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| Symbol | Description |
|
| Index set of heats, |
| Index of heat, |
| Index set of slabs, |
| Index of slab, ; the index is sorted according to times when slabs are cut in chronological order |
| Sub index set of slabs contained in heat , |
| Casting duration of slab of heat |
| Index of processes, , process 1 is steelmaking, process 2 is LF refining, process 3 is RH refining, and process 4 is continuous casting |
| Index set of machines in process , |
| Index of machine, |
| Processing time of heat on machine |
| Heat casting sequence relationship. when the heat is casted immediately after heat , otherwise |
| Minimum/maximum delay from machine to machine |
| Processing time of slab in HR process |
| Minimum/maximum delay between two continuously rolled slabs |
| Shortest delivery time from the position where slab is cut to reheating furnace |
| Minimum residence time of slab in reheating furnace |
| Slab rolling sequence relationship; when Slab is rolled immediately after slab , otherwise |
|
| , if heat is assigned to machine , and , otherwise, |
| if Heat and heat are assigned on the same machine and heat is processed before heat , and , otherwise, |
| Start time of heat in process , |
| Time when slab is cut, |
| Time when slab is charged into reheating furnace |
| The latest finish time of all heats in the continuous casting process |
| The latest finish time of all slabs in the HR process |
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