A mathematical model of a production system is a description of the system using mathematical concepts equations, graphs, process maps. The model provides an abstraction that reduces the system to its essential characteristics.
Using mathematical tools such as linear programming and queueing theory, the mathematical model representation can help explain the behavior of the system. For example, models can explain how different components of the system interact with each other. They can also make predictions about future behavior of the system, such as maximum throughput achievable, where bottlenecks are located, and how much inventory is built up as the system operates.
Any modeling of any production system should incorporate the relationships of Operations Science. It is common for companies to construct models that poorly reflect reality because of a limited understanding of Operations Science. Math is not the same as science. One can, and people often do, construct precise mathematical models that are wrong because the math does not reflect underlying Operations Science driving system behavior.