facility.py
#!/usr/bin/python # Copyright 2018, Gurobi Optimization, LLC # Facility location: a company currently ships its product from 5 plants # to 4 warehouses. It is considering closing some plants to reduce # costs. What plant(s) should the company close, in order to minimize # transportation and fixed costs? # # Note that this example uses lists instead of dictionaries. Since # it does not work with sparse data, lists are a reasonable option. # # Based on an example from Frontline Systems: # http://www.solver.com/disfacility.htm # Used with permission. from gurobipy import * # Warehouse demand in thousands of units demand = [15, 18, 14, 20] # Plant capacity in thousands of units capacity = [20, 22, 17, 19, 18] # Fixed costs for each plant fixedCosts = [12000, 15000, 17000, 13000, 16000] # Transportation costs per thousand units transCosts = [[4000, 2000, 3000, 2500, 4500], [2500, 2600, 3400, 3000, 4000], [1200, 1800, 2600, 4100, 3000], [2200, 2600, 3100, 3700, 3200]] # Range of plants and warehouses plants = range(len(capacity)) warehouses = range(len(demand)) # Model m = Model("facility") # Plant open decision variables: open[p] == 1 if plant p is open. open = m.addVars(plants, vtype=GRB.BINARY, obj=fixedCosts, name="open") # Transportation decision variables: transport[w,p] captures the # optimal quantity to transport to warehouse w from plant p transport = m.addVars(warehouses, plants, obj=transCosts, name="trans") # You could use Python looping constructs and m.addVar() to create # these decision variables instead. The following would be equivalent # to the preceding two statements... # #open = [] #for p in plants: # open.append(m.addVar(vtype=GRB.BINARY, # obj=fixedCosts[p], # name="open[%d]" % p)) # #transport = [] #for w in warehouses: # transport.append([]) # for p in plants: # transport[w].append(m.addVar(obj=transCosts[w][p], # name="trans[%d,%d]" % (w, p))) # The objective is to minimize the total fixed and variable costs m.modelSense = GRB.MINIMIZE # Production constraints # Note that the right-hand limit sets the production to zero if the plant # is closed m.addConstrs( (transport.sum('*',p) <= capacity[p]*open[p] for p in plants), "Capacity") # Using Python looping constructs, the preceding would be... # #for p in plants: # m.addConstr(sum(transport[w][p] for w in warehouses) <= capacity[p] * open[p], # "Capacity[%d]" % p) # Demand constraints m.addConstrs( (transport.sum(w) == demand[w] for w in warehouses), "Demand") # ... and the preceding would be ... #for w in warehouses: # m.addConstr(sum(transport[w][p] for p in plants) == demand[w], "Demand[%d]" % w) # Save model m.write('facilityPY.lp') # Guess at the starting point: close the plant with the highest fixed costs; # open all others # First, open all plants for p in plants: open[p].start = 1.0 # Now close the plant with the highest fixed cost print('Initial guess:') maxFixed = max(fixedCosts) for p in plants: if fixedCosts[p] == maxFixed: open[p].start = 0.0 print('Closing plant %s' % p) break print('') # Use barrier to solve root relaxation m.Params.method = 2 # Solve m.optimize() # Print solution print('\nTOTAL COSTS: %g' % m.objVal) print('SOLUTION:') for p in plants: if open[p].x > 0.99: print('Plant %s open' % p) for w in warehouses: if transport[w,p].x > 0: print(' Transport %g units to warehouse %s' % \ (transport[w,p].x, w)) else: print('Plant %s closed!' % p)
