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Pplan: A project planning problem Description Over the next 6 months we have three projects which can
be done. Each of these projects has a profile of manpower
requirements over its lifetime, and a benefit which accrues
each month when the project has been completed.
Our problem is to determine when each project is to start,
subject to the constraint that in no month can we try to
use more manpower than is available. Further explanation of this example:
'Xpress Python Reference Manual'
Source Files By clicking on a file name, a preview is opened at the bottom of this page.
pplan.py '''******************************************************* * Python Example Problems * * * * file pplan.py * * Example for the use of the Python language * * (Manpower planning problem) * * * * (c) 2019-2024 Fair Isaac Corporation * *******************************************************''' import xpress as xp DUR = [3, 3, 4] RESMAX = [5, 6, 7, 7, 6, 6] BEN = [10.2, 12.3, 11.2] RESUSE = [[3, 4, 2, 0, 0, 0], [4, 1, 5, 0, 0, 0], [3, 2, 1, 2, 0, 0]] RProj = range(3) NTime = 6 RTime = range(NTime) prob = xp.problem() x = prob.addVariables(RProj, RTime, vartype=xp.binary) start = [prob.addVariable(ub=NTime - DUR[p] + 1) for p in RProj] # Objective, to be maximized: Benefit. If project p starts in month # t, it finishes in month t+DUR(p)-1 and contributes a benefit of # BEN(p) for the remaining NTime-(t+DUR(p)-1) months. MaxBen = xp.Sum(BEN[p]*(NTime-t-DUR[p]+1) * x[p, t] for p in RProj for t in range(NTime - DUR[p])) # Resource availability # A project starting in month s is in its t-s+1'st month in month t: prob.addConstraint(xp.Sum(RESUSE[p][t-s] * x[p, s] for p in RProj for s in range(t+1)) <= RESMAX[t] for t in RTime) # Logical Constraints: Each project starts once and only once: prob.addConstraint(xp.Sum(x[p, t] for t in RTime) == 1 for p in RProj) # Connect variables x(p,t) and start(p) prob.addConstraint(xp.Sum(t*x[p, t] for t in RTime) == start[p] for p in RProj) # Finish everything by the end of the planning period prob.addConstraint(start[p] <= NTime - DUR[p] + 1 for p in RProj) prob.setObjective(MaxBen, sense=xp.maximize) prob.optimize() print(" Objective: ", prob.attributes.objval) print(' ', end='') for t in RTime: print("{:5d}".format(t), end='') print('') for p in RProj: print('{:3d}:'.format(p), end='') for t in RTime: sol = prob.getSolution(start[p]) if t < sol: char = ' ' elif t < sol + DUR[p]: char = '*' else: char = 'B' print(" {}".format(char), end='') print('') | |||||||||||

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