This paper introduces the edge-based contiguous p-median (ECpM) problem to partition the roads in a network into a given number of compact and contiguous territories. Two binary programming models are introduced, both of which incorporate a network distance. The first model requires an exponential number of cut set-based constraints to model contiguity; it is paired with a separation scheme that usually generates only a small number of these constraints, namely, a branch-and-cut (B&C) algorithm. The second model utilizes a polynomial number of shortest-path constraints to model contiguity and can be solved with off-the-shelf solvers. The respective solution approaches are tested on road networks with over 2,700 nodes and close to 3,400 edges, yielding models with over 9.6 million binary variables. Solving the model based on shortest path contiguity (SPC) constraints via standard branch and bound attains speedups in computational time of up to 17x relative to the cut set-based B&C implementation. In addition, the SPC constraints are demonstrated to be supervalid inequalities of the edge-based p-median (EpM) model (i.e., for which contiguity is not explicitly required), meaning that they may cut off integer-feasible solutions and some, but not all, of the optimal solutions of this simpler problem. Finally, the paper explores structural insights and connections between ECpM and the edge-based districting (EBD) problem, which enforces an additional work balance criterion. An existing model that utilizes cut set-based contiguity constraints was unable to find a feasible solution within 12 hours for any of the tested instances, while an SPC-based EBD model was able to solve most of these to optimality.
Adhiraj Singh, Deepanshu Mody, Ghina Al Shdaifat +4cs.CL
Recent work has shown that subword vocabularies can be trained to optimize compression for a specific inference rule rather than relying on greedy heuristics such as Byte Pair Encoding (BPE). We extend this approach to greedy left-to-right longest-match decoding, the fast and widely used inference rule underlying WordPiece. We introduce Joint Optimization for Greedy Longest-Match Tokenization (JOLT), which formulates vocabulary learning as an integer program over vocabulary-selection and segmentation-choice variables. Greedy-consistency constraints ensure that each optimized segmentation exactly matches the segmentation produced by longest-match decoding under the selected vocabulary, aligning the training objective with deployment-time tokenization. To scale the optimization, we solve a linear programming relaxation and selectively introduce higher-order segmentations only for unresolved pretokens. The resulting relaxation is nearly integral: rounded solutions fall within 0.008 - 0.176 % of the LP lower bound on the training scope. The bound also shows that BPE is already within 1 - 2 % of the best achievable compression under greedy longest-match decoding, while JOLT closes 89.6 - 99.4 % of the remaining gap. On held-out validation data across four training scopes and vocabulary sizes of 32,000 and 64,000, JOLT produces up to 0.78 % fewer tokens than BPE, with improvements generally increasing as the training scope grows. These results demonstrate that inference-aligned vocabulary optimization can recover most of the limited compression headroom left by BPE while providing a certificate of near-optimality.
For years, supply chain planning at e-commerce firms has operated as a collection of isolated projects. Each planning task from static network planning to dynamic warehouse assortment planning requires analysts to spend weeks building models from scratch, calibrating and persuading executives to act on outputs they cannot verify. Three barriers drive this: bespoke models proliferate because standardization is difficult (operational fragmentation); once unified, the combinatorial scale of millions of SKUs, thousands of nodes, and intricate routing logic exceeds what solvers can handle within a tight window (computational intractability); and a mathematically optimal solution still fails to be implemented if the executives do not trust it (implementation hurdle). To bridge this gap, we propose and implement the Simulation-Propose-then-OR-Dispose method, deployed as JD.com's NetSim platform. The central insight is decoupling: simulation proposes by generating and evaluating the full set of operationally valid candidate paths-absorbing all idiosyncratic business logic, while an integer program disposes by selecting the globally optimal subset. Computationally, matrix-vectorized CPU/GPU accelerated simulation achieves a 10-100 times speedup over serial methods, and a list scheduling algorithm reduces coupled-order processing from hours to minutes. Operationally, we establish a closed loop via an intelligent diagnosis engine. Since 2025, NetSim has optimized end to-end services for over 20,000 suppliers, the cross-regional fulfillment rate dropped from 6.1% to 4.9%, and the average monthly carbon reduction is approximately 5,745 tCO2e. SPORD moves simulation from monitoring to active planning. The transparent outputs turn skeptical executives into engaged collaborators, and the modular architecture ensures that the next planning requires just configuration, not reconstruction.