Source-linked AI summary
Demand forecasting in supply chain: The impact of demand volatility in the presence of promotion
Mahdi Abolghasemi, Richard Gerlach, Garth Tarr, Eric Beh
TL;DR
Promotion-related volatility makes demand difficult to forecast across series with different CoV levels, creating a need for models that capture diverse demand behavior. The paper decomposes demand into baseline and promotional components, proposes a hybrid forecasting model, and empirically compares statistical and machine-learning models. The hybrid model is robust across volatility levels, while ARIMAX, DLR, and SVR perform well in specified settings and ETSX performs poorly for volatile series.
Problem
Promotion can make demand volatile across the entire series, complicating forecasting across different CoV levels and increasing supply-chain uncertainty and costs.
Method
The study analyzes 843 promoted demand series, decomposes demand into baseline and promotional components, and compares hybrid, statistical, and machine-learning forecasting models using price as an explanatory variable.
Results
The hybrid model has the highest accuracy across moderate and highly volatile demands; ARIMAX improves with covariates, while ETSX performs poorly for volatile series and DLR and SVR remain robust across CoV levels.
Takeaways & Limitations
Decomposition is useful for volatile demand, and model performance varies with volatility, making robust model selection important across demand categories.
Takeaways & Limitations
The study lacks tidy data for all variables contributing to demand volatility and therefore relies on price as the available influential factor.
Abstract
from arXiv · showhide
The demand for a particular product or service is typically associated with different uncertainties that can make them volatile and challenging to predict. Demand unpredictability is one of the managers' concerns in the supply chain that can cause large forecasting errors, issues in the upstream supply chain and impose unnecessary costs. We investigate 843 real demand time series with different values of coefficient of variations (CoV) where promotion causes volatility over the entire demand series. In such a case, forecasting demand for different CoV require different models to capture the underlying behavior of demand series and pose significant challenges due to very different and diverse demand behavior. We decompose demand into baseline and promotional demand and propose a hybrid model to forecast demand. Our results indicate that our proposed hybrid model generates robust and accurate forecast across series with different levels of volatilities. We stress the necessity of decomposition for volatile demand series. We also model demand series with a number of well known statistical and machine learning (ML) models to investigate their performance empirically. We found that ARIMA with covariate (ARIMAX) works well to forecast volatile demand series, but exponential smoothing with covariate (ETSX) has a poor performance. Support vector regression (SVR) and dynamic linear regression (DLR) models generate robust forecasts across different categories of demands with different CoV values.
ARTICLE HISTORY
The paper focuses on demand volatility, promotions, forecasting models, and robust forecasts.
- The study centers on demand volatility and promotion effects in forecasting.
1. Introduction
Demand forecasting supports supply-chain planning but becomes difficult when promotions and other uncertainties make demand volatile. Such volatility can increase forecasting errors and operational costs, motivating models that capture its underlying behavior.
- Demand forecasting informs planning, order fulfilment, production, and inventory decisions.
- Promotions can create demand volatility before, during, and after promotional periods.
- Demand volatility complicates forecasting and can increase stock-outs, inventory, and capacity-utilization costs.
2. Literature review
Supply-chain uncertainty makes accurate demand forecasting difficult, while conventional models may fail when demand is volatile or influenced by external variables. Covariate-based and causal models are therefore evaluated as alternatives.
- Supply-chain uncertainties and volatile markets make demand forecasting challenging and can produce unnecessary operational costs.
- Conventional univariate time-series models may perform poorly when volatility and influencing variables affect demand.
- ARIMAX and ETSX incorporate explanatory variables alongside time-series structure for volatile-demand forecasting.
3. Methodology
The methodology evaluates forecasting models using price and demand data, emphasizing decomposition of promotional demand into baseline and promotional components. The study compares hybrid, statistical, and machine-learning approaches for volatile demand.
- 3.1. Hybrid Model: The hybrid model decomposes demand into baseline demand and promotional uplift because promotional and non-promotional behavior differ.
- 3.1. Hybrid Model: ARIMA estimates baseline demand, while piecewise regression forecasts promotional uplifts across price ranges.
- 3.1. Hybrid Model: The hybrid procedure forecasts decomposed components separately and then sums them where appropriate.
- Forecasting Models: ARIMAX adds price as a covariate to an ARIMA model, while ETSX adds price as a regressor to exponential smoothing.
- 3.4. Dynamic Linear Regression: DLR accommodates sudden and massive changes without assuming a regular or stable underlying pattern.
- 3. Methodology: The study uses price and demand time series as inputs for forecasting.
- Machine-Learning Models: SVR minimizes generalized error rather than ordinary least-squares error when learning numerical outputs.
4. Data
The dataset contains 843 SKUL demand series from a food manufacturing company spanning 112 weeks, with substantial variation linked to promotions. Series are grouped into low, moderate, and high volatility using CoV, and sales vary across price levels over time.
- The dataset covers 843 stock keeping unit locations across 112 weeks of aggregated retailer demand from a food manufacturing company.
- Promotion creates substantial differences between promotional and non-promotional demand levels and contributes significantly to CoV.
- 311 SKULs are low-volatility, 255 moderate-volatility, and 277 high-volatility, with average CoVs of 0.32, 0.75, and 1.71, respectively.
- Moderate-volatility products average 1763 units of demand, ranging from 31 to 37,911 units, while the 90% quantile is 3273 units.
- For a particular SKUL, the loglog sales-price relationship shows price fixed over several price levels while sales vary over time.
5. Empirical results and discussion
The evaluation compares eight-step-ahead forecasting models across demand series with different volatility levels using MASE. Results favor decomposition-based and robust models, while volatility affects models unevenly.
- Experimental setup: The evaluation uses the first 104 weeks for training and the final eight weeks for testing eight-step-ahead forecasts with known prices as covariates.Forecasts are generated using a rolling-origin procedure.
- Evaluation: Tables 2 and 3 report eight-step-ahead MASE accuracy and p-values for model performance across different CoV values.MASE provides a scale-independent evaluation criterion across demand series with different scales.
- Model comparisons: For low-volatility series, ARIMAX has the lowest MASE, while adding covariates improves ARIMA but not ETS accuracy.All models except ETSX outperform the benchmarks in the reported comparisons.
- Robustness to volatility: HR-ARIMA is the only model reported as robust across all volatility levels, while DLR and SVR also maintain robust performance across categories.The magnitude of MASE generally increases with CoV, but HR-ARIMA is more robust to CoV changes.
- Model comparisons: ETSX and ETS accuracy decreases as CoV increases, whereas ANN accuracy declines dramatically for higher-volatility series.ETSX is reported as having poor performance for volatile time series.
- Hybrid model: The hybrid regression time-series model has the highest accuracy for moderate and highly volatile demand by decomposing promotional and non-promotional demand.It combines piecewise regression for promotional demand with ARIMA for non-promotional demand.
6. Conclusion
The study examines 843 promotion-impacted demand series across different volatility levels and finds that volatility can significantly alter forecasting accuracy. It decomposes demand into baseline and promotional components and constructs a piecewise regression model.
- 843 promotion-impacted demand series were categorized as low, moderately, or highly volatile using CoV.CoV measures the relative volatility of demand time series.
- Demand volatility may significantly change forecasting accuracy across different CoV levels.
- The proposed approach decomposes demand into baseline demand and promotional demand before constructing a piecewise regression model.Promotional demand is described as uplift caused by promotion.