Solving Resource Allocation Problems using PuLP in Python: Step-by-Step Tutorial

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Resource allocation problems arise in various real-world scenarios, such as production planning, project management, and scheduling. Linear programming is a powerful tool for solving such problems. PuLP is a Python library that provides a user-friendly interface to create and solve linear programming models.

In this tutorial, we will learn how to use PuLP to solve a resource allocation problem. Specifically, we will consider the following problem:

• We have three resources: labor, materials, and machines.
• We have three tasks that require different amounts of resources:
• We have a limited amount of each resource available:
• We want to maximize the total profit of completing the tasks. Each task has a different profit:

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Problem formulation

We can formulate this problem as a linear programming problem with the following decision variables:

• x1: the number of times task 1 is completed
• x2: the number of times task 2 is completed
• x3: the number of times task 3 is completed

The objective function is to maximize the total profit, which is given by:

maximize 5x1 + 4x2 + 8x3

The constraints are as follows:

• The total amount of labor used cannot exceed 6 hours:

2x1 + x2 + 3x3 ≤ 6

• The total amount of materials used cannot exceed 5 units:

x1 + 2x2 + x3 ≤ 5

• The total amount of machines used cannot exceed 7 units:

2x1 + 2x2 + x3 ≤ 7

• The number of times each task is completed must be a non-negative integer:

x1, x2, x3 ≥ 0

Now that we have formulated the problem, we can use PuLP to solve it.