The dioid algebraic model, which is developed in this paper, captures the discontinuous nature of Discrete-Event Dynamic Systems and has widespread applicational capabilities. As a further improvement over existing dioid algebraic models, decision making capability is introduced to the developed dioid algebraic model. With this new capability, sequencing decisions at each machine can be represented in the model. Furthermore, the developed algebraic model is capable of representing job and resource unavailability, technological constraints, alternative process plans, and is easily modifiable to include new jobs and exclude finished jobs. In a possible application, the model can be used in representing dynamic scheduling problems and can be used as an important part of a real-time control and scheduling scheme of a manufacturing system. (C) 2004 Elsevier B.V. All rights reserved.