Robust sequencing of heterogeneous items in Bucket Brigade systems

Problem definition: Serial production and assembly systems apply work-sharing, most commonly based on the Bucket Brigade approach. Differently from typical analysis, we assume item heterogeneity, which may create blockages and reduced efficiency. The problem is how to sequence the entering items in order to minimize this potential inefficiency. Academic/Practical Relevance: The framework models real-world processes such as mixed-model assembly lines involving the simultaneous assembly of multiple product variants, and order picking with workload distributed along the picking aisle according to the number of items to be picked. Methodology: To analyze such systems, we propose a measure for robustly quantifying the generated blockage inefficiency (BI) as a proxy for the makespan. As the BI might be large or small depending on the sequence of items, several strategies are proposed to analytically and numerically identify robust sequences with no-blockage or with minimal BI. Results: We provide several, nested notions of no-blockage, each ensuring the existence of a robust no-blockage sequence. Infinitely many sets of item types satisfying no-blockage in any sequence are identified. We show that no-blockage in a robust sense is implied in particular by first-order distributional dominance sequencing. Hamiltonian path and Traveling Salesman Problem modeling with corresponding ILP formulations are proposed as exact and approximate computational methods of robust sequences with no-blockage or minimal BI. Sequencing based on steady-state hand-off positions is also proved useful. Analyzing robust sequencing more generally when blockage is possible, we show an asymptotic result by which the robust BI of any efficient sequence approaches zero in the limit as the sequence length tends to infinity. Managerial Implications: In general, sequencing items is a practically relevant and effective managerial strategy, as it typically substantially reduces the robust BI, and often eliminates it entirely. The latter is particularly relevant when the number of items is large.