Models

Question 1

Transportation

Answer 1

let Cij be the cost per units of transportation from origin i to destination j
let Xij be the no. of units shipped from origin i to destination j
Min sum of all CijXij
s.t. sum of all routes going out of i ≤ Si (supply)
sum of all routes coming in of j ≤ Dj (demand)

Question 2

Transhipment

Answer 2

let Xij be the no. of units shipped from node i to node j
let Cij be the cost per unit shipped from node i to node j
Min sum of all CijXij
s.t. O - I ≤ Si (origin node)
O - I = 0 (transhipment node)
I - O = Dj (destination node)

Question 3

Assignment

Answer 3

let Xij (binary) - 1 if agent i is assigned to task j, 0 otherwise
let Cij be the cost of assigning agent i to task j
Min sum of all CijXij
s.t. sum of all task for each agent ≤ 1 (k if the agent can do k no. of task)
sum of all agents possible to be assigned to the task = 1 (if not enough agents, make imaginary agents and cont.)