Development of an optimization model for dynamic multi-depot vehicle routing with capacity limits and time-dependent demands

The object of the study is the vehicle routing. The problem to be solved is the static plans often overload particular depots and spread delays across routes. A mixed-integer nonlinear programming model is proposed to simultaneously decide depot assignment, route construction, and departure times, with capacity monitored across periods. The model captures non-linear, load sensitive travel costs and uses adaptive tightening of feasible service intervals to reduce tardiness. The model is solved via outer approximation warm started by a pool of high-quality routes. Across realistic multi period benchmarks, the method reduces total distribution cost and late delivery penalties relative to single depot and static multiple depot baselines. Gains are largest when demand spikes are localized at a few depots, because cross depot reassignment and retimed departures redistribute workload without adding vehicles. Two mechanisms explain the results: capacity accounting that prevents over commitment at congested depots, and coordinated departure time control that limits mid-day delay propagation. Compared with formulations that pre generate trips or treat variability only implicitly, the proposed approach maintains depot feasibility as demand evolves within the horizon. Key features include joint depot assignment with departure time decisions, period wise capacity tracking, and non-linear cost modeling within an exact outer approximation framework compatible with warm started metaheuristics. Practically, the approach supports planning in e commerce, pharmaceutical, and grocery distribution where delivery windows are tight and peaks are frequent. Numerical results show that the model reduces total operating costs by 18%, lowers late-delivery penalties by 27%, improves vehicle utilization by 12%, and decreases average waiting time by 37.5% compared to static baselines