Patricia Neri

4月 142018
 

SAS Visual Forecasting 8.2 effectively models and forecasts time series in large scale. It is built on SAS Viya and powered by SAS Cloud Analytic Services (CAS).

In this blog post, I will build a Visual Forecasting (VF) Pipeline, which is a process flow diagram whose nodes represent tasks in the VF Process.  The objective is to show how to perform the full analytics life cycle with large volumes of data: from accessing data and assigning variable roles accurately, to building forecasting models, to select a champion model and overriding the system generated forecast. In this blog post I will use 1,337 time series related to a chemical company and will illustrate the main steps you would use for your own applications and datasets.

In future posts, I will work in the Programming application, a collection of SAS procedures and CAS actions for direct coding or access through tasks in SAS Studio, and will develop and assess VF models via Python code.

In a VF pipeline, teams can easily save forecast components to the Toolbox to later share in this collaborative environment.

Forecasting Node in Visual Analytics

This section briefly describes what is available in SAS Visual Analytics, the rest of the blog discusses SAS Visual Forecasting 8.2.

In SAS Visual Analytics the Forecast object will select the model that best fits the data out of these models: ARIMA, Damped trend exponential smoothing, Linear exponential smoothing, Seasonal exponential smoothing, Simple exponential smoothing, Winters method (additive), or Winters method (multiplicative). Currently there are no diagnostic statistics (MAPE, RMSE) for the model selected.

You can do “what-if analysis” using the Scenario Analysis and Goal Seeking functionalities. Scenario Analysis enables you to forecast hypothetical scenarios by specifying the future values for one or more underlying factors that contribute to the forecast. For example, if you forecast the profit of a company, and material cost is an underlying factor, then you might use scenario analysis to determine how the forecasted profit would change if the material cost increased by 10%. Goal Seeking enables you to specify a target value for your forecast measure, and then determine the values of underlying factors that would be required to achieve the target value. For example, if you forecast the profit of a company, and material cost is an underlying factor, then you might use Goal Seeking to determine what value for material cost would be required to achieve a 10% increase in profit.

Another neat feature in SAS Visual Analytics is that one can apply different filters to the final forecast. Filters are underlying factors or different levels of the hierarchy, and the resulting plot incorporates those filters.

Data Requirements for Forecasting

There are specific data requirements when working in a forecasting project, a time series dataset that contains at least two variables: 1) the variable that you want to forecast which is known as the target of your analysis, for example, Revenue and 2) a time ID variable that contains the time stamps of the target variable. The intervals of this variable are regularly spaced. Your time series table can contain other time-varying variables. When your time series table contains more than one individual series, you might have classification variables, as shown in the photo below. Distribution Center and Product Key are classification variables. Optionally, you can designate numerical variables (ex: Discount) as independent variables in your models.

You also have the option of adding a table of attributes to the time series table. Attributes are categorical variables that define qualities of the time series. Attribute variables are similar to BY variables, but are not used to identify the series that you want to forecast. In this post, the data I am using includes Distribution Center, Supplier Name, Product Type, Venue and Product Category. Notice that the attributes are time invariant, and that the attribute table is much smaller than the time series table.

The two data sets (SkinProduct and SkinProductAttributes) used in this blog contain 1,337 time series related to a chemical company. This picture shows a few rows of the two data sets used in this post, note that DATE intervals are regularly spaced weeks. The SkinProduct dataset is referred as the Time Series table in the SkinProductAttributes dataset as the Attribute Data.

Introduction SAS Visual Forecasting 8.2

Developing Models in SAS Visual Forecasting 8.2

Step One: Create a Forecasting Project and Assign Variables

From the SAS Home menu select the action Build Models that will take you to SAS Model Studio, where you select New Project, and enter 1) the Name of your project, 2) the Type of project, make sure you enter “Forecasting” and 3) the data source.

Introduction SAS Visual Forecasting 8.2

In the Data tab,  assign the variables roles by using the icon in the upper right corner.

