Researchers P.K. Sudhakar, J. Maria Arockia Dass, S. Arulanad and Akhilesh Kumar Yadav collected 34 sequential production observations from a footwear manufacturing environment, capturing manpower, cycle time, operator skill and performance ratings, allowance factors, processing time, the standard minute value known as SMS, and pairs per hour, or PPH. Each record corresponds to a step in the production sequence — marking, skiving, fusing, stitching, attaching — and the observations were sorted chronologically to preserve the temporal structure that time-series forecasting requires. PPH was explicitly treated as a derived efficiency indicator, calculated from cycle time and standard minute values rather than measured independently, a choice the authors make to avoid overstating the independence of the response variable.

The team benchmarked three models on identical footing. Linear regression related PPH to manpower and task time, explaining roughly 76.5 percent of the variation in productivity, with both predictors highly significant at p < 0.001 and a residual standard error of 4.42. Holt’s exponential smoothing was implemented in the ETS state-space framework, specifically an ETS(M,N,N) specification with multiplicative errors, no trend and no seasonality, its smoothing parameters estimated by maximum likelihood rather than hand tuning. ARIMA, the third contender, models temporal dependence through autoregressive, differencing and moving-average components, with the model order selected from autocorrelation and partial autocorrelation plots supported by information criteria such as the Akaike Information Criterion.

To evaluate genuine out-of-sample skill rather than how well a model can memorize its own training data, the 34 observations were split chronologically into 27 training and 7 test records — an 80:20 partition applied consistently to all three models, with no random shuffling, to prevent information leakage from future observations into model estimation. Performance was scored with root mean squared error, mean absolute error and mean absolute percentage error, supplemented by residual diagnostics including autocorrelation plots and Ljung-Box tests.

On the headline comparison, ARIMA came out ahead. It achieved the lowest test-set error of the three headline models, with an RMSE of 8.0866, an MAE of 8.0342 and a MAPE of 13.71 percent, compared with an RMSE of 10.06 and MAE of 9.49 for linear regression and an RMSE of 10.26 and MAE of 9.67 for Holt’s method in the comparative table. The ARIMA forecast itself remained stable at roughly 54 to 55 pairs per hour, with confidence intervals that widened gradually as the horizon extended and no significant residual autocorrelation. The authors attribute ARIMA’s edge to its ability to capture the temporal dependence and stochastic variation inherent in a sequence-dependent production process — structure that a static regression simply cannot represent.

The Diebold-Mariano test, which assesses whether the difference in accuracy between two forecasting models is statistically significant, added nuance. ARIMA outperformed linear regression with a DM statistic of -3.1183 and a p-value of 0.0018, a difference the authors describe as highly significant. Against the mean model, ARIMA’s advantage was weaker (DM statistic -1.7252, p = 0.0845), marginally significant at the 10 percent level but not at the conventional 5 percent threshold. A separate comparison reported Holt’s method as statistically distinguishable from linear regression (p = 0.01704). The authors are careful to note that a significant p-value in one test does not by itself establish model superiority; that judgment rests on the objective error metrics.

The Holt’s analysis carries its own methodological subtleties. Applied to the full 34-observation series, the ETS(M,N,N) model yielded an initial level of 53.79 PPH, a smoothing parameter of 0.20, and in-sample errors of RMSE 10.35, MAE 7.63 and MAPE 12.92 percent — figures the authors explicitly flag as fitting diagnostics, not forecasting performance. Under the chronological 80:20 procedure, the training-set errors were RMSE 11.07, MAE 8.26 and MAPE 13.75 percent, while the out-of-sample test set produced an RMSE of 6.83, an MAE of 3.95 and a MAPE of 7.89 percent. The Ljung-Box test on the model residuals returned a Q-statistic of 6.43 with 7 degrees of freedom and a p-value of 0.491, indicating no significant remaining autocorrelation up to lag 7. Residual plots showed errors oscillating around zero with a slight rightward skew and a few lags near the confidence bounds, and the authors caution that the widening spread of residuals toward the end of the series hints at possible heteroscedasticity.

Beyond throughput, the study attempted a dual perspective by tracking an energy-related indicator alongside PPH. The mean energy index was approximately 1.46 for the actual data, 1.40 for Holt’s forecasts and 1.50 for the linear regression estimates; the regression estimate sat slightly above the observed value, which the authors read as evidence that the linear model offers predictive insight but limited power to minimize energy consumption in this setting. Importantly, the paper’s own conclusion draws a firm boundary here: the work does not quantify actual energy consumption or demonstrate measurable improvements in energy efficiency or sustainability. The results should be interpreted as a forecasting framework that can support informed production planning, not as direct evidence of energy savings.

That honesty about scope is one of the study’s more notable features. The authors state plainly that the analysis used data from a single footwear production environment, which limits generalizability to other manufacturing systems; that the focus was short-term forecasting, excluding seasonal patterns and long-term operational dynamics; and that external factors such as machine breakdowns, maintenance schedules, supplier disruptions and workforce absenteeism were not incorporated into the models. They also acknowledge that the ETS(M,N,N) specification, by omitting trend and seasonal components, could be a limitation if the series displayed long-term movements, and that sharp shifts around certain time points may signal structural breaks the model does not account for. The multiplicative error structure additionally requires strictly positive data.

The broader motivation is a gap the authors identify in the manufacturing analytics literature: most published work emphasizes computationally demanding AI architectures, while comparatively few studies benchmark interpretable, lightweight statistical models that can run on real-time shop-floor data in facilities without deep AI infrastructure. Deep learning and hybrid approaches often achieve strong predictive performance, the authors note, but at the cost of complexity and reduced transparency — a problem in footwear manufacturing, where decisions about task sequencing, workforce allocation and changeover planning must be explainable to non-technical stakeholders. The study positions its three-model comparison as a practical decision-support tool for short-term production planning in settings with little or no seasonality, and suggests future work validating the framework on larger, more diverse industrial datasets, exploring hybrid statistical-machine-learning approaches, and integrating real-time Industrial Internet of Things data and digital twin technologies. For now, the message for manufacturers is measured: among the methods tested on this dataset, ARIMA delivered the most accurate short-term forecasts, while simpler models remain credible, transparent alternatives whose value depends on the operational priorities of the line they serve.

Subject of Research: Comparative short-term forecasting of footwear production efficiency using linear regression, Holt's exponential smoothing and ARIMA on real shop-floor data

Article Title: Comparative forecasting of footwear production efficiency using linear regression, Holt’s exponential smoothing, and ARIMA for sustainable manufacturing

Article References: Sudhakar, P. K., Dass, J. M. A., Arulanad, S., & Yadav, A. K. (2026). Comparative forecasting of footwear production efficiency using linear regression, Holt’s exponential smoothing, and ARIMA for sustainable manufacturing. Results in Engineering, 32, Article 113458. https://doi.org/10.1016/j.rineng.2026.113458

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113458

Keywords: footwear manufacturing, forecasting, ARIMA, linear regression, exponential smoothing, ETS model, pairs per hour, production efficiency, time series analysis, Diebold-Mariano test, sustainable manufacturing, Industry 4.0