Basics of optimization

Supply Chain Analytics in Python

Aaren Stubberfield

Supply Chain Analytics Mgr.

What is a supply chain

  • A Supply Chain consist of all parties involved, directly or indirectly, in fulfilling a customer’s request.¹
  • Includes:
    • Suppliers
    • Internal Manufacturing
    • Outsourced Logistics Suppliers (i.e. Third Party Suppliers)
1 Chopra, Sunil, and Peter Meindl. _Supply Chain Management: Strategy, Planning, and Operations._ Pearson Prentice-Hall, 2007.
Supply Chain Analytics in Python

What is a supply chain optimization

  • Involves finding the best path to achieve an objective based on constraints

diagram of material flowing from suppliers to customers

Supply Chain Analytics in Python

Crash course in LP

  • Linear Programing (LP) is a Powerful Modeling Tool for Optimization

  • Optimization method using a mathematical model whose requirements are linear relationships

  • There are 3 Basic Components in LP:

    • Decision Variables - what you can control
    • Objective Function - math expression that uses variables to express goal
    • Constraints - math expression that describe the limits of a solutions
Supply Chain Analytics in Python

Introductory example

Use LP to decide on an exercise routine to burn as many calories as possible.

Pushup Running
Minutes 0.2 per pushup 10 per mile
Calories 3 per pushup 130 per mile

Constraint - only 10 minutes to exercise

Supply Chain Analytics in Python

Basic components of an LP

Decision Variables - What we can control:

  • Number of Pushups & Number of Miles Ran

Objective Function - Math expression that uses variables to express goal:

  • Max (3 * Number of Pushups + 130 * Number of Miles)

Constraints - Math expression that describe the limits of a solutions:

  • 0.2 * Number of Pushups + 10 * Number of Miles ≤ 10
  • Number of Pushups ≥ 0
  • Number of Miles ≥ 0
Supply Chain Analytics in Python

Example solution

Optimal Solution:

  • 50 Pushups
  • 0 Miles Ran

Calories Burned: 150

chart of acceptable solutions to exercise example, including the optimal point

Supply Chain Analytics in Python

LP vs IP vs MIP

Terms Decision Variables
Linear Programing (LP) Only Continuous
Integer Programing (IP) Only Discrete or Integers
Mixed Integer Programing (MIP) Mix of Continuous and Discrete
Supply Chain Analytics in Python

Summary

  • Defined Supply Chain Optimization
  • Defined Linear Programing and Basic Components
    • Decision Variables
    • Objective Function
    • Constraints
  • Defined LP vs IP vs MIP
Supply Chain Analytics in Python

Let's practice!

Supply Chain Analytics in Python

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