The roles assigned in this post are typical of role assignments in forecasting projects. Notice these variables are in the Time Series table. Also, notice that the classification variables are ordered from highest to lowest hierarchy:

Time Variable: Date
Dependent Variable: Revenue
Classification Variables: Distribution Center and Product Key

In the Time Series table, you might have additional variables you’d like to assign the role “independent” that should be considered for model generation. Independent variables are the explanatory, input, predictor, or causal variables that can be used to model and forecast the dependent variable. In this post, the variable “Discount” is assigned the role “independent”. To do this assignment: right click on the variable, and select Edit Variables.

To bring in the second dataset with the Attribute variables, follow the steps in this photo:

 

Step two: Automated Modeling with Pipelines

The objective in this step is to select a champion model.  Working in the Pipelines tab, one explores the time series plots, uses the code editor to modify the default model, adds a 2nd model to the pipeline, compares the models and selects a champion model.

After step one is completed, select the Pipelines Tab

The first node in the VF pipelines is the Data node. After right-clicking and running this node, one can see the time series by selecting Explore Time Series. Notice that one can filter by the attribute variables, and that the table shows the exact historical data values.

Auto-forecasting is the next node in the default pipeline. Remember that we are modeling 1,332 time series. For each time series, the Auto-forecasting node automatically diagnoses the statistical characteristics of the time series, generates a list of appropriate time series models, automatically selects the model, and generates forecasts. This node evaluates and selects for each time series the ARIMAX and exponential smoothing models.

One can customize and modify the forecasting models (except the Hierarchical Forecasting model) by editing the model’s code. For example, to add the class of models for intermittent demand to the auto- forecasting node, one could open the code editor for that node and replace these lines
rc = diagspec.setESM();
rc = diagspec.setARIMAX();
with:
rc = diagspec.setIDM();

To open the code editor see photo below. After changes, save code and close the editor.

At this point, you can run the Auto Forecasting node, and after looking at its results, save it to the toolbox, so the editing changes are saved and later reused or shared with team members.

By expanding the Nodes pane and the Forecasting Modeling pane on the left, you can select from several models and add a 2nd modeling node to the pipeline

The next photo shows a pipeline with the Naïve Forecast as the second model. It was added to the pipeline by dropping its node into the parent node (data node). This is the resulting pipeline:

After running the Model Comparison node, compare the WMAE (Weighted Mean Absolute Error) and WMAPE (Weighted Mean Absolute Percent Error) and select a champion model.

You can build several pipelines using different model strategies. In order to select a champion model from all the models developed in the pipelines one uses the Pipeline Comparison tab.

Before you work on any overrides for your forecasting project, you need to make sure that you are working with the best pipeline and modeling node for your data. SAS Visual Forecasting selects the best fit model in each pipeline. After each pipeline is run, the champion pipeline is selected based on the statistics of fit that you chose for the selection criteria. If necessary, you can change the selected champion pipeline.

Step Three: Overrides

The Overrides tab is used to manually adjust the forecasts in the future. For example, if you want to account for some promotions that your company and its competitors are running and that are not captured by the models.

The Overrides module allows users to select subsets of time series at the aggregate level by selecting attribute values in the attribute table that you defined in the data tab. The filters based on the attributes are highly customizable and do not restrict you to use the hierarchy that was used for the modeling. The section of a filter using attribute is often referred to as faceted search. Whenever you create a new filter based on a selection of values of the attributes (also known as facets), the aggregate for all series that match the facets will be displayed on your main panel.

There is a wealth of information in the Overrides overview: 1) a list of the BY variables, as well as attribute variables, available to use as filters.

2) a Plot of the Time Series Aggregation and Overrides displaying historical and forecast data, and

3) a Forecast and Overrides table which can be used to create, edit and submit, override values for a time series based on external factors that are not included in the forecast models

Conclusion

Using SAS Visual Forecasting 8.2 you can effectively model and forecast time series in large scale. The Visual Forecasting Pipeline greatly facilitates the automatic forecasting of large volumes of data, and provides a structured and robust method with efficient and flexible processes.

References

An introduction to SAS Visual Forecasting 8.2 was published on SAS Users.

