A Life-Cycle Technology Upgrade Scheduling Model

Technology upgrades are a central lever for sustainability, yet many optimization models primarily account for use-phase emissions and treat embodied impacts and technological change exogenously. We propose a multi-period mixed-integer optimization framework that couples upgrade timing, technology choice, and operations with a life-cycle assessment (LCA) structure. The model (i) separates use-phase and embodied impacts at the transition level, (ii) supports time-weighted valuation of impacts through a flexible weighting sequence (time value of carbon), and (iii) incorporates endogenous learning-by-doing that can reduce both investment costs and embodied impacts of future upgrades. We derive an exact Benders (L-shaped) decomposition that separates discrete upgrade dynamics from a linear operating subproblem. Computational experiments illustrate model behavior and report runtimes under an outer-loop implementation with open-source solvers, highlighting that decomposition becomes most beneficial when extensions substantially enlarge the dispatch layer (e.g., scenario expansion). Experiments also show that ignoring embodied impacts can mis-rank upgrade schedules and even violate life-cycle caps, that stronger time-weighting pushes upgrades earlier, and that learning can make staged upgrades economically preferable.