Together with process network synthesis for new process design, the retrofit design of chemical processing network has common binary decision variables of unit existence.
Since the pre-terminal set lies in the terminal mode which contains origin, this eliminates the need for binary decision variables to model mode transitions after the trajectory enters in pre-terminal set, thereby reducing the on-line complexity although at the expense of optimality.
Consequently, the mathematical formulation will include binary decision variables with the following constraints: 9) For each edge in the AG, a binary decision variable denoted by (x_{ji}^{k} in {0,1}) is introduced.
The open-or-close decisions for the facilities are binary decision variables and the production and transportation flow decisions are continuous decision variables.
The number of binary decision variables in the resulting MILP is small enough for it to be solved with a solver.
Constraints (7) and (8) show binary decision variables and decision variables of product flow and the related constraints.
Binary decision variables indicate whether a product is set up or not and continuous decision variables reflect the lot size of each product in the block.
The binary decision variables s a reflect the inclusion of an epitope a to the solution set.
For a graph G = (V, E) corresponding to the motif finding problem, where V = V1 ∪... ∪ V N and E = {(u, v): u ∈ V i, v ∈ V j, i ≠ j}, we introduce a binary decision variable x u for every vertex u, and a binary decision variable y uv for every edge (u, v).
For each edge in the AG, a binary decision variable denoted by (x_{ji}^{k} in {0,1}) is introduced.
