The state of Calizona will soon be opening centers14 in 12 of its county seats i = 1,

c, 100 to promote solid waste recycling programs. Each selected site will service a district of surrounding counties.

The state wants to minimize the sum of distances di, j populations pi in counties i must travel to their district center at j. But they would also like to come as close as possible (in total deviation) to having 3 centers in each of the 4 Environment Department regions. Counties i = 1,

c, 12 make up region 1, i = 13,

c, 47 region 2, i = 48,

c, 89 region 3, and i = 90,

c, 100 region 4.

(a) Formulate a 2-objective ILP model of this facility location problem using the main decision variables 1i, j = 1,

c, 1002 xi, j ! •

1 if county i is served by a center at j 0 otherwise xi ! e 1 if country j gets a center 0 otherwise

(b) Explain the meaning of an efficient point solution to your model of part

(a) and describe how one could be computed.