[SOLVED] CS Workforce_Planning_expression_form

Workforce_Planning_expression_form

Workforce Planning (Expression Form)

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begin{array}{rll}
displaystyle min_{xin mathbb{R}^7} & x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 \
,{rm s.t.} & begin{array}[t]{rcl}
x_1 + x_4 + x_5 + x_6 + x_7 & geq & 14 \
x_1 + x_2 + x_5 + x_6 + x_7 & geq & 13 \
x_1 + x_2 + x_3 + x_6 + x_7 & geq & 15 \
x_1 + x_2 + x_3 + x_4 + x_7 & geq & 16 \
x_1 + x_2 + x_3 + x_4 + x_5 & geq & 19 \
x_2 + x_3 + x_4 + x_5 + x_6 & geq & 18 \
x_3 + x_4 + x_5 + x_6 + x_7 & geq & 11 \
x_i & geq & 0 ~~~~ forall ~i
end{array}
end{array}

# Import PuLP modeler functions
from pulp import *
!pip install pulp
from pulp import *

# Create the prob variable to contain the problem data
prob = LpProblem(Workforce_Planning_Problem,LpMinimize)

# All variables are created with a lower limit of zero
x1=LpVariable(x1,0)
x2=LpVariable(x2,0)
x3=LpVariable(x3,0)
x4=LpVariable(x4,0)
x5=LpVariable(x5,0)
x6=LpVariable(x6,0)
x7=LpVariable(x7,0)

# The objective function is added to prob first
prob += x1 + x2 + x3 + x4 + x5 + x6 + x7, Total number of workers

# The five constraints are entered
prob += x1 + x4 + x5 + x6 + x7 >= 14.0, People that work on Monday
prob += x1 + x2 + x5 + x6 + x7 >= 13.0, People that work on Tuesday
prob += x1 + x2 + x3 + x6 + x7 >= 15.0, People that work on Wednesday
prob += x1 + x2 + x3 + x4 + x7 >= 16.0, People that work on Thursday
prob += x1 + x2 + x3 + x4 + x5 >= 19.0, People that work on Friday
prob += x2 + x3 + x4 + x5 + x6 >= 18.0, People that work on Saturday
prob += x3 + x4 + x5 + x6 + x7 >= 11.0, People that work on Sunday

# The problem data is written to an .lp file
#prob.writeLP(WorkforceModel.lp)

# The problem is solved using PuLPs choice of Solver
prob.solve()

# The status of the solution is printed to the screen
print(Status: %s % LpStatus[prob.status])

Status: Optimal

Workforce_Planning_Problem:
1*x1 + 1*x2 + 1*x3 + 1*x4 + 1*x5 + 1*x6 + 1*x7 + 0
SUBJECT TO
People_that_work_on_Monday: x1 + x4 + x5 + x6 + x7 >= 14

People_that_work_on_Tuesday: x1 + x2 + x5 + x6 + x7 >= 13

People_that_work_on_Wednesday: x1 + x2 + x3 + x6 + x7 >= 15

People_that_work_on_Thursday: x1 + x2 + x3 + x4 + x7 >= 16

People_that_work_on_Friday: x1 + x2 + x3 + x4 + x5 >= 19

People_that_work_on_Saturday: x2 + x3 + x4 + x5 + x6 >= 18

People_that_work_on_Sunday: x3 + x4 + x5 + x6 + x7 >= 11

x1 Continuous
x2 Continuous
x3 Continuous
x4 Continuous
x5 Continuous
x6 Continuous
x7 Continuous

# Each of the variables is printed with its resolved optimum value
for v in prob.variables():
print(%s = %.2f % (v.name, v.varValue))

# The optimised objective function value is printed to the screen
print(Total number of workers = %f % value(prob.objective))

Total number of workers = 22.000000

for x in prob.variables():
print (Name:%s % x.name)
print (Value: %f % x.varValue)
print (Category:%s % x.cat)
print (Lower Bound: %f % x.lowBound)
print (Upper Bound: %s
% x.upBound)

Name:x1
Value: 4.000000
Category:Continuous
Lower Bound: 0.000000
Upper Bound: None

Name:x2
Value: 7.000000
Category:Continuous
Lower Bound: 0.000000
Upper Bound: None

Name:x3
Value: 1.000000
Category:Continuous
Lower Bound: 0.000000
Upper Bound: None

Name:x4
Value: 4.000000
Category:Continuous
Lower Bound: 0.000000
Upper Bound: None

Name:x5
Value: 3.000000
Category:Continuous
Lower Bound: 0.000000
Upper Bound: None

Name:x6
Value: 3.000000
Category:Continuous
Lower Bound: 0.000000
Upper Bound: None

Name:x7
Value: 0.000000
Category:Continuous
Lower Bound: 0.000000
Upper Bound: None

for (name,constraint) in prob.constraints.items():
print (Name:, name)
print (Constraint:, constraint)
print (Lower Bound: , constraint.getLb())
print (Upper Bound: , constraint.getUb())
print (Value: , pulp.value(constraint))
print (Sense: , constants.LpConstraintSenses[constraint.sense])
print (Constant:, constraint.constant)
print (Slack: , constraint.slack)
print (Slack (Feas):, constraint.slack if constraint.sense < 0 else -constraint.slack)print (” “) Name: People_that_work_on_MondayConstraint: x1 + x4 + x5 + x6 + x7 >= 14.0
Lower Bound:14.0
Upper Bound:None
Value:0.0
Sense:>=
Constant: -14.0
Slack:-0.0
Slack (Feas): 0.0

Name: People_that_work_on_Tuesday
Constraint: x1 + x2 + x5 + x6 + x7 >= 13.0
Lower Bound:13.0
Upper Bound:None
Value:4.0
Sense:>=
Constant: -13.0
Slack:-4.0
Slack (Feas): 4.0

Name: People_that_work_on_Wednesday
Constraint: x1 + x2 + x3 + x6 + x7 >= 15.0
Lower Bound:15.0
Upper Bound:None
Value:0.0
Sense:>=
Constant: -15.0
Slack:-0.0
Slack (Feas): 0.0

Name: People_that_work_on_Thursday
Constraint: x1 + x2 + x3 + x4 + x7 >= 16.0
Lower Bound:16.0
Upper Bound:None
Value:0.0
Sense:>=
Constant: -16.0
Slack:-0.0
Slack (Feas): 0.0

Name: People_that_work_on_Friday
Constraint: x1 + x2 + x3 + x4 + x5 >= 19.0
Lower Bound:19.0
Upper Bound:None
Value:0.0
Sense:>=
Constant: -19.0
Slack:-0.0
Slack (Feas): 0.0

Name: People_that_work_on_Saturday
Constraint: x2 + x3 + x4 + x5 + x6 >= 18.0
Lower Bound:18.0
Upper Bound:None
Value:0.0
Sense:>=
Constant: -18.0
Slack:-0.0
Slack (Feas): 0.0

Name: People_that_work_on_Sunday
Constraint: x3 + x4 + x5 + x6 + x7 >= 11.0
Lower Bound:11.0
Upper Bound:None
Value:0.0
Sense:>=
Constant: -11.0
Slack:-0.0
Slack (Feas): 0.0

x1.varValue + x2.varValue + x3.varValue + x4.varValue + x5.varValue + x6.varValue + x7.varValue

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