Paper #220

The Mergeable Storage Location Assignment Problem: A Flow-Based Decomposition with Energy and Carbon Accounting

Ermal Belul, Marwane Bouznif, Dritan Nace and Antoine Jouglet

Presenting author: Ermal Belul

Session: I17

Abstract

The Storage Location Assignment Problem (SLAP) determines warehouse handling costs and energy consumption. We introduce the Mergeable Storage Location Assignment Problem (MSLAP), which allows adjacent locations to be merged, increasing capacity for high-demand products and reducing replenishment frequency. A direct cost-minimizing integer program formulates MSLAP exactly but its dense overlap constraints stall at industrial scale. We recast the problem on an extended flow network with proportional side constraints and solve it in three phases: greedy initialization, flow-based topology exploration, and exact bipartite matching. On a real instance (1,543 products, 3,285 locations), the flow model reaches in one minute a cost the direct model cannot match in two hours, validating four times as many merges. Optimal assignment cuts material-handling energy by about 12%, meeting a 10% target; among compliant layouts the recommended one reduces operating cost by roughly a third, most of it from merging. Station workload balance improves by 21%, an observed side effect of spreading merges across the grid.