1月 252018
 

Most people who work with optimization are familiar with Linear and Integer Programming, to their toolkit they could add Constraint Programming. Constraint Programming is a powerful technique that is used to solve powerful “real-world” problems in a variety of areas, such as, planning, scheduling, DNA Sequencing, computer graphics and natural language processing.

Constraint Programming is a powerful paradigm which can be used by itself or in combination with Integer Programming. In this article, I’ll show you how to implement a simple Constraint Programming example that solves Sudoku puzzles using the CLP functionality in SAS Optimization.

Have you ever wondered after working in a particularly difficult Sudoku puzzle if the puzzle can be solved? Would you like to schedule your child’s little league games like a pro using the Round-Robin tournament format, just like it is done in professional sport leagues?

If so, Constraint Programming is the answer. But what is Constraint Programming?  Let’s start answering this question by reviewing the familiar Linear and Integer Programming formulations and then comparing them with the one for Constraint Programming.

Most people have heard about Linear Programming and Integer Programming, where the typical mathematical structure for an Integer Programming model is:

Max    c1x1+ c2x2+ … + cnxn

Subject to
a11x1 + a12x2+ … + a1nxnb1
….
an1x1+ an2x2+ … + annxnbn

xj  integer for  all j = 1 to n

These equations describe a problem where the goal (or objective) is to maximize a metric that is related to a set of variables (x1, …, xn) to be determined by solving the problem. The goal (or objective) to be maximized could be, for example, profit, amount of food distributed, etc. The set of variables are related to the goal, and in a typical marketing problem would represent marketing campaigns, customer response, channels used to distribute those campaigns, etc. Constraints are the rules that relate the variables to the available resources to solve the problem. In a marketing problem, b1 could represent the available budget, …, bn could represent the capacity of the call center.

When all variables are continuous we have a linear program; when some of the variables must be integers, we have a mixed integer programming problem. Notice that the constraints in the formulation above simply describe a logical relationship among several variables. Because each variable must take an integer value, their domain is the set of integers.

In Constraint Programming the relationships between variables are stated in the form of constraints. Constraints specify the properties of a solution to be found. A key insight for Constraint Programming is to understand that a constraint is simply a logical relationship among several finite unknowns (or variables), each taking a value in a finite domain. A constraint thus restricts the possible values that the variables can simultaneously take, it represents some partial information about the variables of interest.

An example of a scheduling problem described using the Constraint Programming approach is below All tasks relationships are of type “FS” which means “finish-to-start” and can be used to indicate which task precedes another one:

Forall (j in Jobs)

/* Indicates which task precedes another one */
Forall (t in 1..nbTasks-1)

task [j,t]   FS   task[j, t+1];

forall ( j in Jobs)

/* Indicates which tools to be used */

forall ( t in Tasks)

requires task[j,t] = (tool[j,t];

In this scheduling problem, the goal is to find the task sequence for each job while satisfying the constraints on task precedence and tool availability.

More formally, a Constraint Program can be defined using a triple X, D, C, where

  • X = { X1, …, Xn}  is a finite set of variables
  • D = {D1, …, Dn}  is a finite set of domains, where Di is a finite set of possible values that the variable Xi can take. Di is known as the domain of variable Xi
  • C = {C1, …, Cn}  is a finite set of constraints that restrict the values that the variables can simultaneously take.

Constraint solvers find an assignment to the variables that satisfies all the constraints using constraint propagation, backtracking, branch and bound algorithms or local search. There are many specialized resources (books, articles, etc.) that describe these methods.

Many times for complex problems, a hybrid approach is used, that is, an approach that uses Integer Programming, Constraint Programming and Heuristic procedures.

Let’s solve the simple Send More Money and the Sudoku puzzles to make clear the formal Constraint Program formulation given above.

