Procurement Process Optimization with Python

Procurement management is a strategic approach to acquiring goods or services from preferred vendors within your defined budget, on or before a specific deadline.

Your supply and demand require a minimum level of inventory to meet your store's demand.

In this article, we will present a simple methodology using Non-Linear Programming to design an optimal inventory replenishment strategy for a mid-size retail store, considering:

• Transportation Costs from the Supplier Warehouse to the Store Reserve ($/Carton)
• Costs to finance your inventory (% of inventory value in $)
• Reserve (Store’s Warehouse) Rental Costs for storage ($/Carton)

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Scenario

Problem Statement

As a Store Manager at a mid-sized retail location, you are responsible for setting replenishment quantities in the ERP.

For each SKU, when the inventory level is below a certain threshold, your ERP sends an automatic Purchase Order (PO) to your supplier.

You need to balance stock capacity, transportation costs, and inventory costs to determine the right quantity for your PO.

• 1 supplier that receives your orders via EDI connection (with your ERP) and ships them using a 3rd Party Transportation company at your expense
• 60 active stock-keeping units (SKUs) with a purchasing price ($/carton) and a yearly sales quantity (Cartons/year)
• Transportation using a 3rd party company that operates parcel delivery, invoiced per carton ($/Carton)
• Storage Location (Store’s Reserve) with a capacity of 480 boxes stored on shelves

To simplify the comprehension, let’s introduce some notations

Annual Demand per SKU

Transportation

b = 42.250 $
A = -0.3975 $/Carton

Costs of Capital

As a mid-sized business, we assume your cost of capital is quite high: 12.5%.

Storage Costs

In this model, we suppose that we have the best landlord in the world.

She invoices us by carton-occupied, using the average value per year.

We will not pay for the empty locations.

Imax= 480
Rmonth= 2,000 $/Month

Question

Which Quantity per replenishment Qi should you set in the ERP to minimize the total costs?

Build your Model

Unlike the previous article in the series, we won’t use PuLP because this isn't a linear programming problem.

We will use SciPy's optimisation functions to solve this non-linear minimisation problem.

Declare your decision variables

What are you trying to decide?

We want to set the quantity per replenishment order sent by our ERP to the supplier.

However, to simplify our calculation we will use the number of replenishment per year Ri as a decision variable.

The replenishment quantity will be calculated using the formula below.

Note: We accept a replenishment case quantity that is not an integer.

Declare your objective function

What do you want to minimise?

The purchase cost is not included in the objective function, as it falls outside the scope of our optimisation targets.

Code

Define the constraints

What are the limits on resources that will determine your feasible region?

This is where problems start, as we have a non-linear constraint (1/Ri).

Solve the model and prepare the results

What are the results of your simulation?

Initial Guess

Unlike Linear Programming, we need to provide an initial vector for a potential solution to the algorithm in the first iteration.

Here, we’ll assume 2 replenishments per year for all SKUs is a viable option.

Solve

Conclusion

This optimized solution is 56% better than the initial guess of 2 replenishment per year for all references.

We can see that our solution is primarily driven by transportation costs, with a maximum stock of 356 boxes.

Are you familiar with inventory management?

This solution can be integrated with inventory management policies to provide a comprehensive solution for purchasing and storing products.

For more details, I have a complete tutorial.

About Me

Let’s connect on LinkedIn and Twitter. I am a Supply Chain Engineer who is using data analytics to improve logistics operations and reduce costs.