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Chapter 5
Network design in the supply chain
Problem (1,2)
Presented by
Mohamed Fawzy

Answer (question 1)

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.Dj = Annual trips needed to state jKi = number of trips that can be handled from a home office As explained, in this model there is no restriction fi = Annualized fixed cost of setting up a home officecij = Cost of a trip from home office i to state jyi = 1 if home office i is open, 0 otherwisexij = Number of trips from home office i to state j. It should be integral and non-negative| 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).

SYMBOL | INPUT| CELL|
Dj| Annual trips needed to state j| E7:E22|
cij| Transportation cost from office i to state j| G7:G22,I7:I22,K7:K22,M7:M22| fi| fixed cost of setting up office i| G26,I26,K26,M26|
xij| 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)With this we solve the model to obtain the following results: State | Total # of trips | Trips from LA | Cost from LA | Trips from Tulsa | Cost from Tulsa | Trips from Denver | Cost From Denver | Trips from Seattle | Cost from Seattle | Washington | 40 | - | 150 | - | 250 | - | 200 | 40 | 25 | Oregon | 35 | - | 150 | - | 250 | - | 200 | 35 | 75 | California | 100 | 100 | 75 | - | 200 | - | 150 | - | 125 | Idaho | 25 | - | 150 | - | 200 | - | 125 | 25 | 125 | Nevada | 40 | 40 | 100 | - | 200 | - | 125 | - | 150 | Montana | 25 | - | 175 | - | 175 | - | 125 | 25 | 125 | Wyoming | 50 | - | 150 | - | 175 | 50 | 100 | - | 150 | Utah | 30 | - | 150 | - | 150 | 30 | 100 | - | 200 | Arizona | 50 | 50 | 75 | - | 200 | - | 100 | - | 250 | Colorado | 65 | - | 150 | - | 125 | 65 | 25 | - | 250 | New Mexico | 40 | - | 125...
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