# Decision-driven optimization

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From the quantitative supply chain perspective, economic drivers represent the financial quantification of the positive and negative outcomes of supply chain decision. Economic drivers shape supply chain optimization challenges into tractable optimization problems; where the optimization metric happens to be financial. Through the quantification of the economic drivers, it becomes possible to assess the dollars of error associated to imperfect decisions, originally based on imperfect data such as demand forecasts. Those economic drivers are introduced as a counter point of business-agnostic metrics which remain widely used such as MAPE (mean absolute percentage error). Those business-agnostic metrics are frequently harmful because they "dress" supply chain problems as numerical optimization problems, while relying on largely arbitrary optimization criterion.

## Statistical forecasts are one-eyed

Demand forecasting tools and methods have one clear goal: computing more accurate forecasts. Forecasts are deemed as accurate according to various metrics known and selected for their mathematical and statistical properties. While such metrics might be excellent from a mathematical perspective, they are fundamentally domain agnostic, and ignore, by design, any business-specific drivers or constraints.

While it might seem counter-intuitive, statistical forecasts are fundamentally driven by the chosen error metric. Choosing the MSE (mean square error) rather than the MAD (mean absolute error) has drastic consequences on the accuracy of a given model. At first sight, it might look like the error metric has little impact. After all, a forecasting model produces the same demand forecast no matter which metric is being used afterward to assess its result. However, any company that relies on statistical forecasting is deemed to make choices – frequently implicit choices – about which forecasting models are used; and as soon as accuracy measurements are introduced, the company starts favoring the models that behave better in relation to the above-mentioned metrics.

Generic statistical metrics (ex: MAPE, MAD, MSE, etc.) don’t have any business affinity. Simply put, these metrics put an emphasis on the percentages of error rather than the dollars of error. While minimizing the percentages of error may be a good thing, there are unfortunately too many counter examples to this. Statistical metrics don’t provide any kind of guarantee that the financial outcome of a decision derived from a forecast is going to be optimal or even profitable. Sometimes, economic drivers happen to be only loosely correlated with generic statistical metrics, but this happens by “chance”, and relying on chance is not a proper methodology for supply chain optimization. In practice, this issue is typically amplified by the counter-intuitive nature of most situations where the purely statistical metrics diverge from business performance metrics.

Example. Let’s consider a product sold in a store with only 1 unit sold on average per week, with a lead time of 1 day (every day replenishment). The best median demand forecast for this product for any given day is zero units. An average forecast might have produced a fractional quantity of 1/7, but the median forecast just indicates zero. While the 1-day demand to be covered is very close to zero, the actual stock that needs to be held to properly service customers is probably much larger; 2 or 3 units are likely to be required in order to meet customers’ expectations in terms of the quality of service. The problem here is not that the forecast is inaccurate, because if the demand is stationary and truly random then the forecasts we just mentioned are perfectly accurate from a statistical perspective. The problem is that business-specific drivers have been ignored.

## Decoupling forecasting from supply chain optimization

Economic drivers represent a specific break down of the supply chain optimization challenges, where the business-specific aspects – i.e. the economic drivers – are decoupled from the business-agnostic aspects – i.e. the purely statistical forecasts. In this section, we briefly review the benefits of this break down as well as its limitations.

As far as numerical optimization goes, there is a general principle that states that it’s always preferable to optimize the problem as a whole, rather than to optimize parts of the problem in isolation. However, this point only remains true as long as addressing the optimization challenge from a monolithic perspective remains technically feasible. Yet, most supply chain literature, and us as well, tends to agree on the fact that demand forecasting is a complicated undertaking which combines statistics, algorithms, software engineering, and possibly distributed computing when a cloud computing platform is involved. Thus, isolating the demand forecasting aspect of the challenge offers the possibility to deliver advanced demand forecasts without burdening the technology with a myriad of domain-specific considerations.

Likewise, a similar advantage is obtained by isolating the supply chain optimization logic from the demand forecasting logic. As supply chain optimization remains "protected" from the technicalities involved in demand forecasting, this makes it possible to delve much deeper into the fine details of the economic drivers: caps on storage space, price breaks, varying stock-out costs, varying obsolescence costs, etc. Having a more detailed understanding of the economic drivers generates better decisions that are more closely aligned with the risks and opportunities of a company.

Example: Let’s consider a company that has two warehouses and serves exactly the same parts from both warehouses. The two warehouses are located nearby, but out of habit, all customers tend to always order the parts they need from the same warehouse. When a part becomes no longer available in this specific warehouse, the warehouse staff call the other warehouse to investigate the availability of the part in the other warehouse, and if the part is available there, it is then shipped to the warehouse that finds itself out of stock.

