Pulp 3 3 2

pulp 3.3.2

Overview

PuLP is a Python library for formulating and solving linear programming (LP), mixed-integer linear programming (MILP), and binary programming problems. It provides a clean, declarative API for building optimization models and dispatches to any installed solver (CBC included by default; supports HiGHS, GLPK, Gurobi, CPLEX, MOSEK, XPRESS, SCIP, COPT, SAS, CHOCO, MIPCL, and more).

Install with pip install "pulp[cbc]==3.3.2" — the [cbc] extra bundles the CBC solver so prob.solve() works out of the box without separate solver setup.

PuLP 3.3.2 introduces prob.add_variable() / add_variable_dicts() / add_variable_matrix() as the preferred API. The legacy LpVariable() constructor still works but emits deprecation warnings (removed in PuLP 4.0).

Usage

Quick Start

from pulp import LpProblem, LpMinimize, value

prob = LpProblem("MyProblem", LpMinimize)

# Create variables attached to the problem
x = prob.add_variable("x", lowBound=0, upBound=4)
y = prob.add_variable("y", lowBound=-1, upBound=1)
z = prob.add_variable("z", lowBound=0)          # upper bound is +∞

# Objective
prob += x + 4*y + 9*z, "Objective"

# Constraints
prob += x + y <= 5, "C1"
prob += x + z >= 10, "C2"
prob += -y + z == 7, "C3"

# Solve (uses default CBC solver)
status = prob.solve()

print(f"Status: {LpStatus[status]}")
for v in prob.variables():
    print(f"{v.name} = {v.varValue}")
print(f"Objective = {value(prob.objective)}")

Variable Categories

b = prob.add_variable("binary_var", cat="Binary")        # 0 or 1
i = prob.add_variable("int_var", lowBound=0, cat="Integer")
c = prob.add_variable("cont_var", lowBound=0)            # continuous (default)

Named Constraints and Variables

Always name constraints for debugging, sensitivity analysis, and resolve workflows:

prob += x + y <= 5, "capacity"       # named constraint
c = prob.get_constraint_by_name("capacity")  # retrieve later
print(c.pi)   # dual value (shadow price)
print(c.slack)

Common Expression Helpers

• lpSum([x1, x2, ...]) — sum of variables or expressions
• lpDot(coeffs, vars) — dot product of two lists
• value(expr) — evaluate expression with solved variable values

from pulp import lpSum, lpDot, value

# Sum: 3*x + 4*y
prob += lpSum([3*x, 4*y]) <= 100

# Dot product
costs = [2, 5, 3]
vars_list = [x1, x2, x3]
prob += lpDot(costs, vars_list)          # 2*x1 + 5*x2 + 3*x3

# Retrieve value after solving
print(value(x))                          # safe even if not solved yet

Gotchas

• Use prob.add_variable(), not LpVariable() — The legacy constructor emits deprecation warnings and variables are not automatically attached to the model. In PuLP 4.0, LpVariable() standalone will be removed.
• Use prob.add_variable_dicts() / add_variable_matrix(), not LpVariable.dicts() / matrix() — Same deprecation applies.
• PULP_CBC_CMD is deprecated — Use COIN_CMD() or install HiGHS (pip install highspy) for better performance.
• Constraint constant is stored as LHS, not RHS — When modifying constraints for resolve, the constant on the left-hand side is negated relative to the right-hand side. E.g., x + y <= 10 stores constant -10.
• prob.solve() returns status code, not bool — Check with LpStatus[status] == "Optimal" rather than truthiness.
• Dual values (pi) require LP relaxation — Solvers typically only return duals for continuous LP problems, not MILP. Solve the LP relaxation first if you need shadow prices.
• prob.roundSolution() rounds integer variables — Useful after solving a relaxed LP to get near-integer solutions before re-solving with integer constraints.
• Variable names cannot contain -+[] ->/ — These characters are replaced with _. Use alphanumeric names with underscores.

References

• 01-core-api — LpProblem, LpVariable, LpAffineExpression, LpConstraint classes and operators
• 02-variable-creation — add_variable, add_variable_dicts, add_variable_matrix with examples
• 03-solvers — Solver selection, configuration, availability checks, time limits
• 04-model-patterns — Transportation, assignment, blending, facility location, Sudoku, cutting stock
• 05-advanced-topics — Sensitivity analysis, resolve, column generation, stochastic programming, warm starts