HW2Key - HOMEWORK 2 SOLUTION KEY 5.1 (a) The objective of...

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HOMEWORK 2 SOLUTION KEY 5.1 (a) The objective of this model is to decide optimal locations of home offices, and number of trips from each home office, so as to minimize the overall network cost. The overall network cost is a combination of fixed costs of setting up home offices and the total trip costs. There are three constraint sets in the model. The first constraint set requires that a specified number of trips be completed to each state j , the second constraint set limits the number of trips that each consultant can take and the third constraint set prevents trips from a home office i unless there is at least one consultant assigned to that office. Also, note that there is no capacity restriction at each of the home offices. Optimization Model: Parameters : n = 4 : possible home office locations. m = 16 : number of states. D j = Annual trips needed to state j K = maximum number of consultants that can be assigned to a home office f i = Annualized fixed cost of setting up a home office c ij = Cost of a trip from home office i to state j Decision variables: y i = 1 if home office i is open, 0 otherwise x ij = Number of trips from home office i to state j. It should be integral and non-negative z i = the number of consultants at site I (for the second method) MODEL: There are two different methods to model this problem. First Method: In this first method, instead of defining a decision variable for the number of consultants assigned to a home site, you can simply solve the following model. Then you can calculate the number of consultants needed at site i by 1 /25 n ij i x = for all j =1,…,m. {} 11 1 1 1 Minimize Subject To for all 1,. .., for all 1,. .., 0 for all 1,. .. nn m i i ij ij ii j n ij j i m ij i j ij fy cx xD j m xM y i n xZ i == = = = + + ≤= ∈∪ = ∑∑ , ; 1,. .., 0,1 for all 1,. .., i nj m yi n = ∈=
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Second Method: 11 1 1 1 Minimize Subject To for all 1,. .., 25 for all 1,.
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HW2Key - HOMEWORK 2 SOLUTION KEY 5.1 (a) The objective of...

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