Chapter 5 - Chapter 5: Network Design in the Supply Chain...

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Unformatted text preview: Chapter 5: Network Design in the Supply Chain Exercise Solutions 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 two constraint sets in the model. The first constraint set requires that a specified number of trips be completed to each state j and the second constraint set prevents trips from a home office i unless it is open. Also, note that there is no capacity restriction at each of the home offices. While a feasible solution can be achieved by locating a single home office for all trips to all states, it is easy to see that this might not save on trip costs, since trip rates vary between home offices and states. We need to identify better ways to plan trips from different home offices to different states so that the trip costs are at a minimum. Thus, we need an optimization model to handle this. Optimization model: n = 4: possible home office locations. m = 16: number of states. D j = Annual trips needed to state j K i = number of trips that can be handled from a home office As explained, in this model there is no restriction f i = Annualized fixed cost of setting up a home office c ij = Cost of a trip from home office i to state j 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 1 1 1 n i 1 m j 1 Subject to 1 (5.1) 1 (5.2) {0,1} 1,... (5.3) n n m i i ij ij i i j ij j ij i i i Min f y c x x D for j ,...,m x K y for i ,...,n y for i n = = = = = + = = = = & & Please note that (5.2) is not active in this model since K is as large as needed. However, it will be used in answering (b). 1 SYMBOL INPUT CELL D j Annual trips needed to state j E7:E22 c ij Transportation cost from office i to state j G7:G22,I7:I22, K7:K22,M7:M22 f i fixed cost of setting up office i G26,I26,K26,M26 x ij number of consultants from office i to state j. F7:F22,H7:H22, J7:J22,L7:L22 obj. objective function M31 5.1 demand constraints N7:N22 (Sheet SC consulting in workbook exercise5.1.xls) 2 With this we solve the model to obtain the following results: State Tot al # of trips Trip s from LA Cost from LA Trip s from Tuls a Cost from Tulsa Trips from Denve r Cost From Denver Trips from Seattl e Cost from Seattle Washington 40 - 1 50 - 2 50 - 2 00 4 0 25 Oregon 35 - 1 50 - 2 50 - 2 00 3 5 75 California 10 0 10 0 75 - 2 00 - 1 50 - 1 25 Idaho 25 - 1 50 - 2 00 - 1 25 2 5 1 25 Nevada 40 4 0 1 00 - 2 00 - 1 25 - 1 50 Montana 25 - 1 75 - 1 75 - 1 25 2 5 1 25 Wyoming 50 - 1 50 - 1 75 5 0 1 00 - 1 50 Utah 30 - 1 50 - 1 50 3 0 1 00 - 2 00 Arizona 50 5 0 75 - 2 00 - 1 00 - 2 50 Colorado 65 - 1 50 - 1 25 6 5 25 - 2 50 New Mexico 40 - 1 25 - 1 25 4 0 75 - 3 00 North Dakota 30 - 3 00 - 2 00 3 0 1 50 - 2 00 South Dakota 20 0 3 00 - 1 75 2 0 1 25 - 2 00 Nebraska 30 -...
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Chapter 5 - Chapter 5: Network Design in the Supply Chain...

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