Basics of PuLP modeling

Supply Chain Analytics in Python

Aaren Stubberfield

Supply Chain Analytics Mgr.

What is PuLP

PuLP is a modeling framework for Linear (LP) and Integer Programing (IP) problems written in Python
Maintained by COIN-OR Foundation (Computational Infrastructure for Operations Research)
PuLP interfaces with Solvers
- CPLEX
- COIN
- Gurobi
- etc…

PuLP example – resource scheduling

Consultant for boutique cake bakery that sell 2 types of cakes
30 day month
There is:
- 1 oven
- 2 bakers
- 1 packaging packer – only works 22 days

PuLP example – resource scheduling

Different resource needs for the 2 types of cakes:

	Cake A	Cake B
Oven	0.5 days	1 day
Bakers	1 day	2.5 days
Packers	1 day	2 days

	Cake A	Cake B
Profit	$20.00	$40.00

PuLP example – resource scheduling

Objective is to Maximize Profit
- Profit = 20*A + 40*B
Subject to:
- A ≥ 0
- B ≥ 0
- 0.5A + 1B ≤ 30
- 1A + 2.5B ≤ 60
- 1A + 2B ≤ 22

Common modeling process for PuLP

Initialize Model
Define Decision Variables
Define the Objective Function
Define the Constraints
Solve Model

Initializing model - LpProblem()

LpProblem(name='NoName', sense=LpMinimize)

name = Name of the problem used in the output .lp file, i.e. "My LP Problem"
sense = Maximize or minimize the objective function
- Minimize = LpMinimize (default)
- Maximize = LpMaximize

PuLP example – resource scheduling

Initialize Model

from pulp import *

# Initialize Class
model = LpProblem("Maximize Bakery Profits", LpMaximize)

Define decision variables - LpVariable()

LpVariable(name, lowBound=None, upBound=None, cat='Continuous', e=None)

name = Name of the variable used in the output .lp file
lowBound = Lower bound
upBound = Upper bound
cat = The type of variable this is
- Integer
- Binary
- Continuous (default)
e = Used for column based modeling

PuLP example – resource scheduling

Initialize Class
Define Variables

# Define Decision Variables
A = LpVariable('A', lowBound=0, cat='Integer')
B = LpVariable('B', lowBound=0, cat='Integer')

PuLP example – resource scheduling

Initialize Class
Define Variables
Define Objective Function

# Define Objective Function
model += 20 * A + 40 * B

PuLP example – resource scheduling

Initialize Class
Define Variables
Define Objective Function
Define Constraints

# Define Constraints
model += 0.5 * A + 1 * B <= 30
model += 1 * A + 2.5 * B <= 60
model += 1 * A + 2 * B <= 22

PuLP example – resource scheduling

Initialize Class
Define Variables
Define Objective Function
Define Constraints
Solve Model

# Solve Model
model.solve()
print("Produce {} Cake A".format(A.varValue))
print("Produce {} Cake B".format(B.varValue))

PuLP example – resource scheduling

from pulp import *

# Initialize Class
model = LpProblem("Maximize Bakery Profits",
                   LpMaximize)

# Define Decision Variables
A = LpVariable('A', lowBound=0,
                cat='Integer')
B = LpVariable('B', lowBound=0, 
                cat='Integer')

# Define Objective Function
model += 20 * A + 40 * B

# Define Constraints
model += 0.5 * A + 1 * B <= 30
model += 1 * A + 2.5 * B <= 60
model += 1 * A + 2 * B <= 22

# Solve Model
model.solve()
print("Produce {} Cake A".format(A.varValue))
print("Produce {} Cake B".format(B.varValue))

Summary

PuLP is a Python LP / IP modeler
Reviewed 5 Steps of PuLP modeling process
1. Initialize Model
2. Define Decision Variables
3. Define the Objective Function
4. Define the Constraints
5. Solve Model
Completed Resource Scheduling Example

Let's practice!

Supply Chain Analytics in Python