Smart library services increasingly depend on heterogeneous IoT terminals and edge nodes, whose computing resources must be scheduled under three conflicting objectives—latency, energy, and cost—with a trade-off that shifts with the business cycle. Existing deep-reinforcement-learning (DRL) schedulers mostly scalarize these objectives with fixed weights and therefore cannot re-balance the trade-off as the business context changes. We propose BC-PA-DDQN, a business-cycle-aware preference-adaptive dueling double DQN that conditions the Q-value on a task-level preference vector: each task’s weights combine a task-type prior, a business-period modulation, and a per-task log-normal perturbation, replacing the fixed uniform preference of the baseline PA-DDQN. Because no public library-computing dataset with per-task telemetry exists, we calibrate the business-cycle arrival multipliers and task-type composition from 18 months of real library operational data and model the task-size and SLA distributions from domain knowledge. Over 10 seeds with per-seed paired sign-permutation tests, BC-PA-DDQN significantly outperforms the fixed-preference PA-DDQN ($+0.984$ reward, Holm-corrected $p=0.0234$, 10/10 seeds) and the DDQN/D3QN/greedy/random baselines, and it shows no significant difference from a maximum-entropy SAC baseline ($p=0.56$). A factor test and a leave-one-phase-out test show that the numerical preference carries information beyond the phase label and transfers to unseen phases. The gain is an explicit energy-for-cost trade-off, and the 5316-parameter network is about 3× smaller than SAC.