Difficulty: Intermediate | Prerequisites: Part 1 of these notes (Customer Identification), plus familiarity with time-series models (ARIMA, exponential smoothing, GARCH) and optimisation.
This is Part 2 of the power company case study notes. Part 1 covered the analytics framework and customer identification models. Here we turn to the two remaining sub-problems: estimating the financial cost of leaving power on versus shutting it off, and deciding which shut-offs to prioritise when workers and travel time are limited. These sections bring in time-series forecasting, optimisation, and simulation, and they show how the outputs of one sub-problem feed into the next.
Once you have identified which customers probably will not pay (Part 1), you need to estimate how much it costs to leave their power on versus shutting it off, then decide which shut-offs to do first given limited crews. Cost estimation uses time-series models (ARIMA, GARCH) or regression. Shut-off selection uses optimisation, clustering of physical locations, or simulation to handle variability in travel and shut-off times.
Exponential smoothing
A forecasting method that assigns exponentially decreasing weights to older observations. Think of it as a smart moving average where recent data points matter more than distant ones. Best suited for short-term forecasts when you have a reasonable history of past usage.
ARIMA (Autoregressive Integrated Moving Average)
A time-series model that captures trend and seasonality by combining autoregression (past values predict future values), differencing (to make the series stationary), and moving-average error terms. In simple terms, it looks at patterns in how a customer's usage has changed over time to forecast next month.
GARCH (Generalised Autoregressive Conditional Heteroskedasticity)
A model that estimates the variance (volatility) of a time series, not just its level. Where ARIMA tells you the expected bill amount, GARCH tells you how much that amount might swing. Useful when you need to account for risk in cost estimates.
Regression-based model
Simple regression, tree-based regression, or clustering followed by regression. Effective when you have limited customer-specific history, because you can use cross-sectional data (credit, financial, demographic features) and normalise for seasonality.
Vehicle Routing Model
An advanced optimisation model for determining the best routes for a fleet visiting multiple locations under time and capacity constraints. This is the formal name for the type of model that solves the shut-off scheduling problem.
Simulation (with distribution fitting)
A method for testing how well an expected-value solution holds up under real-world variability. You fit probability distributions to uncertain inputs (drive times, shut-off times, power usage) and run many scenarios to see how often the plan works and where it breaks.
The goal here is to estimate the cost of leaving power on for a non-paying customer versus the cost of shutting it off.
For customers with a long usage history
Given: customer credit, financial data, payment history, and possibly some demographic information
Use: exponential smoothing or ARIMA
To: estimate the amount of power the customer will use next month
These methods work well when there is enough past data, but are effective only for short-term forecasts
For estimating variability in usage
Given: the same data as above
Use: GARCH
To: estimate how much a customer's power usage might vary next month
Also requires sufficient historical data and is limited to short-term forecasts
For customers with shorter or limited history
Given: customer credit, financial data, payment history (if available), and possibly some demographic information
Use: regression-based model (simple regression, tree-based, or clustering followed by regression)
To: estimate the amount of power the customer will use next month
This approach can work even with limited customer-specific data, and the data can be normalised for seasonality
Hybrid approach (modelling non-payment and cost together)
Instead of separating identification and cost estimation, model the amount of money owed directly (zero if the bill is paid). The catch: if there are many zero values alongside a range of positive values, this creates a bimodal distribution. The practical fix is to analyse the zero values and the non-zero values separately.
E[\text{cost of keeping power on}] = p(\text{no pay}) \times E[\text{cost of power next month}]This is the expected loss from leaving a non-payer connected. It multiplies the probability they will not pay by the expected cost of the power they will consume.
E[\text{cost of shutting power off}] = (\text{shut-off cost}) + (1 - p(\text{no pay})) \times (\text{turn-on cost})This is the expected cost of acting. It includes the fixed cost of sending a worker to shut off the power, plus the risk of being wrong: if the customer would have paid (probability 1 - p(no pay)), you also incur the cost of turning the power back on.
The decision rule: shut off power when the expected cost of keeping it on exceeds the expected cost of shutting it off.
The goal is to decide which shut-offs to prioritise, given that there are more locations needing shut-off than available workers and hours.
Data needed
Past data on travel time and speed between locations
Time required to shut off power at each location
Estimate of future power usage per customer
Probability of non-payment per customer (from the identification model)
Approach 1 – Optimisation
Use a binary variable for each customer (1 = shut off, 0 = leave on). The objective function maximises the total cost difference between shutting off and not shutting off, summed across all selected customers. The constraints encode worker hours, travel time, and capacity. In practice, the constraints are difficult to write because travel time depends on the combination of locations visited, not just individual locations.
Approach 2 – Clustering of physical locations
Cluster the physical locations that are prioritised for shut-off. This reduces the number of distinct areas employees need to visit each day, allowing more shut-offs per route. The optimisation model can then be modified to work within clusters rather than across the full geography.
Approach 3 – Simulation
Clustering and optimisation rely on expected values (average drive time, average shut-off time, expected power usage). In reality, there is considerable variability in all of these. Simulation, possibly with distribution fitting, can test how robust the expected-value solutions are. You run many scenarios with randomly drawn values and see how often the plan succeeds, then adjust accordingly.
