DemandLens: Forecasting & Optical Applications

• DemandLens is a forecasting framework using Prophet, external COVID-19 regressors, and SKU-specific hyperparameter optimization for demand estimation in the mattress-in-a-box industry.
• It leverages time-series cross-validation and grid search to reduce forecast errors, achieving statistically significant improvements in MAPE and lowering inventory costs.
• A separate optical application employs multi-level diffractive lenses for extended focus imaging, illustrating the term’s dual usage across technical disciplines.

DemandLens most commonly denotes a Prophet based forecasting framework for the mattress-in-a-box industry that combines external regressors, including COVID-19 indicators, with SKU-specific hyperparameter optimization to improve sales forecasting accuracy and support contract-manufacturer planning (Pillai et al., 14 Sep 2025). In a separate and unrelated optics usage, the term was also applied to ultra-lightweight, compact cameras enabled by a multi-level diffractive lens with extended depth of focus (Banerji et al., 2019). Because the 2025 work formalizes DemandLens as a named forecasting system, the term primarily refers to a product-specific demand-forecasting methodology rather than to an optical device (Pillai et al., 14 Sep 2025).

1. Nomenclature and Scope

The term "DemandLens" is used in two distinct senses in the cited literature. In forecasting, it names a sales-prediction framework built on Facebook Prophet and designed for SKU-level demand estimation in a supply chain with third-party contract manufacturing (Pillai et al., 14 Sep 2025). In optics, it appears as the label for compact cameras made possible by an "on-demand," extended-focus multi-level diffractive lens, where elimination of mechanical refocus is the defining property (Banerji et al., 2019).

This distinction is important because the two usages are methodologically unrelated. The forecasting DemandLens concerns additive time-series decomposition, exogenous regressors, grid search, and time-series cross-validation. The optical usage concerns Fresnel diffraction, engineered phase profiles, grayscale lithography, and extreme depth-of-focus imaging. A common misconception is to treat the term as denoting a single research program; the available sources instead indicate a shared name applied to separate technical contexts.

2. Forecasting Formulation

In its forecasting sense, DemandLens is built on Facebook Prophet, whose core additive decomposition is

$$y_t \;=\; g(t)\;+\;s(t)\;+\;h(t)\;+\;\varepsilon_t,$$

where $g(t)$ captures the non-periodic trend, $s(t)$ models one or more seasonal components, $h(t)$ accounts for holiday and event effects, and $\varepsilon_t$ is the residual error (Pillai et al., 14 Sep 2025). DemandLens extends this formulation by incorporating $m$ external regressors $x_i(t)$, including COVID-19 indicators and lag features:

$$y_t \;=\; g(t)\;+\;s(t)\;+\;h(t)\;+\;\sum_{i=1}^m \beta_i\,x_i(t)\;+\;\varepsilon_t.$$

The external-regressor design is centered on COVID-19 metrics. Raw daily case counts $C_t$ and death counts $d_t$ are smoothed via a 7-day rolling average,

$g(t)$0

and then added to the Prophet model through model.add_regressor('cases_7day_avg') and model.add_regressor('deaths_7day_avg') (Pillai et al., 14 Sep 2025). The stated rationale is that the model can learn how "lockdown intensity," proxied by deaths, and case volumes shift demand. This suggests that DemandLens is not merely a univariate forecasting pipeline, but a demand model that explicitly links epidemiological signals to product sales.

3. SKU-Specific Hyperparameter Optimization

A defining feature of DemandLens is separate hyperparameter search per SKU, motivated by the claim that each mattress variant exhibits distinct demand dynamics (Pillai et al., 14 Sep 2025). The tuned Prophet hyperparameters are:

• $g(t)$1, with range $g(t)$2
• $g(t)$3, with range $g(t)$4
• $g(t)$5, with range $g(t)$6
• seasonality_mode $g(t)$7
• $g(t)$8, with range $g(t)$9
• $s(t)$0, with range $s(t)$1

The optimization objective is minimization of Mean Absolute Percentage Error:

$s(t)$2

DemandLens employs a grid search over the Cartesian product of the above ranges, combined with time-series cross-validation using an expanding window (Pillai et al., 14 Sep 2025). For each SKU, the system trains Prophet on rolling-window CV, computes hold-out MAPE for each hyperparameter tuple, and retains the tuple with the lowest value. The loop is parallelized across SKUs, for example via Python’s joblib.Parallel(n_jobs). A plausible implication is that the framework prioritizes per-product calibration over a globally shared parameterization, which is consistent with heterogeneous SKU behavior in operational demand forecasting.

