def formulate(bpp, args):
prob = DipProblem("Bin Packing")
assign_vars = LpVariable.dicts("x", [(i, j) for i in bpp.BINS
for j in bpp.ITEMS],
cat=LpBinary)
use_vars = LpVariable.dicts("y", bpp.BINS, cat=LpBinary)
waste_vars = LpVariable.dicts("w", bpp.BINS, 0, None)
prob += lpSum(waste_vars[i] for i in bpp.BINS), "min_waste"
for j in bpp.ITEMS:
prob += lpSum(assign_vars[i, j] for i in bpp.BINS) == 1
for i in bpp.BINS:
prob.relaxation[i] += (lpSum(bpp.volume[j] * assign_vars[i, j]
for j in bpp.ITEMS) +
waste_vars[i] == bpp.capacity * use_vars[i])
for i in bpp.BINS:
for j in bpp.ITEMS:
prob.relaxation[i] += assign_vars[i, j] <= use_vars[i]
if args.antisymmetryCutsBins:
for m in range(0, len(bpp.BINS) - 1):
prob += use_vars[bpp.BINS[m]] >= use_vars[bpp.BINS[m + 1]]
if args.antisymmetryCutsItems:
for m in range(0, len(bpp.BINS)):
for n in range(0, len(bpp.ITEMS)):
if m > n:
i = bpp.BINS[m]
j = bpp.ITEMS[n]
prob += assign_vars[i, j] == 0
# Attach the problem data and variable dictionaries
# to the DipProblem
prob.bpp = bpp
prob.assign_vars = assign_vars
prob.use_vars = use_vars
prob.waste_vars = waste_vars
prob.tol = pow(pow(2, -24), old_div(2.0, 3.0))
return prob
def formulate(args):
FIXED_COST = None
ASSIGNMENTS = None
ASSIGNMENT_COSTS = None
if args.module:
m = ilib.import_module(args.module)
LOCATIONS = m.LOCATIONS
PRODUCTS = m.PRODUCTS
DEMAND = m.DEMAND
CAPACITY = m.CAPACITY
if hasattr(m, 'FIXED_COST'):
FIXED_COST = m.FIXED_COST
if hasattr(m, 'ASSIGNMENTS'):
ASSIGNMENTS = m.ASSIGNMENTS
if hasattr(m, 'ASSIGNMENT_COSTS'):
ASSIGNMENT_COSTS = m.ASSIGNMENT_COSTS
else:
LOCATIONS = range(args.numLocations)
PRODUCTS = range(args.numProducts)
DEMAND = [int(i) for i in args.demands]
CAPACITY = args.capacity
if args.fixedCosts != None:
FIXED_COST = [int(i) for i in args.fixedCosts]
if FIXED_COST == None:
FIXED_COST = {i: 1 for i in LOCATIONS}
if ASSIGNMENTS == None:
ASSIGNMENTS = [(i, j) for i in LOCATIONS for j in PRODUCTS]
if ASSIGNMENT_COSTS == None:
ASSIGNMENT_COSTS = {i: 0 for i in ASSIGNMENTS}
prob = DipProblem("Facility Location")
assign_vars = LpVariable.dicts("x", ASSIGNMENTS, 0, 1, LpBinary)
use_vars = LpVariable.dicts("y", LOCATIONS, 0, 1, LpBinary)
prob += (lpSum(use_vars[i] * FIXED_COST[i] for i in LOCATIONS) +
lpSum(assign_vars[j] * ASSIGNMENT_COSTS[j]
for j in ASSIGNMENTS), "min")
# assignment constraints
for j in PRODUCTS:
prob += lpSum(assign_vars[(i, j)] for i in LOCATIONS) == 1
# Aggregate capacity constraints
for i in LOCATIONS:
prob.relaxation[i] += lpSum(
assign_vars[(i, j)] * DEMAND[j]
for j in PRODUCTS) <= CAPACITY * use_vars[i]
# Disaggregate capacity constraints
for i, j in ASSIGNMENTS:
prob.relaxation[i] += assign_vars[(i, j)] <= use_vars[i]
prob.LOCATIONS = LOCATIONS
prob.PRODUCTS = PRODUCTS
prob.assign_vars = assign_vars
prob.use_vars = use_vars
return prob