# Assignment 1.pdf - Assignment #1 INDU6141 Logistic Network...

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Assignment #1 INDU6141 Logistic Network ModelsDue date: Oct. 21, 2019Hard copy submitted at the beginning of the class and before 6 pm. No submission through email isaccepted.Problem 1.Assume that, for a certain company, the estimated annual sales to service level curve r(x) hasbeen determined by means of a simulation method. The resulting equation is r(x) = 950000x - 328000x2,where x denotes the percentage of customers served within 24 hours (e.g. if x=0.7, 70% of customers areserved within 24 hours); r(x) is expressed in \$. The annual logistics costs (in \$) are estimated as 280,000,320,000, 380,000, 410,000, 460,000 and 510,000, with respect to the following values of service leveloffered to customers: 50%, 60%, 70%, 80%, 90% and 100%, respectively. Determine the service level atwhich the maximum estimated annual profit is achieved.Problem 2:Your company has to close 20 of its 125 warehouses. Suppose the CPL hypotheses hold. Howwould you define V1? What is the value of p?Problem 3:Modify the CPL model to take into account that a subset of already existing facilities V1Vcannot be closed (but can be upgraded). Indicate the current fixed cost and capacity of facility i ϵ V1as fiand qi, respectively. Moreover, let fi’’and qi’’be the fixed cost and capacity if facility i ϵ V1is upgraded,respectively.The original CPL model is:Problem 4:Consider the following discrete location problemMin ෍ ෍c୧୨∗ x୧୨୨∈୚୧∈୚+ ෍ f∗ y1
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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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