Bayesian optimal allocation of temporally evolving combat assets under high-reliability constraints

Efficient allocation of critical combat assets under high-reliability requirements is hindered by conventional models that assume homogeneous efficacy, thereby neglecting empirically observed monotonic performance enhancement across procurement batches. To address this gap, we propose a unified Bayesian optimization framework that integrates three methodological components. First, a Multi-Stage Bernoulli Efficacy (MSBE) model is developed to embed monotonic performance improvement as a structural constraint. Second, a sequential inference engine with order-constrained priors is implemented via a hybrid Gibbs-within-Rejection MCMC scheme to ensure physically plausible posterior estimates. Third, an exact Mixed-Integer Linear Programming (MILP) reformulation is derived to yield a provably optimal, closed-form allocation policy. Numerical experiments demonstrate a statistically significant reduction in expected asset consumption compared to conventional benchmarks under stringent reliability targets.