Abstract
In this paper, we focus on an in-line machine model. This model represents systems for the manufacturing of a product in large quantities. Recently, studies relating to the collision probability between jobs have been conducted in such models. In this paper, we extend the known models to a generalized version by considering delivery time between machines. We first present a method for computing a schedule of jobs in the generalized model. Then, we show that the collision probability for the generalized model is the same as that for the model without delivery time. We call this property the redundancy of delivery time. Next, we introduce two optimization problems with collision probability for the generalized model. Using the redundancy of delivery time, it is shown that these optimization problems are equivalent to simpler problems. This finding may prove to be very useful when considering optimization problems with collision probability.