4. Experimental Evaluation

The reported evaluation uses four SKUs corresponding to 10″, 12″, 14″, and 16″ variants, with day-level sales from April 2018 to July 2024, approximately 75 months, and COVID-19 data from January 2020 to March 2023 aligned by date (Pillai et al., 14 Sep 2025). The train period is April 2018 to December 2023, and the test period is January 2024 to July 2024. Two models are compared: Prophet with default hyperparameters ("Baseline Prophet") and DemandLens, defined as SKU-tuned parameters plus COVID regressors.

The aggregate results are reported as follows:

Model	MAPE	RMSE
Baseline Prophet	12.5%	150.2
DemandLens	9.3%	112.5

The corresponding $s(t)$3 is $s(t)$4, and a paired $s(t)$5-test on SKU-level MAPE reductions yields $s(t)$6, which the paper treats as confirmation of statistical significance (Pillai et al., 14 Sep 2025).

SKU-level results further indicate heterogeneous gains:

SKU	Default MAPE	Optimized MAPE
10″	17.6%	13.5%
12″	14.5%	10.8%
14″	23.8%	19.9%
16″	16.4%	15.2%

The corresponding percentage improvements are 23.3% for 10″, 25.5% for 12″, 16.4% for 14″, and 4.9% for 16″, with an average MAPE reduction of all SKUs equal to 17.7% (Pillai et al., 14 Sep 2025). The paper also states that Table III further details 1-, 2-, and 3-month horizons, RMSE, and directional accuracy. A common misunderstanding would be to attribute all performance gains solely to Prophet tuning; the reported framework instead combines SKU-specific optimization with COVID regressors, and the conclusions separately credit explicit COVID-19 regressors with reducing MAPE by 27.3% during lockdowns (Pillai et al., 14 Sep 2025).

5. Supply-Chain Function and Operational Impact

DemandLens is framed as a response to an industry structure in which a limited number of mattress contract manufacturers must manage raw materials, supply chain operations, and inventory for multiple brands (Pillai et al., 14 Sep 2025). The core operational claim is that more accurate sales forecasting helps manufacturers prepare for demand, avoid bottleneck scenarios, and source raw materials at optimal rates.

The reported business effects are stated quantitatively. By reducing forecast error from 12.5% to 9.3% on average, DemandLens is said to enable 17.3% less foam buffer stock, saving (\Delta I\cdot H \approx $s(t)$7$s(t)$8$

with carrying rate $s(t)$9 p.a. and average inventory $h(t)$0. These reported changes are presented as translating into tighter contract-manufacturer coordination, earlier raw-material commitments, and reduced waste.

Monthly-aggregated SKU forecasts are also described as aligning with manufacturing lead times (Pillai et al., 14 Sep 2025). This suggests that the framework is intended not only for forecast-score improvement in the abstract, but for integration into concrete replenishment and production-planning cadences.

6. Limitations, Future Extensions, and Related Optical Usage

The forecasting paper identifies three limitations: data sparsity for newly introduced SKUs, promotional "spike" events requiring dedicated models, and variability in COVID-19 data quality (Pillai et al., 14 Sep 2025). Proposed future enhancements include automated hyperparameter re-tuning as market dynamics shift, cross-SKU meta-learning to improve forecasting for low-volume variants, anomaly-aware modules tailored to major promotions, and interactive visualizations that decompose forecasts into trend, seasonality, holidays, and COVID effects for stakeholder trust and interpretability.

In the unrelated optical literature, "DemandLens" denotes compact cameras enabled by a multi-level diffractive lens that eliminates mechanical refocus by maintaining focus over a broad range of object distances (Banerji et al., 2019). The underlying MDL is designed under the Fresnel approximation, with engineered phase $h(t)$1 and an optimized correction phase $h(t)$2 chosen so that the field remains sharply focused over many planes. At $h(t)$3, the reported focused beam remains diffraction-limited from $h(t)$4 to $h(t)$5, corresponding to a depth of focus of approximately $h(t)$6, with sidelobe suppression of $h(t)$7 or better and imaging over a rectilinear field of view of approximately $h(t)$8 without refocusing or post correction (Banerji et al., 2019). The same source characterizes this as enabling "on-demand," extended-focus imaging and thus "DemandLens" cameras.

The coexistence of these two usages shows that "DemandLens" is not a single technical artifact but a reused label. In current arXiv usage, one sense refers to a Prophet-based forecasting system for SKU-level demand planning, and the other to an extended-depth-of-focus diffractive imaging concept.