The priority trade-off (red dots vs. blue dots)
The lecture illustrates a scenario where four high-priority shut-offs (red dots) are spread far apart, while a larger group of lower-priority shut-offs (blue dots) are clustered close together. The same amount of worker time can handle either the four red dots or the full cluster of blue dots. This is the core tension in shut-off selection: individual priority versus route efficiency.
Vehicle Routing Model
This is the formal optimisation framework for problems of this type. It determines the best routes for a fleet of workers visiting multiple locations, accounting for travel time, service time at each stop, and capacity. It is an advanced model and the course does not expect you to build one, but you should know the name and what it does.
Workforce planning extension
Regardless of which modelling approach is used, the output can also be used to determine how many additional workers to hire to meet the demand for shut-offs.
Students often assume ARIMA and GARCH do the same thing. ARIMA forecasts the level (expected value) of a time series; GARCH forecasts its variance (how much it swings). They answer different questions and can be used together.
Students sometimes apply time-series models to customers with very short histories. Exponential smoothing and ARIMA need a reasonable amount of past data. For new or short-history customers, regression-based models are the better choice.
The hybrid approach (modelling money owed directly) seems simpler, but students often overlook the zero-inflation problem: many bills are zero (paid), creating a distribution that standard regression handles poorly. The fix is to model the zeroes and non-zeroes separately.
Students frequently focus on individual customer priority and ignore route efficiency. The red-dot/blue-dot example makes the point that total value delivered depends on geography, not just per-customer priority scores.
⚠️ Know both expected cost formulas and be able to explain each term. You may be asked to set up the decision rule for whether to shut off a specific customer.
⚠️ Be able to recommend different forecasting models depending on the amount of customer history available (long history = ARIMA/exponential smoothing; short history = regression-based).
⚠️ Understand the trade-off between individual priority and route efficiency. The red-dot/blue-dot scenario is a likely exam or discussion question.
⚠️ Know what the Vehicle Routing Model is and why it is relevant, even if you are not expected to build one.
⚠️ Be prepared to explain why simulation adds value on top of optimisation: it tests whether the expected-value solution holds up under real-world variability.
True or False: ARIMA and GARCH both forecast the expected level of a time series. (False. ARIMA forecasts the level; GARCH forecasts the variance.)
Fill in the blank: E[cost of keeping power on] = ______ x ______. (p(no pay) x E[cost of power next month])
True or False: The Vehicle Routing Model is a classification model. (False. It is an optimisation model for routing.)
True or False: Simulation is used instead of optimisation for shut-off selection. (False. Simulation is used alongside optimisation to test how robust the solution is under variability.)
Fill in the blank: For customers with short payment histories, use a ______-based model rather than ARIMA. (regression)
Q: Using the analytics framework, how would you estimate next month's power usage for a customer with three years of billing history?
A: Given {three years of monthly power usage data, customer credit and financial information}, use {ARIMA or exponential smoothing} to {forecast the amount of power the customer will use next month}.
Q: When would you use GARCH instead of (or alongside) ARIMA?
A: When you need to estimate the variability in a customer's power usage, not just the expected level. GARCH models the variance of the time series. You might use both together: ARIMA for the point forecast and GARCH for a confidence interval around it.
Q: Write out the expected cost of shutting off power and explain each component.
A: E[cost of shutting power off] = (shut-off cost) + (1 - p(no pay)) x (turn-on cost). The shut-off cost is the fixed cost of sending a worker. The second term captures the risk of a false positive: if the customer would have paid (probability 1 - p(no pay)), the company also pays to reconnect them.
Q: Why might clustering physical locations improve the shut-off selection process?
A: Clustering groups nearby locations together, reducing the travel time employees spend moving between shut-offs. This means more shut-offs can be completed per day. The optimisation model can then operate within clusters, making the routing problem smaller and more tractable.
Q: Explain why simulation is useful even after you have an optimisation solution.
A: Optimisation uses expected values for drive times, shut-off times, and power usage. In practice, these vary. Simulation draws random values from fitted distributions and tests the optimisation solution across many scenarios, revealing how often the plan works and where adjustments are needed.
Cost estimation ties directly to earlier modules on time-series forecasting (exponential smoothing, ARIMA, GARCH). Shut-off selection connects to optimisation and simulation topics. The entire case study is a capstone exercise that integrates classification (Part 1), forecasting, optimisation, and simulation into one coherent business problem. The workforce planning extension also links to capacity planning concepts.
Cost estimation, power usage forecasting, exponential smoothing, ARIMA, GARCH, variance forecasting, regression-based forecasting, short customer history, zero-inflated data, expected cost formula, shut-off selection, vehicle routing model, VRM, optimisation, binary decision variable, objective function, location clustering, simulation, distribution fitting, Monte Carlo, workforce planning, capacity constraint, travel time, route efficiency, red dots blue dots, Modules 17–21, discussion cases, UT Austin intro to computer programming