###### Business Trends

# Probabilistic planning for a resilient supply chain plan

As recently mentioned by Gartner, “infinite possibilities require probabilistic supply chain planning” [1]. But what is Probabilistic Supply Chain Planning and how does it look like in real life situations?

SAP has joined forces with the Technical University of Munich to investigate what a more resilient supply chain plan means for our customers and how such a solution could look like in the future.

The goal of this blog is to give an overview of what probabilistic supply chain planning is and how we are approaching it in our project.

# Overview of our project

We focus on the supply planning part of the process. We consider the information about (demand) uncertainty as input: we leverage a number of scenarios (at least 5-10) as input, each of which has a probability attached. These scenarios do not necessarily have to be generated using probabilistic forecasting. A possible approach is to use range-based forecasting.

In principle, such scenarios (incl. their probabilities) can be created manually or with an automated approach.

## What is it about

**Resilient supply planning**(mid-term scope): creating a supply plan to best prepare for multiple futures**Consideration of uncertainty for planning decisions**: include uncertainty of demand and potentially uncertainty of raw material (ordered vs. delivered) in the plan- Analysis and communication of planning output: representation of profit and relevant decisions as ranges (incl. confidence levels)

Based on given demand and raw material uncertain input we generate a supply plan that can cope with different possible scenarios.

A model prototype has already been implemented and is waiting to be tested on real-world customer data.

**We are **therefore actively** searching for a customer willing to do a Pilot Project with us!**

**What is in it for the pilot customer?**

**Profit implications**of decisions including the risk of profit below a certain level (in EUR, US$ etc.)**Resilient decisions**, i.e. being able to adapt to different futures by jointly considering multiple future scenarios (incl. probabilities)**Ranges for future decisions**(as a spread around a single-value base plan) to prepare for potential adjustments early-on- Possibility to
**influence**future**product decisions for SAP IBP**

**What would the pilot customer have to do?**

- Play an
**active role in discussions**to refine the planning setting **Provide**company**data**sets as input to test the jointly developed planning setting- Exchange on how to
**use and communicate the planning results**

Hoping to have caught your interest in the topic, let us now give you an idea of what probabilistic planning means.

# What is Probabilistic Planning

Probabilistic Supply Chain Planning can be interpreted in many ways. Here, we want to focus on two aspects: Probabilistic Forecasting and Probabilistic Supply Planning. The first is about being able to forecast multiple possible futures and their respective probabilities, while the second is about preparing for these futures as best as possible based on given constraints (e.g. for capacity, lead time).

## Why Probabilistic Planning?

Traditional planning methods are deterministic. This means that they use exact, single numbers to approximate uncertain decisions (e.g. production volumes), states (e.g. inventories) and other important relationships.

**Probabilistic Planning** means that instead of considering one fixed scenario (deterministic) you **plan for multiple scenarios**, and each of them has a **probability** attached to it. All together, these scenarios adequately capture the expectation of what the future is most likely to look like, based on current knowledge.

Once you have a prediction on all the possible ways in which uncertain inputs could look like in the future, you need a plan that helps you deal with “multiple possible futures” in an integrated way. Some early decisions will need upfront commitment, while some later decisions are allowed to capture the profit-impact (or else) and be flexible until a certain point into the future.

So probabilistic planning is somewhat the opposite of deterministic planning: **Deterministic**** plans provide exact quantities**** which however are uncertain, while probabilistic methods ****incorporate the uncertainty ****more accurately**. Having a probabilistic plan available allows planners to account for multiple possible futures, and take informed decisions based on economic drivers.

Oftentimes, most of the data needed to generate probabilistic plans is already available in every ERP system. Using this data, probabilistic plans provide richer information, allowing for more informed business decisions. Probabilistic plans can also be manually adjusted as desired.

## Probabilistic Forecasting – find out all possible futures

The first step in any supply chain plan is (demand) forecasting.

A **deterministic forecast** is typically a series of **exact numbers** over a certain time range. It is possible to express results of deterministic forecasts as **ranges of values** (called confidence intervals or confidence bands), but this does not imply that they are (appropriately) probabilistic. The problem with such “range forecasts” can be that they make certain assumptions which might not represent the future accurately (e.g. using normally distributed forecast errors to create confidence levels around a single value forecast).

