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594 CHAPTER 10 Dual Angular Structure with Linking Columns In this type of decomposition, the blocks forming the constraint matrix are linked by a number of variables (columns) as illustrated in Figure 9.3. This structure has a primal-dual relationship with the Block Angular Structure described above. Again, for our hypothetical plant example, a structure of this form can be associated to the case when there are a few variable outside factors that effect all plants. X X X X Z Z X X X X X X X X X X X X X Figure 9.3 Dual Angular Structure. Z Z Z Z Z Block and Dual Angular Structures This is the most general form of decomposition where the blocks forming the constraint matrix have both linking rows and columns as illustrated in Figure 9.4. The decisions involved for the hypothetical plant example now include both resource sharing and external factors. X X Z X X Z X X X Z X X X Z X X X Z X X Z X X Z Y Y Y Y Y Y Y A Figure 9.4 Block and Dual Angular Structure