. We consider two types of allocations of workers to machines, a separate allocation and a carousel allocation. In the separate allocation, each worker takes charge of a unique set of machines and therefore at each machine the same worker operates items every cycle. In the carousel allocation, all workers take charge of all machines in the same order. We derive upper and lower bounds for the expected overall cycle times in U-shaped production lines with these allocations, and propose approximate expressions for the expected overall cycle times. We also show that when the processing, operation, and walking times are constant, the overall cycle time in the carousel allocation is less than or equal to that in the separate allocation under some conditions on the walking times and the number of machines each worker deals with in the separate allocation. In numerical study we discuss the exactness of the proposed approximations and compare these allocations.