{"ID":5676005,"CreatedAt":"2026-07-03T01:40:09.565152011Z","UpdatedAt":"2026-07-04T21:23:35.342999881Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.01489","arxiv_id":"2607.01489","title":"Admission and Assortment Optimization for Multi-size Automated Parcel Lockers","abstract":"We study admission control and capacity design for automated parcel lockers with multiple parcel and locker sizes. A smaller parcel can use a larger locker, but doing so may block a future larger parcel whose rejection is more costly. We formulate the admission problem as a finite-state, infinite-horizon average-cost Markov decision process and solve small instances exactly by relative value iteration. We analyze the always-accept (AA) policy, which admits every feasible parcel into the remaining compatible capacity, and give a sufficient condition for its optimality. Across two-, three-, and four-size experiments, AA is optimal in fast-pickup regimes and nearly optimal when holding times are longer; observed optimality gaps are negligible even when AA is not optimal. We then study the locker-assortment problem, which minimizes facility cost plus optimal expected rejection cost. We give an exact bound-and-enumerate algorithm for moderate-size instances. Although the objective is not discrete convex, exchange-neighborhood local search finds the certified optimum in every instance for which exact certification is computationally tractable, and it scales as a heuristic to larger systems.","short_abstract":"We study admission control and capacity design for automated parcel lockers with multiple parcel and locker sizes. A smaller parcel can use a larger locker, but doing so may block a future larger parcel whose rejection is more costly. We formulate the admission problem as a finite-state, infinite-horizon average-cost M...","url_abs":"https://arxiv.org/abs/2607.01489","url_pdf":"https://arxiv.org/pdf/2607.01489v1","authors":"[\"Carlos Aníbal Suárez\",\"Antoine Deza\",\"Tal Raviv\"]","published":"2026-07-01T21:32:47Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}