8 Transforming data into decisions with linear programming

 

This chapter covers

  • Linear programming
  • Constrained optimization
  • Objective functions
  • Inequality and other constraints

In today’s competitive business environment, managers and decision-makers are constantly challenged to make the most of limited resources. These resources can include time, money, labor, materials, and more. The goal is to maximize efficiency, profitability, or output, or, alternatively, to minimize costs, waste, or time. Achieving this requires careful planning and precise execution. One of the most effective tools for this purpose is linear programming.

Linear programming is a powerful mathematical approach to solving a specific type of constrained optimization problem, where both the objective and the constraints are represented by linear relationships. As a key tool in operations research and management science, linear programming has widespread applications across various industries. From optimizing supply chains to maximizing profits, linear programming helps decision-makers find efficient solutions to complex, resource-limited challenges.

8.1 Problem formulation

8.1.1 The scenario

8.1.2 The challenge

8.1.3 The approach

8.1.4 Feature summaries

8.2 Developing the linear optimization framework

8.2.1 Explanation of linear equations and inequalities

8.2.2 Data definition

8.2.3 Objective function

8.2.4 Constraints

8.2.5 Decision variable bounds

8.2.6 Solving the linear programming problem

8.2.7 Result evaluation

Summary