Send More Money Puzzle

The Send More Money puzzle consists of finding unique digits for the letters D, E, M, N, O, R, S, and Y such that S and M are different from zero (no leading zeros) and the following equation is satisfied:

S E N D
+   M O R E

M O N E Y

Step #1: Define the variables:

S, E, N, D, M, O, R, E, Y

Step #2: Define the Domain of those variables

  1. S, E, N, D, M, O, R, E, Y must take integer values between 1 and 9
  2. S can’t be zero
  3. M can’t be zero

Step #2: Define the Domain of those variables

  1. S * 1000 + E * 100 + N * 10 + D + M * 1000 + O * 100 + R * 10 + E =
    10000 * M + O * 1000 + N * 100 + E * 10 + Y
  2. All variables must be different

The unique solution to this problem is

S E N D M O R Y
9 5 6 7 1 0 8 2

 

And can be found using the CLP procedure in SAS Optimization, with this code

proc clp dom=[0,9] 		/* Define the default domain */
out=out; 			/* Name the output data set */
var S E N D M O R Y; 	        /* Declare the variables */
lincon 				/* Linear constraints */
 
/* SEND + MORE = MONEY */
1000*S + 100*E + 10*N + D + 1000*M + 100*O + 10*R + E
=
10000*M + 1000*O + 100*N + 10*E + Y,
 
 
 
S<>0,                           
M<>0;                          /* No leading zeros */
 
alldiff(); 		/* All variables have pairwise
 				   distinct values*/
run;

The Sudoku Puzzle

Step #1: Define your variables.

We are searching for 81 variables that are arranged in a 9×9 matrix, let Cij represent the value of the cell in the ith row and the jth column, where i=1, …, 9 and j=1, …, 9

Step # 2: Define the Domain of those variables

Cij can take any integer value between 1 and 9

Step # 3: Define the Constraints.

  1. For each row i, all values in that row must be different.
  2. For each column j, all values in that column must be different.
  3. For each 3×3 block Bb all values in that block must be different.

If we start with the initial values

Constraint Programming in SAS Optimization

Then the solution is

Constraint Programming in SAS Optimization

This solution can be found using the CLP procedure in SAS Optimization, with this code (note that the initial puzzle is entered in the step data indata and the final solution is nicely printed with the macro printSol).

data indata;
input C1-C9;
datalines;
. . 5 . . 7 . . 1
. 7 . . 9 . . 3 .
. . . 6 . . . . .
. . 3 . . 1 . . 5
. 9 . . 8 . . 2 .
1 . . 2 . . 4 . .
. . 2 . . 6 . . 9
. . . . 4 . . 8 .
8 . . 1 . . 5 . .
;
run;
%macro store_initial_values;
/* store initial values into macro variable C_i_j */
data _null_;
set indata;
 
array C{9};
do j = 1 to 9;
i = _N_;
call symput(compress("C_" ||  put(i,best.)  || "_"  || put(j,best.)),
put(C[j],best.));
end;
run;
%mend store_initial_values;
%store_initial_values;
 
%macro solve;
proc clp out=outdata;
 
%do i = 1 %to 9;
var (X_&i._1-X_&i._9) = [1,9];
alldiff(X_&i._1-X_&i._9);
%end;
 
%do j = 1 %to 9;
alldiff(
%do i = 1 %to 9;
X_&i._&j
%end;
);
%end;
 
%do s = 0 %to 2;
%do t = 0 %to 2;
alldiff(
%do i = 3*&s + 1 %to 3*&s + 3;
%do j = 3*&t + 1 %to 3*&t + 3;
X_&i._&j
%end;
%end;
);
%end;
%end;
 
 
%do i = 1 %to 9;
%do j = 1 %to 9;
%if &&C_&i._&j ne . %then %do;
lincon X_&i._&j = &&C_&i._&j;
%end;
%end;
%end;
run;
%put &_ORCLP_;
%mend solve;
%solve;
 
%macro printSol;
data final (keep= A1 A2 A3 A4 A5 A6 A7 A8 A9);
set outdata;
array A{9};
%do i = 1 %to 9;
%do j = 1 %to 9;
A(&j)=X_&i._&j;
%end;
output ;
%end;
run;
%mend printSol;
%printSol;

Conclusion

Every optimization person could benefit from using Constraint programming. It is a powerful tool, which can be used in hybrid approaches with Integer Programming and heuristic procedures.

Solving Sudoku puzzles using Constraint Programming in SAS Optimization was published on SAS Users.