TY  - JOUR
TI  - Certified bottleneck transitions and balanced capacity upgrades in robust production–distribution networks
AU  - Okeke Ikenna Stephen
PY  - 2026
JO  - KnowledgeTrend Journal
DO  - 10.5281/zenodo.23349188
UR  - https://doi.org/10.5281/zenodo.23349188
AB  - Manufacturing resources and shipping routes can constrain the same customer commitment, making both uncertainty audits and capacity spending sensitive to changing bottlenecks. This paper develops a certified production–distribution analysis under a static uncertainty model with common resource-coefficient inflation. A reparameterization converts the uncertainty path to a fixed-matrix LP and yields a finite dual-line envelope for maximal supportable commitment stress. A certificate-driven interval procedure traces transitions with explicit upper and lower bounds. A budgeted resource–route upgrade model then derives marginal budget value by minimizing the largest price-normalized multiplier over the entire baseline-optimal dual face. A family with \(k\) simultaneous bottlenecks shows that an arbitrary extreme certificate can overstate marginal value by a factor \(k\), while upgrading only its indicated bottleneck produces zero gain. An explicit two-plant family provides an exact switching law and constructive shipment proof. Computation covers 36 networks with up to 144 shipment variables, 180 budgeted upgrade cases and 25 serial-bottleneck cases. Independently solved primal and dual programs verify the envelope and spending calculations. The method specializes established LP and parametric-optimization principles; its contribution is the linked bottleneck-and-upgrade audit with explicit failure families. All experiments are synthetic.
ER  -