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**Unformatted text preview: **1 ’ ⊆ V 1 cannot be closed (but can be upgraded). Indicate the current fixed cost and capacity of facility i ϵ V 1 ’as fi ’ and qi ’ , respectively. Moreover, let f i ’’ and q i ’’ be the fixed cost and capacity if facility i ϵ V 1’ is upgraded, respectively. The original CPL model is: Problem 4: Consider the following discrete location problem Min c ୧୨ ∗ x ୧୨ ୨∈ మ ୧∈ భ + f ୧ ∗ y୧ ୧∈ భ Subject to x୧୨ ୧∈ భ = 1, jϵV ଶ d ୨ ∗ x ୧୨ ୨∈ మ ≤ q ୧ ∗ y ୧ , iϵV ଵ y ୧୧∈ భ≤ 2 where /V 1 /=3, /V2 /=7, f=[132,138,147] T, q=[1500,1300,2800] T , d=[52,67,88,47,91,45,68]T and c ij =5.0, i ϵ V 1 , j ϵ V 2. Determine optimal solution of the location problem. (hint: q 1 ≥ ∑ ∈ మ , ∈ ଵ ). Problem 5: Extend the CPL model to the case of demand varying over the planning horizon of 5 time periods. Assume that, once opened, a facility cannot be closed. You need to redefine all variables and parameters with an additional subscript t to indicate time period....

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