📝 SummarXiv

Abstract

This study introduces the Box Allocation Problem (BAP), a novel optimization challenge in the $1.4 billion UK meal kit delivery market. BAP involves assigning orders across multiple production facilities to minimize daily recipe variations while adhering to capacity and eligibility constraints over a 15-day planning horizon. We formulate BAP as a mixed-integer linear programming (MILP) problem and systematically compare the performance of the COIN-OR Branch and Cut (CBC) solver with heuristic methods, including Tabu Search and Iterative Targeted Pairwise Swap. Scalability experiment on instances with up to 100,000 orders show that CBC consistently achieves optimal solutions in under two minutes, maintaining optimality even under dynamic conditions with fluctuating factory capacities and changing customer orders. By reducing day-to-day recipe discrepancies, this approach supports more accurate ingredient forecasting, decreases food waste, and improves operational efficiency across multi-factory network. These results provide the first comprehensive solution framework for temporal allocation problems in meal kit delivery operations.