Restricted Search over All Possible Scheduling

All options to this approach aim to calculate a schedule for a specific number of operations and after that to schedule the initial operation or other operations and to iterate this process that is rolling horizon optimization.

Each possible sequence of operations can be presented via a decision tree. All edges or branches of the tree corresponds to an operation's assignment to a station, all node presenting a partial schedule that is determined via the sequences of edges which lead from root to this node. From all nodes, several edges are originating that present all probable next assignments of operations to stations. The concept of bound and branch algorithms is to construct a partial decision tree that causes the optimal solution. The tree is decreased via cutting off those branches that will only cause solutions those are worse than the best solution found thus far or can be excluded via a bound of the cost functional on the optimum that can be calculated from the solutions acquired thus far. In the recent case that is for scheduling along with respect to minimal tardiness no capable bounds are identified hence a consideration of all potentially optimal solutions is merely feasible in several cases along with various jobs and various machines. Particularly, this is not possible to provide efficient bounds in dynamic situations.