b. For this part, the single arc that leaves each service facility is replaced by 3 arcs representing the piecewise linear service cost.

A typical service station (say station 1) has an arc structure as below. The unit cost and upper bound are given for each arc.

Arc 1: (p1, b1/3); Arc 2: (1.2 p1, b1/3); Arc 3: (1.5p1, b1/3).

Note that cost is increasing with quantity, so the linear solver handles the convex cost function correctly.

c. For those locations designated as collection facilities, provide two nodes, pi and pi’. The arc between them has the capacity of the facility as an upper bound. We assume that there are k collection facilities identified and numbered from 1 to k. There are m service facilities defined numbered 1 through m.

An arc passing from the collection facility i to the service facility j, has the unit cost e(i, j).