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Firestns: A set-covering model for emergency service provision Description Minimize the total number of firestations that are required to service a set of towns within a specified permissible travel time. Further explanation of this example:
'Xpress Python Reference Manual'
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fstns.py '''******************************************************* * Python Example Problems * * * * file fstns.py * * Example for the use of the Python language * * (Firestation siting problem) * * * * (c) 2018-2024 Fair Isaac Corporation * *******************************************************''' from __future__ import print_function import xpress as xp RTown = range(6) # Range of towns TIMELIMIT = 20 # Max. time allowed to reach any town TIME = [[0, 15, 25, 35, 35, 25], [15, 0, 30, 40, 25, 15], [25, 30, 0, 20, 30, 25], [35, 40, 20, 0, 20, 30], [35, 25, 35, 20, 0, 19], [25, 15, 25, 30, 19, 0]] '''This sets SERVE(t,s) to true if the time between the two towns is within the time limit. We can then use SERVE to define a set of constraints (see below). It is as well possible not to use the array SERVE and move the test directly into the definition of the constraints. ''' SERVE = [[TIME[t][s] <= TIMELIMIT for t in RTown] for s in RTown] p = xp.problem() # 1 if ambulance at town; 0 if not openst = [p.addVariable(vartype=xp.binary) for _ in RTown] # Objective: minimize number fire stations p.setObjective(xp.Sum(openst[s] for s in RTown)) # Serve each town t by an open station s p.addConstraint(xp.Sum(openst[s] for s in RTown if SERVE[t][s]) >= 1 for t in RTown) p.optimize() # Solve the MIP-problem # Print out the solution print("Solution:\n Minimum number of firestations: ", p.getObjVal()) for s in RTown: print(" open(", s, "): ", p.getSolution(openst[s]), sep='') print("\n ", end='') for s in RTown: print(s, " ", end='', sep='') print('') for t in RTown: if p.getSolution(openst[t]) == 1: print(" ", t, ": ", end='') for s in RTown: if SERVE[t][s]: print("Y ", end='') else: print(". ", end='') print('') | |||||||||||

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