prodmix_soco.py

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"""
Copyright (c) by Joao Pedro PEDROSO, Masahiro MURAMATSU and Mikio KUBO, 2012
"""
from pyscipopt import Model, quicksum, multidict
 
 
def prodmix(I, K, a, p, epsilon, LB):
    """prodmix:  robust production planning using soco
    Parameters:
        I - set of materials
        K - set of components
        a[i][k] -  coef. matrix
        p[i] - price of material i
        LB[k] - amount needed for k
    Returns a model, ready to be solved.
    """
 
    model = Model("robust product mix")
 
    x, rhs = {}, {}
    for i in I:
        x[i] = model.addVar(vtype="C", name="x(%s)" % i)
    for k in K:
        rhs[k] = model.addVar(vtype="C", name="rhs(%s)" % k)
 
    model.addCons(quicksum(x[i] for i in I) == 1)
    for k in K:
        model.addCons(rhs[k] == -LB[k] + quicksum(a[i, k] * x[i] for i in I))
        model.addCons(quicksum(epsilon * epsilon * x[i] * x[i] for i in I) <= rhs[k] * rhs[k])
 
    model.setObjective(quicksum(p[i] * x[i] for i in I), "minimize")
 
    model.data = x, rhs
    return model
 
 
def make_data():
    """creates example data set"""
    a = {(1, 1): .25, (1, 2): .15, (1, 3): .2,
         (2, 1): .3, (2, 2): .3, (2, 3): .1,
         (3, 1): .15, (3, 2): .65, (3, 3): .05,
         (4, 1): .1, (4, 2): .05, (4, 3): .8
         }
    epsilon = 0.01
    I, p = multidict({1: 5, 2: 6, 3: 8, 4: 20})
    K, LB = multidict({1: .2, 2: .3, 3: .2})
    return I, K, a, p, epsilon, LB
 
 
if __name__ == "__main__":
    I, K, a, p, epsilon, LB = make_data()
    model = prodmix(I, K, a, p, epsilon, LB)
    model.optimize()
    print("Objective value:", model.getObjVal())
    x, rhs = model.data
    for i in I:
        print(i, ": ", model.getVal(x[i]))