PULP example

pulp_example.py

import pulp as lp
from pulp import lpSum
from pulp import LpVariable


def mixture():
	prob = lp.LpProblem("example mixture", lp.LpMinimize)
	
	# Parameters
	elements = ["Lead", "Zinc", "Tin"]
	alloy_no = range(1, 10)
	
	alloy = {1:{"Lead": 0.2, "Zinc": 0.3, "Tin": 0.5},
	         2:{"Lead": 0.5, "Zinc": 0.4, "Tin": 0.1},
	         3:{"Lead": 0.3, "Zinc": 0.2, "Tin": 0.5},
	         4:{"Lead": 0.3, "Zinc": 0.4, "Tin": 0.3},
	         5:{"Lead": 0.3, "Zinc": 0.3, "Tin": 0.4},
	         6:{"Lead": 0.6, "Zinc": 0.3, "Tin": 0.1},
	         7:{"Lead": 0.4, "Zinc": 0.5, "Tin": 0.1},
	         8:{"Lead": 0.1, "Zinc": 0.3, "Tin": 0.6},
	         9:{"Lead": 0.1, "Zinc": 0.1, "Tin": 0.8}}
	
	costs = {1: 7.3,
	         2: 6.9,
	         3: 7.3,
	         4: 7.5,
	         5: 7.6,
	         6: 6.0,
	         7: 5.8,
	         8: 4.3,
	         9: 4.1}
	
	target = {"Lead": 0.3,
	          "Zinc": 0.3,
	          "Tin" : 0.4}
	
	# Variable
	alloy_vars = LpVariable.dicts("Alloy", alloy_no, 0)
	
	# Objective
	prob += lpSum([costs[i]*alloy_vars[i] for i in alloy_no])
	
	# Constraints
	for i in alloy_no:
		prob += lpSum([alloy[i][j] for j in elements]) == 1
	
	for j in elements:
		prob += lpSum([alloy[i][j] * alloy_vars[i] for i in alloy_no]) == target[j]
	
	print prob
	stat = prob.solve()
	print lp.LpStatus[stat]

	if lp.LpStatus[stat] == "Optimal":
		for v in prob.variables():
			print v.name, "=", v.varValue
			
		print "Cost = ", lp.value(prob.objective)

def transport():
	prob = lp.LpProblem("example transport", lp.LpMinimize)
	
	# Parameters
	fact = [1, 2]
	dest = ["a", "b", "c"]
	
	upper = {1: 250, 2:450}
	demands = {"a":200, "b":200, "c":200}
	cost = {1:{"a":3.4, "b":2.2, "c":2.9},
	        2:{"a":3.4, "b":2.4, "c":2.5}}

	# Variable
	trans_var = lp.LpVariable.dicts("dest", (fact, dest), 0)
	
	# Objective
	Routes = [(i, j) for i in fact for j in dest]
	prob += lpSum([cost[i][j] * trans_var[i][j] for (i, j) in Routes])
	
	# Constraints
	for i in fact:
		prob += lpSum([trans_var[i][j] for j in dest]) <= upper[i]
	
	for j in dest:
		prob += lpSum([trans_var[i][j] for i in fact]) == demands[j]
		
	
	# Result
	print prob
	stat = prob.solve()
	print lp.LpStatus[stat]
	if lp.LpStatus[stat] == "Optimal":
		for v in prob.variables():
			print v.name, "=", v.varValue
			
		print "Cost = ", lp.value(prob.objective)
		
if '__main__' == __name__:
	mixture()
	transport()