MIE376 Mathematical Programming Lecture Notes Daniel Frances 2011 4 or Max Σ (90P 1 i + 80 i P 2 i ) µ i + Σ (70Q 1 i + 60Q 2 i ) λ i Σ (8P 1 i + 6P 2 i ) µ i + Σ (7Q 1 i + 5 i Q 2 i ) λ i + s 1 = 80; Σµ i =1 Σλ i = 1 µ i , λ i , s 1 ≥ 0 Note that since we are assuming that ALL the potential offers are known in advance, therefore the variables in this new LP are the linear combination coefficients µ i , and λ e as well as the slack iron s1. It is at this point that we start to see a hint of the same phenomenon as column generation. The potential offers are the equivalent of the Cut Types, whereas µ i and λ i . perform the same role as the number of each of the cut-types to be selected. Dantzig-Wolfe Iterations Before we start we always need to be able to refer to the master coordinator problem Max Σ (90P 1 i + 80 i P 2 i ) µ i + Σ (70Q 1 i + 60Q 2 i ) λ i Σ (8P 1 i + 6P 2 i )
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Linear combination, Coordinator, Offers, slack iron s1, master coordinator problem