Modified Max-Plus Linear representation for inserting time buffers

The Max-Plus Linear (MPL) representation is known as a useful solution of scheduling problems for a class of discrete event systems. In such systems, an initial schedule is frequently changed due to unpredictable disturbances. On the other hand, the Critical Chain Project Management (CCPM) method is an effective management tool for protecting projects from delays. In view of this, we have proposed a method of applying the concepts in the CCPM framework to the MPL representation, to control undesirable state changes. In our previous method, several time buffers were virtually inserted as new processes to avoid delays. With this method, however, it is difficult to figure out the relationship between the original structure and the modified one after the CCPM has been applied. Hence this paper proposes a method for taking into account time buffers without installing new virtual processes in the MPL-CCPM representation.