# The Driving Force (TDF) – Optimal food production planning #SWI2024

The Driving Force (TDF) is the creator of the BuyFresh platform that helps small- to medium-scale food producers sell their products online. The production plan is one of the important day-to-day decisions that bakers make to optimize their profit. However, they often need more mathematical background to make an optimal production plan. To support their operations, we would like a tool that helps them make this production plan.

Problem Description

The news vendor problem is a well-known problem with a known optimal solution. However, adding multiple products that influence each other makes this problem considerably harder. Considering that part of the out-of-stock will switch to another product is important for an optimal production plan. Furthermore, when a product is in stock, it is also possible to sell auxiliary products. The goal is to develop an optimal production plan given these variables while also considering the maximum production capacity of the producer.

To address this challenge, you will be given a product selection where each product has a known price and cost. Normally, other important parameters are estimated using historical sales data. However, for the SWI solution, you can assume that the demand for each product follows a Poisson distribution with a known mean. If a product is no longer in stock, there is a probability that a customer will leave and not buy anything or switch to another product. Finally, when a customer buys a product, there is a chance of cross-selling another product as well. Tables containing this information that roughly represent two suppliers will be shared with the participants. All products are made at night and can only be sold the next day.

Desired Outcome

The goal is to find an optimal production plan. Since decision-makers have a hard time trusting methods they do not fully understand, it should be an understandable model for non-mathematicians. Furthermore, the effect of a suggested production plan on profit, lost sales, and leftovers, both with regard to expectations as well as risks, should be easy to see and compare with another plan. Furthermore, the model should be robust for small errors in the chosen parameters since the estimations from data are known to be slightly inaccurate.