Bao Gia Hoang | Searcharxiv

arXiv2026

Cycle time minimization for the simple assembly line balancing problem under peak power constraints

Peak power limits restrict concurrent tasks and may increase assembly-line cycle time. To the best of our knowledge, this study is the first to minimize cycle time for the simple assembly line balancing problem type 2 (SALBP-2) with a fixed number of workstations and a fixed limit on total instantaneous power. An exact satisfiability (SAT) method finds feasible schedules, searches systematically for shorter cycles, and proves optimality when possible. Two reproducible formulas define looser and tighter power limits for 72 cases based on the standard SALBP library, with Gurobi and CPLEX providing commercial MIP and CP comparisons. Relative to standard SALBP-2 optima, the two limits increase the best-known cycle time by 16.49% and 61.02% on average. The best-performing SAT configurations find a feasible solution for every case, solve more cases to optimality than each commercial solver, and when both prove optimality, are almost always faster under the reported settings.

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arXiv2025

Compact SAT Encoding for Power Peak Minimization

The Simple Assembly Line Balancing Problem with Power Peak Minimization (SALBP-3PM) minimizes maximum instantaneous power usage while assigning $n$ tasks to $m$ workstations and determining execution schedules within given cycle time constraints. This NP-hard problem couples workstation assignment, temporal sequencing, and power aggregation, presenting significant computational challenges for exact optimization methods. Existing Boolean Satisfiability (SAT) and Maximum Satisfiability (MaxSAT) approaches suffer from baseline encodings generating $O(m^2)$ clauses per precedence edge. We introduce a Compact SAT Encoding (CSE) achieving $O(m)$ clauses per transitive precedence edge using sequential counter techniques. We instantiate four optimization variants: Clause-Based iterative SAT, Pseudo-Boolean (PB) Constraint iterative SAT, MaxSAT, and Incremental SAT. Comprehensive experimental evaluation on benchmark instances demonstrates consistent performance improvements over state-of-the-art approaches, enabling exact optimization on previously intractable industrial-scale instances. The encoding principles generalize to other assembly line balancing variants and broader scheduling problems with precedence constraints.

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