transshipment.py

# http://index-of.es/Varios-2/Practical%20Python%20AI%20Projects%20Mathemathical%20Models%20of%20Optimization%20Problems%20with%20Google%20OR-Tools.pdf
# coding: utf-8
"""
Example code for solving the transshipment problem. (pg. 111)

Input is an NxN numpy matrix (referenced here as D)
where row N is the demand and column N is the supply for each location 0 through N-1.

To solve, call the solve_model() function with matrix D as the input.
"""
import numpy as np
from ortools.linear_solver import pywraplp

def ObjVal(x):
 return x.Objective().Value()
 
def SolVal(x):
    if type(x) is not list:
        return 0 if x is None else x if isinstance(x, (int, float)) else x.SolutionValue() if x.Integer() is False else int(x.SolutionValue())
    elif type(x) is list:
        return [SolVal(e) for e in x]
        
def newSolver(name):
    return pywraplp.Solver(name,\
                           pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
 
def solve_model(D):
    s = newSolver('Transshipmentuproblem')
    n = len(D[0]) - 1
    B = sum([D[-1][j] for j in range(n)])
    G = [[s.NumVar(0, B if D[i][j] else 0, '') for j in range(n)] for i in range(n)]
    
    for i in range(n):
        s.Add(sum(G[i][j] for j in range(n)) - sum(G[j][i] for j in range(n)) == D[i][-1] - D[-1][i])
        
    Cost = s.Sum(G[i][j]*D[i][j] for i in range(n) for j in range(n))
    s.Minimize(Cost)
    rc = s.Solve()
    return rc, ObjVal(s), SolVal(G)