Pplan: A project planning problem

'''*******************************************************
  * Python Example Problems                             *
  *                                                     *
  * file pplan.py                                       *
  * Example for the use of the Python language          *
  * (Manpower planning problem)                         *
  *                                                     *
  * (c) 2019-2025 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('')