PyOR 1.0.0

Python Operations Research — LP, Simplex, Transportation, Assignment, PERT/CPM, Curve Fitting & more

PyOR — Python Operations Research Library

PyOR is a comprehensive, educational Operations Research library for Python.
It covers all major OR methods with clear docstrings, step-by-step output, and optional plots.

---

📦 Installation

pip install PyOR
# With plotting support
pip install PyOR[plot]

---

🗂️ Modules & Methods

#	Method	Class / Function
1	Linear Programming Formulation	LinearProgram
2	Graphical Method	GraphicalMethod
3	Simplex Method	SimplexMethod
4	Dual Simplex Method	DualSimplex
5	Big-M Method	BigMMethod
6	Transportation — North-West Corner	north_west_corner()
7	Transportation — Least Cost	least_cost_method()
8	Transportation — Vogel's Approximation	vogel_approximation()
9	Transportation — MODI (Optimality)	modi_method()
10	Assignment Problem	AssignmentProblem
11	Project Management (PERT / CPM)	PERTCPMNetwork
12	Curve Fitting — Least Squares	CurveFitter
13	Cubic Spline Interpolation	CubicSplineFitter

---

🚀 Quick Examples

1. Linear Programming

from pyOR import LinearProgram

lp = LinearProgram(
    c         = [-3, -5],           # maximise 3x₁ + 5x₂
    A_ub      = [[1,0],[0,2],[3,2]],
    b_ub      = [4, 12, 18],
    objective = 'max'
)
result = lp.solve()
lp.display()
# → x1=2, x2=6, Z*=36

2. Graphical Method

from pyOR import GraphicalMethod

gm = GraphicalMethod(
    c           = [3, 5],
    constraints = [(1, 0, '<=', 4),
                   (0, 2, '<=', 12),
                   (3, 2, '<=', 18)],
    objective   = 'max'
)
result = gm.solve()
gm.display()
gm.plot()           # requires matplotlib

3. Simplex Method

from pyOR import SimplexMethod

sm = SimplexMethod(
    c         = [5, 4, 3],
    A         = [[6,4,2],[3,2,5],[5,6,5]],
    b         = [240, 270, 420],
    objective = 'max'
)
result = sm.solve()
sm.display(show_tableaux=True)

4. Dual Simplex Method

from pyOR import DualSimplex

ds = DualSimplex(
    c        = [2, 3],
    A        = [[1,1],[1,0],[0,1]],
    b        = [4, 2, 3],
    senses   = ['<=','<=','<='],
    objective= 'min'
)
ds.solve()
ds.display()

5. Big-M Method

from pyOR import BigMMethod

bm = BigMMethod(
    c        = [2, 3],
    A        = [[1,1],[1,0],[0,1]],
    b        = [4, 2, 3],
    senses   = ['<=','>=','>='],
    objective= 'min'
)
bm.solve()
bm.display()

6–9. Transportation Problem

from pyOR import north_west_corner, least_cost_method, vogel_approximation, modi_method

cost   = [[2, 3, 1], [5, 4, 8], [5, 6, 8]]
supply = [120, 80, 80]
demand = [150, 70, 60]

# Initial BFS methods
north_west_corner(cost, supply, demand)
least_cost_method(cost, supply, demand)
vogel_approximation(cost, supply, demand)

# Optimal solution using MODI
result = modi_method(cost, supply, demand, initial_method='vam')
print("Optimal Cost:", result['total_cost'])

10. Assignment Problem

from pyOR import AssignmentProblem

ap = AssignmentProblem(
    cost_matrix = [[9,2,7,8],
                   [6,4,3,7],
                   [5,8,1,8],
                   [7,6,9,4]],
    objective   = 'min',
    row_names   = ['Worker A','Worker B','Worker C','Worker D'],
    col_names   = ['Job 1','Job 2','Job 3','Job 4']
)
ap.solve()
ap.display()

11. PERT / CPM

from pyOR import PERTCPMNetwork

# CPM
activities = [
    {'name':'A','depends':[],       'duration':4},
    {'name':'B','depends':[],       'duration':5},
    {'name':'C','depends':['A'],    'duration':3},
    {'name':'D','depends':['B'],    'duration':4},
    {'name':'E','depends':['C','D'],'duration':6},
]
net = PERTCPMNetwork(activities)
net.solve()
net.display()

# PERT with probability
activities_pert = [
    {'name':'A','depends':[],'optimistic':2,'most_likely':4,'pessimistic':6},
    {'name':'B','depends':['A'],'optimistic':3,'most_likely':5,'pessimistic':9},
]
net2 = PERTCPMNetwork(activities_pert)
net2.solve()
net2.display(show_probability=15)
print(net2.completion_probability(15))

12. Curve Fitting

from pyOR import CurveFitter

cf = CurveFitter(x=[1,2,3,4,5], y=[2.1,3.9,6.1,8.1,10.1])

# Linear
cf.fit('linear')
cf.display()
cf.plot()

# Polynomial degree 2
cf.fit('polynomial', degree=2)
cf.display()

# Exponential, Power, Logarithmic, Reciprocal
for model in ['exponential', 'power', 'logarithmic', 'reciprocal']:
    cf.fit(model)
    print(f"{model}: R² = {cf.result['r_squared']:.4f}")

13. Cubic Spline

from pyOR import CubicSplineFitter

sf = CubicSplineFitter(
    x=[0, 1, 2, 3, 4],
    y=[0, 1, 0, 1, 0],
    bc_type='natural'
)
sf.fit()
sf.display()

# Evaluate at a point
y_val = sf.evaluate(1.5)
dy    = sf.derivative(1.5, order=1)
print(f"S(1.5) = {y_val},  S'(1.5) = {dy}")

sf.plot()

---

📐 Dependencies

Package	Version
numpy	≥ 1.21
scipy	≥ 1.7
matplotlib	≥ 3.4 (optional, for plots)

---

🧪 Running Tests

pip install PyOR[dev]
pytest tests/ -v

---

📜 License

MIT © 2025 PyOR Contributors