Equal-Sized Partition Problem: Application in Spinning and Yarn Production

Abstract

Equal-Sized Partition (ESP) problem originates from real-world yarn production planning, where cotton bales that are characterized by type, color, and micronaire must be selected and divided into equal-sized groups (one per production day) such that the counts of each type and color grade differ by at most 1 across groups, while minimizing the maximum difference in average Mic between any two groups. A spinning company in Hue province, Vietnam, previously relied on a manual three-step process to solve this challenge. This study proves the NP-hardness of ESP, introduces intelligent computational approaches for its complex steps, proposes a dynamic programming algorithm for exact micronaire discretization in the first step, and develops a constraint-based local search metaheuristic for assigning bales to days in the third step. Experiments on five months of historical company data show substantial improvements over the manual method, resulting in the adoption of the proposed solution for daily operations.