Operational Weighting Changes Cooperative Forecast Valuation: A Residual-Fixed Sensitivity Analysis for Federated Demand Forecasting
Abstract
Predictive-score-based valuation often allocates value from residual or accuracy improvements while leaving the map to downstream operational value implicit. We study federated
demand forecasting among firms as a transferable-utility cooperative game whose characteristic function is an inventory-motivated weighted reduction in predictive residual scale.
Weights combine the normal-loss expected-cost coefficient in holding and shortage costs
with a √
Li + 1 protection-period scaling factor under an i.i.d. one-step error benchmark;
they supply a relative inventory-motivated weighting rule rather than a calibrated estimator of realized inventory cost, and are not claimed to coincide with realized path inventory
cost under a finite-horizon single-echelon diagnostic. Coalition models use exact federated
ridge on additive training statistics Ti = (Ai
, bi
, ni) with size-scaled regularization (including the intercept). The design caches residual maps and changes only operational weights,
so that, conditional on each seed’s fixed residual map, ranking and normalized-allocation
shifts are induced by weighting rather than refitting. Along a mean-normalized path from
equal weights to the largest tested effective weight imbalance (κeff ≈ 2.94), Spearman agreement with the unweighted residual ranking falls from 1 to 0.89–0.77 for n ∈ {4, 6, 8} (40
seeds), with full-rank-change rates up to 1.00 and exhaustive assignment dispersion (4! = 24,
6! = 720, 8! = 40320) showing that, within the tested DGP and weight multiset, fixed κeff
does not uniquely determine rank agreement. In an n=4 finite-horizon path-cost diagnostic
using average cost per hold-out period, residual-weighted and path-cost Shapley rankings are
negatively correlated (bootstrap CIs exclude zero). We report analytically computed first
rank-change thresholds along the mean-normalized path, Wilson intervals, and robustness
under fixed versus size-scaled ridge and moderate sample-size heterogeneity.
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BibTeX
@misc{khoshakhlagh2026operational,
title = {{Operational Weighting Changes Cooperative Forecast Valuation: A Residual-Fixed Sensitivity Analysis for Federated Demand Forecasting}},
author = {Sajjad Khoshakhlagh},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23457715},
url = {https://zenodo.org/records/23457715},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Operational Weighting Changes Cooperative Forecast Valuation: A Residual-Fixed Sensitivity Analysis for Federated Demand Forecasting
AU - Sajjad Khoshakhlagh
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23457715
UR - https://zenodo.org/records/23457715
AB - Predictive-score-based valuation often allocates value from residual or accuracy improvements while leaving the map to downstream operational value implicit. We study federated demand forecasting among firms as a transferable-utility cooperative game whose characteristic function is an inventory-motivated weighted reduction in predictive residual scale. Weights combine the normal-loss expected-cost coefficient in holding and shortage costs with a √ Li + 1 protection-period scaling factor under an i.i.d. one-step error benchmark; they supply a relative inventory-motivated weighting rule rather than a calibrated estimator of realized inventory cost, and are not claimed to coincide with realized path inventory cost under a finite-horizon single-echelon diagnostic. Coalition models use exact federated ridge on additive training statistics Ti = (Ai , bi , ni) with size-scaled regularization (including the intercept). The design caches residual maps and changes only operational weights, so that, conditional on each seed’s fixed residual map, ranking and normalized-allocation shifts are induced by weighting rather than refitting. Along a mean-normalized path from equal weights to the largest tested effective weight imbalance (κeff ≈ 2.94), Spearman agreement with the unweighted residual ranking falls from 1 to 0.89–0.77 for n ∈ {4, 6, 8} (40 seeds), with full-rank-change rates up to 1.00 and exhaustive assignment dispersion (4! = 24, 6! = 720, 8! = 40320) showing that, within the tested DGP and weight multiset, fixed κeff does not uniquely determine rank agreement. In an n=4 finite-horizon path-cost diagnostic using average cost per hold-out period, residual-weighted and path-cost Shapley rankings are negatively correlated (bootstrap CIs exclude zero). We report analytically computed first rank-change thresholds along the mean-normalized path, Wilson intervals, and robustness under fixed versus size-scaled ridge and moderate sample-size heterogeneity.
ER -