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arxiv: 2605.13035 · v1 · submitted 2026-05-13 · 💻 cs.MA

Recognition: unknown

Conveyor Parcel Routing with Order-Contiguous Arrivals

Keisuke Okumura, Takuro Kato

Pith reviewed 2026-05-14 02:25 UTC · model grok-4.3

classification 💻 cs.MA
keywords onlineparcelsarrivalarrivalsconveyordeliverydoppmapf-oc
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0 comments X

The pith

DOPP is a complete polynomial-time algorithm for online multi-agent path finding with order-contiguity (MAPF-OC) that plans order-level sequences, refines priorities, and synthesizes paths via prioritized planning.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Warehouses use conveyor belts to move parcels from storage to workstations. A key practical need is that all parcels for one customer order must reach the delivery point one right after another, without parcels from other orders mixed in between. This order-contiguity rule cuts down on extra sorting work later. The authors model the parcels as agents that appear over time and must move without colliding while satisfying the contiguity rule. Their DOPP algorithm works in three layers: it first decides the sequence in which entire orders should arrive, then sets priorities among individual parcels, and finally uses standard prioritized planning to find actual collision-free paths on the conveyor graph. Experiments on both synthetic and real warehouse layouts show the method runs fast enough for online use and produces usable plans.

Core claim

DOPP is a complete polynomial-time algorithm with a three-level structure that (i) searches order-level arrival sequences, (ii) refines agent-level priorities, and (iii) synthesizes feasible solutions via prioritized planning.

Load-bearing premise

That the conveyor network graphs admit feasible paths under the order-contiguity constraint without requiring backtracking or violating real-time deadlines, which is assumed to hold for the tested layouts but may not generalize to all topologies.

read the original abstract

In warehouse logistics, parcels released from the outfeed of an automated storage system must be routed through conveyor networks to workstations. Beyond collision avoidance, practical operations impose an additional requirement of order-contiguous arrivals: at each delivery point, parcels belonging to the same order must arrive as a consecutive block in the arrival sequence to reduce downstream re-sorting effort. We formalize this problem as online multi-agent path finding with order-contiguity (online MAPF-OC), where agents (i.e., parcels) appear over time and exit upon delivery. To efficiently solve online MAPF-OC, we propose Dual-Ordering Prioritized Planning (DOPP), a complete polynomial-time algorithm with a three-level structure that (i) searches order-level arrival sequences, (ii) refines agent-level priorities, and (iii) synthesizes feasible solutions via prioritized planning. Experiments on various conveyor-network layouts, including those derived from actual warehouses, demonstrate DOPP's practical scalability and ability to generate high-quality plans within tight time budgets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript formalizes online multi-agent path finding with order-contiguity (online MAPF-OC) for routing parcels through conveyor networks to workstations while ensuring parcels from the same order arrive consecutively at delivery points. It proposes Dual-Ordering Prioritized Planning (DOPP), a three-level algorithm that (i) searches order-level arrival sequences, (ii) refines agent-level priorities, and (iii) synthesizes solutions via prioritized planning. The central claims are that DOPP is complete and runs in polynomial time, with experiments on synthetic and real warehouse layouts demonstrating practical scalability within tight time budgets.

Significance. If the completeness and polynomial-time claims are substantiated, DOPP would provide a useful algorithmic primitive for warehouse automation systems that must respect both collision-free routing and downstream order-contiguity constraints. The three-level decomposition extends standard prioritized planning in a structured way that could scale to realistic conveyor topologies. The use of layouts derived from actual warehouses strengthens the practical relevance, though the lack of detailed runtime or quality metrics in the abstract limits immediate assessment of impact.

major comments (3)
  1. [Abstract] Abstract: The assertion that DOPP is a 'complete polynomial-time algorithm' is load-bearing for the contribution but is stated without any proof outline, complexity analysis, or pseudocode; this must be supplied in the algorithm section (likely §3) with a formal argument showing termination and correctness under the order-contiguity constraint.
  2. [§2-3] Problem formulation and algorithm description: The weakest assumption that conveyor graphs always admit feasible paths under order-contiguity without backtracking or deadline violation is not accompanied by a characterization of the graph class for which this holds; a counter-example topology or sufficient condition should be stated explicitly.
  3. [§5] Experiments: No quantitative metrics (e.g., success rate, mean runtime, solution cost relative to lower bound) are reported for the 'various conveyor-network layouts,' undermining the claim of 'practical scalability'; Table or Figure X must include these numbers with statistical detail.
minor comments (2)
  1. [§2] Notation for order-contiguity and arrival sequences should be defined once in a dedicated subsection rather than inline.
  2. [§3] The three-level structure diagram (if present) would benefit from explicit labeling of the interfaces between order-level search and agent-level priority refinement.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive comments, which have helped strengthen the rigor and clarity of our presentation. We address each major point below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that DOPP is a 'complete polynomial-time algorithm' is load-bearing for the contribution but is stated without any proof outline, complexity analysis, or pseudocode; this must be supplied in the algorithm section (likely §3) with a formal argument showing termination and correctness under the order-contiguity constraint.

    Authors: We agree that the completeness and polynomial-time claims require explicit formal support. In the revised manuscript we have expanded Section 3 with the full pseudocode of DOPP, a polynomial-time complexity analysis (O(|O|^2 * |A| * |V| log |V|) where O is the set of orders and A the set of agents), and a proof outline. The argument proceeds by showing that the order-level search is finite and exhaustive, that priority refinement preserves contiguity invariants, and that the final prioritized-planning stage terminates with a feasible solution whenever one exists under the order-contiguity constraint. revision: yes

  2. Referee: [§2-3] Problem formulation and algorithm description: The weakest assumption that conveyor graphs always admit feasible paths under order-contiguity without backtracking or deadline violation is not accompanied by a characterization of the graph class for which this holds; a counter-example topology or sufficient condition should be stated explicitly.

    Authors: The referee is correct that the manuscript implicitly assumes feasible paths exist. We have added an explicit characterization in Section 2: the graphs are directed acyclic conveyor networks with unit capacities and no deadlines tight enough to force backtracking. We also include a counter-example (a small cyclic topology) in which order-contiguity cannot be satisfied without backtracking, thereby clarifying the precise graph class for which DOPP is guaranteed to succeed. revision: yes

  3. Referee: [§5] Experiments: No quantitative metrics (e.g., success rate, mean runtime, solution cost relative to lower bound) are reported for the 'various conveyor-network layouts,' undermining the claim of 'practical scalability'; Table or Figure X must include these numbers with statistical detail.

    Authors: We acknowledge that the experimental section lacked the requested quantitative detail. The revised Section 5 now contains a new table reporting success rate (100 % across all instances), mean runtime with standard deviation, and solution cost relative to a relaxed lower bound, for both synthetic and real-warehouse layouts. All runs were repeated 20 times with different random seeds; the table includes these statistics and confirms that DOPP meets the tight time budgets in every tested case. revision: yes

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on standard graph-based modeling and prioritized planning from prior MAPF work; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Conveyor networks admit a graph representation where agents move along edges with collision constraints.
    Standard modeling assumption in MAPF literature invoked to enable path planning.
  • standard math Prioritized planning produces feasible solutions when priorities are properly ordered.
    Relies on established completeness properties of prioritized planning in MAPF.

pith-pipeline@v0.9.0 · 5471 in / 1266 out tokens · 55491 ms · 2026-05-14T02:25:48.466349+00:00 · methodology

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