A** probabilistic forecast** on the other hand, is a series of probability distributions for each time period of the forecasting horizon. This means, it** provides probabilities for all possible values at every point in time, based on the real distribution and behavior of uncertain demand**. They are expressed as vague ranges of values which are more likely to contain the true realized values later on than a deterministic single value estimate.

In general, one can work with both range forecasts or full-fledged probabilistic forecasts, but results of course improve with the richness and quality of the considered input.

Below an example of range forecast (i.e. forecasting with confidence intervals/bands) using a classical statistical model [2] and an example of a forecast generated using deep learning probabilistic forecasting [3].

One last point that needs to be made: probabilistic forecasting is usually related to demand uncertainty. However, while demand is usually the main source of uncertainty in supply chains, it is not the only one: shipments can be late, suppliers may not be able to deliver in full and so on.

The same methods used to forecast uncertain demand can in general be applied to forecast other relevant factors (such as raw material availability) and their likelihood.

Finally, while it is clear that **probabilistic distributions create an infinite number of possibilities, in reality it is often only feasible to deal with a finite number of options**. In the following, we talk about scenarios meaning that a choice has been done on a finite number of options.

## Probabilistic Planning – prepare for all possible futures

**Probabilistic planning** means first and foremost **creating a supply plan that can take **different **uncertainties into account**. These uncertainty factors can be forecasted.

As mentioned before, while the best approach would be to have a full-fledged probabilistic forecast, as a starting point one could also set up the scenarios using a range-based forecast. As already mentioned, this is actually a deterministic forecast, but it can be easier to generate and can be a good starting point to have different scenarios to work on, as long as the forecast more accurately captures the future.

Once the forecast scenarios are available, it is time to generate a supply plan. However, such a **supply chain plan is **also **subject to constraints**: capacities, lead times and so on. So, the task in this phase is to **find all feasible decisions**, given all the considered futures and to accurately balance the timing of decisions: there might be some with higher urgency and some which can be postponed. The guiding principle for this is an objective such as the maximization of profit, revenue or service level (or striving towards any other desirable target).

This kind of plan can be done in multiple ways. For example, one could compute a supply plan for each of the scenarios separately. Each of these plans would have a probability attached, corresponding to the initial probability of the picked scenarios. However, this means that once a decision has been made to plan for one of the scenarios, the decisions might not be good for any of the other scenarios or might not even be feasible anymore. This can lead to disruptions in the supply chain.

From a methodology perspective, there are a number of different options to approach stochastic (probabilistic) planning – each of which has its own purpose and is best applicable in a specific decision context.

The word stochastic refers to something that cannot be exactly predicted because it contains a component of randomness. **Stochastic planning means preparing for a range of potential outcomes in an effective way**. Not all stochastic approaches are also probabilistic (since not all necessarily work with probabilities) but for the purposes of this blog, we do not need to distinguish further.

Stochastic methodologies have been discussed and refined in academics for a long time. Depending on what should be achieved and how uncertainty is considered, options are for example Robust Optimization (which conservatively explores certain worst cases), Stochastic Programming (which uses a sampled explicit approximation of the future) or Dynamic Programming for Markov Decision Processes (which is based on states representing different versions of the future). [4]

**Conclusion**

We strongly believe that probabilistic methods play a key role in the future of supply chain planning. They represent the right way to go for areas that contain uncertainty, including for all types of forecasting and the subsequent planning situations.

Traditional deterministic planning methods base their decisions on the mistaken assumption that uncertain values can be approximated by a single average number. As a direct consequence of this assumption, plans are often infeasible at the time they are created and manual interventions are continuously needed.

Be the first to get insights and join us on our project to help us shape the supply chain plan of the future!

**Contacts**

- Main Contacts
- Laura Tozzo – Product Manager SAP IBP for Demand
- Thorsten Greil – PhD candidate at TUM and co-author of this blog

- Additional Contacts
- Stephan Kreipl – CPO of SAP IBP
- Martin Grunow – Professor and Chair of Production & SCM at TUM
- Ruediger Eichin – Head of Industry-University Collaboration TUM – SAP
- Katharina Wollenberg – Industry-University Collaboration Lead TUM – SAP

# References

[1] Gartner Speaker – Amber Salley

[4] A unified framework for stochastic optimization (Warren B.Powell)