## A case for probabilistic forecasting

As we have seen in the previous section, separating demand forecasting from business optimization offers the possibility to execute a supply chain optimization strategy that leverages both advanced forecasting analytics and a fine-grained view on the business itself. However, it must be noted that when producing demand forecasts, the forecasting engine knows nothing about the business-specific factors that are relevant from a supply chain optimization perspective. However, the business scenarios that have the most financial impact are usually the extreme scenarios – “extreme” from a statistical perspective. For example, it’s the unexpectedly high demand that usually causes stock-outs, while it’s the unexpectedly low demand that usually causes inventory write-off.

Classic forecasting tools put great emphasis on mean or median forecasts, which completely misses the point from a business point of view. Indeed, no matter how accurate this type of forecast might be, if the business scenario of interest lies at the statistical extreme, then the forecasting tool will fail to provide the relevant statistical projection to quantitatively assess the probable financial output of the business scenario. In contrast, probabilistic forecasting tools assess the respective probabilities for all possible demand levels, which in turn, offers the possibility to assess all possible business scenarios. In practice, quantitative supply chain require probabilistic forecasts to work at all.

Unsurprisingly, probabilistic forecasts require a lot more computing resources that their classic single-valued counterparts, because, in a way, probabilistic forecasts are “brute-forcing” the forecasting challenge. Since the forecasting engine does not know the relevant business scenarios to be taken into account, it merely produces a far-reaching statistical answer that (approximately) covers all possible scenarios. In practice, thanks to access to vast computing resources at very low prices via cloud computing platforms, the increased computing requirements needed for generating probabilistic forecasts are mostly a non-issue given that the right technology is available.

## A brief review of common economic drivers

Economic drivers define the positive and negative outcomes of a supply chain decision. The calculation of these outcomes requires the actual observation of the yet-to-be-observed demand, but if a demand forecast is available, the outcomes can be simulated in turn. Economic drivers are intended to cover all the business ramifications that result from a decision, and not merely the short-term financial results. In practice, establishing economic drivers is frequently akin to performing back-of-the-envelope calculations that take into consideration various business scenarios.

One of the most common supply chain decisions consists of ordering one more unit for one item. If there is immediate demand for the ordered unit, the company will service the unit at a profit. This represents the gain associated with the ordering decision. If there is no immediate demand for the item, the company will have to incur the carrying costs of stocking this extra unit. This represents the cost associated with the ordering decision. Establishing the economic drivers for an ordering decision consists of writing down both the resulting gains and the resulting costs of the decision for a given demand scenario.

Besides gains and costs, constraints also shape the range of acceptable supply chain decisions:
• Storage capacity: Stores and warehouses have maximum capacities, preventing any additional ordering that goes beyond a certain amount of stock.
• MOQs: Suppliers only accept orders that are beyond minimum order quantities - expressed, for example, in number of units or amount ordered. Those MOQs can also be interpreted and modeled as fixed costs on supplier purchase orders.
• Capital costs: The company has limited access to liquidity, and hence needs to cap its inventory capital allocation. Gaining access to more capital can be highly time-consuming for the management of the company, and may not be aligned with the strategic orientations either.
• Transport capacity: When importing goods from overseas, orders may have to be properly sized so that they can fit exactly within one container. Containers have both a maximum weight and a maximum volume. Containers can also be interpreted as a form a fixed cost on purchase orders.

Economic drivers need to account for all of the above-mentioned constraints, and many more in practice. Indeed, if constraints are not accounted for, then the system that combines the demand forecasts with the economic drivers would most likely suggest decisions that could not actually be executed in reality; such as trying to fill a warehouse beyond its storage capacity.

## Lokad’s perspective on economic drivers

Lokad provides a a probabilistic forecasting engine. Although data must be properly qualified and sanitized before being injected into the forecasting engine, our forecasting engine will then allow to automate the statistical forecasting operation in its entirety with zero statistical configuration. Lokad’s forecasting engine works out-of-the-box for numerous verticals (commerce, manufacturing, aerospace ...).

Economic drivers are incredibly diverse however. In order to manage such diversity, Lokad has introduced Envision, a domain-specific programming language that is dedicated to supply chain optimization. The visible output of Envision consists of producing dashboards, however, Envision’s primary function is to embed ecnomic drivers into forecasts through scripts so that optimized decisions – e.g. quantities to be reordered today - can be computed automatically.

The proper combination of economic drivers and probabilistic forecasts requires policies that can take advantage of those data. For example, the prioritized ordering policy is particularly adequate to deliver quantities to be ordered that fully balance the business inventory risks with the demand forecasts.

In practice, reviewing and formalizing the economic drivers, combining these drivers with probabilistic forecasts, qualifying and sanitizing historical data, generating optimized decisions that match the exact set of applicable business constraints; all these tasks are performed by Lokad’s team through a monthly subscription to an inventory optimization service.

## References

Streetlight effect and forecasting, Joannes Vermorel, September 2015