1 Milk truck routing

A local dairy wishes to determine the minimum cost plan for picking up its daily supply of milk from the four farms that send their milk to the dairy. The distance (in miles) between the dairy (D) and each farm, and also between each pair of farms, is given in the table below. The table also gives the amount of milk to be collected from each farm each day. (The distance between locations is the same in both directions, so for each pair of locations the distance is only reported once.)

The dairy has one milk truck that can carry at most 10 tons of milk at a time. Because of the weight limit, the milk truck will need to make multiple trips each day to collect the milk from all the farms. Each trip may pick up milk from one or more farms, provided the total collected in the trip does not exceed the truck limit.

1.1 Problem

Formulate an integer program to help the dairy assign farms to the trips so that the total daily cost of picking up the milk is minimized. (Hint: model the problem as a set covering problem. The first step will be to list all possible routes a truck can take.)

**I am interested in the objective functions and constraints and how you got the constraints. Thank You

Distance D F1 F2 F3 F4 D 5 12 7 15 F1 4 10 7 F2 14 20 F3 8 F1 F2 F3 F4 Milk (tons) 7 2 6 3 - Distance D F1 F2 F3 F4 D 5 12 7 15 F1 4 10 7 F2 14 20 F3 8 F1 F2 F3 F4 Milk (tons) 7 2 6 3