Compact SAT and MaxSAT Encodings for Business-to-Business Meeting Scheduling with Idle-Time Balancing

Long Duc Nguyen; Tuyen Van Kieu; Khanh Van To

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arXiv · 2608.00614

Compact SAT and MaxSAT Encodings for Business-to-Business Meeting Scheduling with Idle-Time Balancing

Long Duc Nguyen·Tuyen Van Kieu·Khanh Van To

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Abstract

Business-to-business meeting scheduling assigns requested pairwise meetings to time slots and locations under availability, capacity, conflict, and precedence constraints. The published Boolean formulation retains meeting-slot assignments that propagation can eliminate and encodes precedence relations with pairwise clauses. We present compact SAT and MaxSAT encodings based on solution-preserving domain filtering, variables shared at selected precedence boundaries, and an objective that minimizes the range of participants' internal idle-slot totals. Experiments on 126 official and 100 higher-density derived instances examine domain filtering, precedence representation, transitive relations, and optimization method. Compared with an adapted published MaxSAT formulation using the same objective, the proposed encoding reduces the median clause count by 40.3% and median peak memory usage by 55.9%. Domain filtering alone reduces assignment variables by 24.1% and clauses by 16.2%. Sharing variables at selected precedence boundaries reduces clauses by 0.5%-1.0% on official precedence instances and by up to 5.5% at the highest derived density. The idle-time measure distinguishes one-slot interruptions from longer waits, while aggregate idle time provides a complementary measure. Compared with Gurobi, a leading commercial solver, all three SAT and MaxSAT methods solve every official instance with lower median total times.

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Long Duc Nguyen, Tuyen Van Kieu, Khanh Van To. 2026-08-01. Compact SAT and MaxSAT Encodings for Business-to-Business Meeting Scheduling with Idle-Time Balancing. https://arxiv.org/abs/2608.00614

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