'''******************************************************* * Python Example Problems * * * * file coco.py * * Example for the use of the Python language * * (Complete Coco Problem. * * Specify phase by PHASE parameter. * * Data input in the model, not via data files.) * * * * (c) 2018-2024 Fair Isaac Corporation * *******************************************************''' import xpress as xp PHASE = 5 '''* Phase = 3: Multi-period parameterised model; mines always open * Phase = 4: Mines may open/closed freely; when closed save 20000 per month * Phase = 5: Once closed always closed; larger saving ''' NT = 4 # Number of time periods RP = [0, 1] # Range of products (p) RF = [0, 1] # Range of factories (f) RR = [0, 1] # Range of raw materials (r) RT = [i for i in range(NT)] # time periods (t) CPSTOCK = 2.0 # Unit cost to store any product p CRSTOCK = 1.0 # Unit cost to store any raw mat. r MXRSTOCK = 300 # Max. amount of r that can be stored each f and t Post = [i for i in range(0, NT+1)] prob = xp.problem() # Amount of product p made at factory f make = prob.addVariables(RP, RF, RT, name='make') # Amount of product p sold from factory f in period t sell = prob.addVariables(RP, RF, RT, name='sell') # Amount of raw material r bought for factory f in period t buy = prob.addVariables(RR, RF, RT, name='buy') # Stock level of product p at factory f at start of period t pstock = prob.addVariables(RP, RF, Post, name='pst') # Stock level of raw material r at factory f at start of period t rstock = prob.addVariables(RR, RF, Post, name='rst') # 1 if factory f is open in period t, else 0 openm = prob.addVariables(RF, RT, name='openm', vartype=xp.binary) REV = [[400, 380, 405, 350], [410, 397, 412, 397]] CMAKE = [[150, 153], [75, 68]] CBUY = [[100, 98, 97, 100], [200, 195, 198, 200]] COPEN = [50000, 63000] REQ = [[1.0, 0.5], [1.3, 0.4]] MXSELL = [[650, 600, 500, 400], [600, 500, 300, 250]] MXMAKE = [400, 500] PSTOCK0 = [[50, 100], [50, 50]] RSTOCK0 = [[100, 150], [50, 100]] # Objective: maximize total profit MaxProfit = ( xp.Sum(REV[p][t] * sell[p, f, t] for p in RP for f in RF for t in RT) - # revenue xp.Sum(CMAKE[p][f] * make[p, f, t] for p in RP for f in RF for t in RT) - # prod. cost xp.Sum(CBUY[r][t] * buy[r, f, t] for r in RR for f in RF for t in RT) - # raw mat. cost xp.Sum(CPSTOCK * pstock[p, f, t] for p in RP for f in RF for t in range(1, NT+1)) - # p stor. cost xp.Sum(CRSTOCK * rstock[r, f, t] for r in RR for f in RF for t in range(1, NT+1))) # r stor. cost if PHASE == 4: # Factory fixed cost MaxProfit -= xp.Sum((COPEN[f] - 20000) * openm[f, t] for f in RF for t in RT) elif PHASE == 5: MaxProfit -= xp.Sum(COPEN[f] * openm[f, t] for f in RF for t in RT) prob.setObjective(MaxProfit, sense=xp.maximize) # Product stock balance prob.addConstraint(pstock[p, f, t+1] == pstock[p, f, t] + make[p, f, t] - sell[p, f, t] for p in RP for f in RF for t in RT) # Raw material stock balance prob.addConstraint(rstock[r, f, t+1] == rstock[r, f, t] + buy[r, f, t] - xp.Sum(REQ[p][r]*make[p, f, t] for p in RP) for r in RR for f in RF for t in RT) # Capacity limit at factory f prob.addConstraint(xp.Sum(make[p, f, t] for p in RP) <= MXMAKE[f] * openm[f, t] for f in RF for t in RT) # Limit on the amount of prod. p to be sold prob.addConstraint(xp.Sum(sell[p, f, t] for f in RF) <= MXSELL[p][t] for p in RP for t in RT) # Raw material stock limit prob.addConstraint(xp.Sum(rstock[r, f, t] for r in RR) <= MXRSTOCK for f in RF for t in range(NT)) if PHASE == 5: # Once closed, always closed prob.addConstraint(openm[f, t+1] <= openm[f, t] for f in RF for t in range(NT - 1)) # Initial product levels prob.addConstraint(pstock[p, f, 1] == PSTOCK0[p][f] for p in RP for f in RF) # Initial raw material levels prob.addConstraint(rstock[r, f, 1] == RSTOCK0[r][f] for r in RR for f in RF) if PHASE < 4: prob.addConstraint(openm[f, t] == 1 for f in RF for t in RT) prob.optimize() # Solve the LP or MIP-problem # Print out the solution print("Solution:\n Objective: ", prob.attributes.objval) hline = 60*"-" print("Total profit: ", prob.attributes.objval) print(hline) print(8*" ", "Period", end='') for t in range(NT+1): print("{:8}".format(t), end='') print("\n", hline) print("Finished products\n", "=================") for f in RF: print(" Factory", f) for p in RP: print(3*" ", "P", p, ": Prod", 12*" ", end='', sep='') for t in RT: print("{:8.2f}".format(prob.getSolution(make[p, f, t])), end='') print('') print(8*" ", "Sell", 12*" ", end='', sep='') for t in RT: print("{:8.2f}".format(prob.getSolution(sell[p, f, t])), end='') print('') print(7*" ", "(Stock)", end='') for t in range(NT+1): print(" (", "{:4.1f}".format(prob.getSolution(pstock[p, f, t])), ")", end='', sep='') print('') print(hline) print("Raw material\n", "============") for f in RF: print(" Factory", f) for r in RR: print(3*" ", "R", r, ": Buy", 12*" ", end='', sep='') for t in RT: print("{:8.2f}".format(prob.getSolution(buy[r, f, t])), end='') print('') print(8*" ", "Use", 12*" ", end='', sep='') for t in RT: print("{:8.2f}".format(sum(REQ[p][r] * prob.getSolution(make[p, f, t]) for p in RP)), end='') print('') print(7*" ", "(Stock)", end='') for t in range(NT+1): print(" (", "{:4.1f}".format(prob.getSolution(rstock[r, f, t])), ")", end='', sep='') print('') print(hline)