Analytics Investment in EOQ Systems: Joint Ordering- and Holding-Cost Reduction Under Benefit Realisation Risk

Analytics programmes can reduce EOQ ordering and holding costs, but expenditure is committed before planned benefits are fully realised. This study extends an established joint cost reduction formulation with a post-optimisation benefit realisation evaluation. Deterministic planning selects the replenishment quantity and planned reductions under annualised quadratic expenditure and reduction caps. Multi-start optimisation and grid verification are followed by sensitivity analysis, three 5000-replication Monte Carlo scenarios, paired fixed- and adaptive-quantity comparisons, and a cap-matched cubic expenditure experiment. At the illustrative quadratic baseline, annual cost falls from 10,000 to 8669.08, a 13.31% saving. Fixed-quantity mean savings are 8.74% under uniform uncertainty and 8.45% under a mean-matched triangular distribution. Adapting the quantity raises the uniform mean to 8.79% and reduces loss severity on the investigated adverse-effectiveness map without eliminating all losses. All original Monte Carlo replications outperform the matched classical EOQ within the sampled realisation range [0.75, 1.00]. The cubic experiment changes optimal decisions, savings, and loss boundaries, partly because its interior expenditure is lower. The results distinguish operational rigidity from unrecovered committed expenditure. Parameters and uncertainty distributions are illustrative, and numerical thresholds are specification-dependent.