Supply Chain Optimization with Python

Find the optimal locations of your manufacturing facilities to meet your customers’ demand and reduce production costs

Supply Chain Optimization with Python

Find the optimal locations of your manufacturing facilities to meet your customers’ demand and reduce production costs

Article originally published on Medium.

Supply chain optimization makes the best use of data analytics to find an optimal combination of factories and distribution centres to match supply and demand.

Because of the current surge in shipping costs, companies start to challenge their current footprint to adapt to the post-covid “New Normal”.

In this article, we will present a simple methodology using Linear Programming for Supply Chain Optimization considering

  • Fixed production costs of your facilities ($/Month)
  • Variable production costs per unit produced ($/Unit)
  • Shipping costs ($)
  • Customer’s demand (Units)
Should we keep outsourcing with shipping costs that have tripled in the last 12 months?

I. Scenario

Problem Statement

As the Head of Supply Chain Management of an international manufacturing company, you want to redefine the Supply Chain Network for the next 5 years considering the recent increase in shipping costs and the forecasts of future demand.

Supply Chain Network Optimization
Map of your Supply Chain Network — (Image by Author)

Your Supply Chain Network

  • 5 markets in Brazil, USA, India, Japan, Germany
  • 2 types of manufacturing facilities: low capacity and high capacity sites
  • Shipping costs ($/container)
  • Customer’s demand (Units/year)

Manufacturing Facility Fixed Costs

  • Capital Expenditure for the equipment (Machines, Storage, ..)
  • Utilities (Electricity, Water, ..)
  • Factory management, administrative staff
  • Space Rental

These costs depend on the country and the type of plant.

Manufacturing Site Fixed Costs — (Image by Author)

Production Variable Costs

  • Production lines operators
  • Raw materials
Manufacturing Site Fixed Costs — (Image by Author)

For instance, the variable cost of a unit produced in Germany is 13$/Unit.

Shipping Variable Costs

  • Cost per container ($/Container)
  • Assumption: 1 container can contain 1000 units
Sea Freight Shipping Costs ($/Container) — (Image by Author)

For instance, if you want to ship a container from Germany to Japan it will cost you 1,231 ($/Container).

Manufacturing Capacity by Site

Manufacturing Site Capacity — (Image by Author)

For instance, a high capacity factory in Brazil can produce 1,500,000 (Units/month).

Customers' demand per market

Manufacturing Site Capacity — (Image by Author)
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You can find the full code in this Github repository: Link

II. Results


Let us try three scenarios

  • Scenario 1: initial parameters
  • Scenario 2: we increase the production capacity of India (x2)
  • Scenario 3: surging shipping costs due to container shortage

Scenario 1: Initial Scenario

  • Brazil plant is producing for the local market and the USA
Facilities: 1 high capacity plant
('Brazil','Brazil') = 145,000 (Units/Month)
('Brazil','USA') = 1,250,000 (Units/Month)
  • India plants produce for all countries except Brazil
Facilities: 1 high capacity plant and 1 low capacity plant
('India','Germany') = 90,000 (Units/Month)
('India','India') = 160,000 (Units/Month)
('India','Japan') = 200,000 (Units/Month)
('India','USA') = 1,550,000 (Units/Month)
  • Japan needs to produce locally because of the limited capacity of India
Facilities: 1 high capacity plant
('Japan','Japan') = 1,500,000 (Units/Month)

Final Costs

💡
Total Costs = 62,038,000 ($/Month)

Scenario 2: Outsourcing to low costs regions

What if we double the size of high capacity plants in India?

Let us try to double the size of the India High Capacity plant with the assumption that it will double the fixed costs.

  • Brazil plant is still producing for the local market and the USA
Facilities: 1 high capacity plant
('Brazil', 'Brazil') = 145,000 (Units/Month)
('Brazil', 'USA') = 1,250,000 (Units/Month)
  • India plants produce for all countries except Brazil
Facilities: 2 high capacity and 1 low capacity plants
('India','Germany') = 90,000 (Units/Month)
('India','India') = 160,000 (Units/Month)
('India','Japan') = 1,700,000 (Units/Month)
('India','USA') = 1,550,000 (Units/Month)
  • Japan does not produce locally anymore.
💡
Final Costs-19.4(%) vs. Scenario 1
Total Costs = 51,352,000 ($/Month)

Scenario 3: surging shipping costs due to containers shortage

What if we have containers cost multiplied by 5?

  • Brazil is producing for the local market only
Facilities: 1 low capacity plant
('Brazil', 'Brazil') = 145,000 (Units/Month)
  • The USA started to produce for the local market and Japan
Facilities: 1 high capacity plant
('USA', 'Japan') = 200,000 (Units/Month)
('USA', 'USA') = 1,300,000 (Units/Month)
  • India closed its low capacity factory
Facilities: 1 high capacity plant
('India', 'Germany') = 90,000 (Units/Month)
('India', 'India') = 160,000 (Units/Month)
('India', 'USA') = 1,500,000 (Units/Month)
  • Japan starts to produce for its local market
Facilities: 1 high capacity plant
('Japan','Japan') = 1,500,000 (Units/Month)

Because of their limited production capacity, Japan and the USA still rely on the Indian plant.

Final Costs

Total Costs = 92,981,000 ($/Month)

III. Build your Model

We will be using the PuLP library of python. PuLP is a modelling framework for Linear (LP) and Integer Programming (IP) problems written in Python maintained by COIN-OR Foundation (Computational Infrastructure for Operations Research).

1. Declare your variables, parameters and model

  • LpMinimize: your objective is to minimize your costs
  • lowBound =0: you cannot have negative values of units produced

2. Define the objective and add constraints

3. Solve your model and analyze the results

III. Conclusion & Next Steps


Conclusion

This model gives you the flexibility to simulate several scenarios influencing operational and commercial parameters.

  • What if the demand explodes in India?
  • What if we have to close our plant in Brazil?
  • What if we triple the production capacity in Japan?

Scenario 3 showed is an example of a shipping costs surge that could push companies to switch to a more local footprint with plants producing for their local market only.

Improve your model

This simple model can help you to get the potential of linear optimization for Supply Chain Network Optimization. We can easily improve this model by adding constraints

  • Storage Costs
  • Carbon emissions limitations (CO2 = f(distance, weight))
  • Delivery lead time
  • Customer Clearance Fees
  • Currency change

Feel free to share suggestions of additional constraints to improve the model and meet the business requirements in your own industry.

References

[1] Computational Infrastructure for Operations Research, Optimization with PuLP (Documentation), Link