Forecasting optimization and objective function

Exploratory analysis The clearest way to examine a regular time series manually is with a line chart such as the one shown for tuberculosis in the United States, made with a spreadsheet program.

Forecasting optimization and objective function

There is currently a lot of buzz about using machine learning ML techniques for predicting the future state of a supply chain demand forecasting being the most popular use case.

ML algorithms predict future behavior based on past occurrences and their associated environment. In this blog post, we aim to start a new kind of buzz by talking about using ML for prescribing how supply chains should operate in order to achieve an optimal state.

We will use a case to highlight the application of ML for supply chain optimization. Imagine a supermarket that sells a certain brand of potato chips, called Super Crispies. The demand for Super Crispies on a given day depends on a lot of factors, like the day of the week demand is higher near the weekendweather demand is higher on hotter, sunnier daysand even macroeconomic factors like the stock market Super Crispies are a high-end item, so demand is higher when the market is doing well.

These are called features. The supermarket has kept terrific data on historical sales of Super Crispies, including not only the demand, but also the values of the features, on each day. How many cases of Super Crispies should the supermarket hold in inventory?

If we knew the probability distribution for the demand on a day with these particular values of the features — for example, a normal distribution with a mean of 9. One way to get around this missing data is by fitting a distribution to the historical demands for days with the same features as today.

For example, here is a histogram of demands on days with degrees, sun, and so on: This distribution is drawn on the plot, as well. Using this information, the newsvendor problem then tells us that the optimal safety stock level is 5.

Capacity Planning

As you can see, the lognormal distribution is not a great fit, however. This is not surprising, given that we have only 14 total data points matching these values of the features.

Nevertheless, this is an intuitive and reasonable way to solve this problem. We call it separated estimation and optimization SEO — we first estimate the demand distribution, and then use that in an optimization model the newsvendor problem to solve the problem.

Even though the SEO approach is common and effective, we recently asked ourselves whether the current availability of richer data sources might suggest that machine learning ML could be a useful tool for optimizing inventory — of Super Crispies or any other product.

DNN tries to build a model that relates inputs like temperature, day of the week, etc. But the demand for Super Crispies does not have such a simple relationship to the features. DNN has proven very effective in teasing out complicated relationships like this one.

Deep learning assesses the quality of a solution using a loss function, which measures how far the output is from its target. If the output is a demand prediction, then the loss function would measure how close the prediction was to the actual demands — sort of like a forecast error.

Forecasting optimization and objective function

While DNN is well suited for predictive analytics tasks such as demand forecasting, it is less commonly used for prescriptive analytics — optimization — which is what we aimed to make it do in our paper.

In fact, our loss function is very similar to the newsvendor objective function. In our paper, we test our DNN method for optimizing inventory levels by using a data set containing 13, demand records for 23 product categories from a supermarket retailer in and available here.

The features in this data set are department, day of week, and month of year. We used our DNN method to optimize the inventory level for a range of holding cost values, keeping the shortage cost fixed. We also implemented several other ML algorithms that do not use deep learning.

Here are the results: The red curve plots the cost of the DNN method. The yellow curve is for the SEO method discussed above. The other curves represent other ML methods. As you can see, our method beats the other methods.

On the other hand, once the model is trained, it can recommend new inventory levels in real time.1. Introduction. In their analysis of research in time series forecasting, covering the period – and summarizing over papers, De Gooijer and Hyndman conclude that the use of prediction intervals and densities, or probabilistic forecasting, has become much more common over the years, as ‘practitioners have come to understand the limitations of point forecasts’.

Demystifying AI

Supply chain network design is a powerful modeling approach proven to deliver significant reduction in supply chain costs and improvements in service levels by better aligning supply chain strategies.

Forecasting Defined Forecasting is "A statement about the future" (Anonymous, ). Operations management is designed to support forecasted performances and events.

Specifically, operations managers allocate personnel, time, and resources in order to meet the demands of forecasts. Optimization and Objective Function.

A Novel Search Interval Forecasting Optimization Algorithm cooperative coevolution was designed to overcome the hard-to-determine parameters.

In this paper, we proposed a novel search interval. Forecasting is the planning tool to predict the future outcomes based on historical data and experience, knowledge of the management.

It is very important for the company for developing new products or product line in the marketplace. Optimization and Objective Function.

Explore math with pfmlures.com, a free online graphing calculator.

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