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# Hobart Inc. is planning to re-configure its distribution network. Potential warehouse locations are Omaha,

Detroit, Tampa, Phoenix, Hartford, and Casper. There are still 4 market regions: North, East, South, and West of United States. Table 2 below presents annual capacities and fixed costs for potential warehouse locations, regional demand, and variable shipping cost per unit between warehouse locations and markets. Given the information above, what is the optimal network configuration for Hobart? That is, where should we locate the warehouses and how should we allocate the demand to minimize the total fixed and variable costs?

(a) Write down the explicit mathematical formulation for this problem using the data in Table 2. That is, define decision variables, objective function, and each of the required constraints using the parameters given in Table 2.

(b) In order to reduce the complexity of coordination, Hobart Inc. now considers the condition that each market should be supplied using only a single warehouse. Taking this consideration into account, what will be the optimal network configuration for Hobart Inc. following the data provided in question 2 with Table 2. Write down the explicit mathematical formulation for this problem using the data in Table 2. That is, define decision variables, objective function, and each of the required constraints using the parameters given in Table 2.

Table 2:
Shipping Cost per unit (\$ / unit)
Markets
North
East
South
West
Capacity
Fixed costs (\$)
Omaha
6
10
35,000
200,000
Detroit
9
12
13
50,000
400,000
Facility
Tampa
14
16
U
40,000
150,000
Phoenix
14
12
3
4
25,000
Hartford
5
w
100,000
12
10
12,000
300,000
Casper
5
7
8
5
35,000
250,000
Demand
45000
20000
30000
30000

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