Sequencing heterogeneous orders in Bucket Brigade order-picking lines

Bucket Brigade (BB) is a common approach for dynamic work-sharing in order-picking lines. Differently from typical analysis, we assume heterogeneous orders, which creates blockages and reduced efficiency. The problem is how to sequence entering orders with the aim of minimizing this potential inefficiency. The proposed framework models order-picking lines with workload distributed along the picking aisle according to the number of items to be picked in each pick face. We propose a measure for quantifying the generated blockage inefficiency (BI) as a proxy for the makespan. As the BI depends on the sequence of orders, several strategies are proposed to identify sequences with no-blockage or with minimal BI. We provide several practical sequencing policies. Sequencing based on no-blockage notions and steady-state hand-off positions is proved useful, and no-blockage is implied by first-order distributional dominance sequencing. Traveling salesman problem and Hamiltonian path modeling is proposed as an exact computational method of item-specific sequences with minimal or no blockage in a strong sense. A simple policy ensures low BI for large sets of orders, for which we show an asymptotic result: the BI of any efficient sequence approaches zero in the limit as the sequence length tends to infinity. In general, sequencing orders is a practically relevant and effective managerial strategy, as it typically substantially reduces the BI and often eliminates it entirely.