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Co m b i n e d  P r o c e s s I n t e g r a t i o n a n d O p t i m i z a t i o n    181


                     FIGURE 8.12        1            2
                     S-graph            U1    5     U2     1      11  Cream 1
                     representing the
                     recipe for the case   3         4
                     study of           U3    7     U2     1      12  Cream 2
                     Example 8.3.
                                        5            6
                                        U4    1     U2     1      13  Conditioner

                                        7            8            14  Shampoo
                                        U5    8     U2     1

                                        9            10
                                        U6    6     U2     1      15  Lotion





                        P3                 Task 8 (Batch 1)
                        P2               Task 4 (Batch 1) Task 4 (Batch 2)
                      Equipment Units  V4  Task 3 (Batch 1)
                        P1



                        V3
                        V2  Task 7 (Batch 1)
                        V1 Task 3 (Batch 2)
                                        78         12             19
                                               Time [h]

                     FIGURE 8.13  Globally optimal schedule for the case study of Example 8.3.




                     integer programming (Douglas, 1988; Biegler, Grossman, and
                     Westerberg, 1997), and integration with PNS (Nagy et al., 2001). In
                     contrast, scheduling and Heat Integration of batch processes are
                     both complex optimization problems and quite different in nature.
                        The problems of scheduling and Heat Integration could be solved
                     sequentially (in either order). Yet because the solution of one problem
                     will affect the other, the result of this simplistic, sequential approach
                     is usually poor. A better solution may result from an integrated
                     consideration of scheduling and Heat Integration. Since there were
                     not too many methods for solving this integrated problem, the
                     effective design and operation of integrated batch systems required
                     development of a new method (Adonyi et al., 2003). The goal was to
                     operate simultaneously those tasks that involve potential heat
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