The assembly system under consideration is composed with several machines, and some of these machines may be identical or able to perform the same operations. The manufacturing system is fully automated, and semi-finished products or components are not stored during the process. A limited flexibility exists since the manufacturing times can be extended within certain limits at the expense of the unavailability of the resource. There are no conflicts between the resources; in other words, the same machine is not used to perform different operations for a same product. Due to the intensity of the flow of products to be manufactured, it is not allowed to reschedule products which have been previously scheduled. Thus, when a new product requirement arrives in the system, we have to take advantage of the idle time windows. The goal is to complete the product as soon as possible. We give a real-time scheduling algorithm which guarantees an optimal makespan to any product which arrives in the assembly system. A numerical example is provided to illustrate this approach.