A relax-and-fix method for clothes inventory balancing scheduling problem

Abstract

The clothes inventory balancing scheduling problem (CIBSP) among branch stores with the allowance of lateral transshipments has gained increasing attentions in fast-fashion apparel industry, especially for the trial sale of new products. To solve the CIBSP faced by a leading apparel company in China, a mixed integer linear programming (MILP) model is first formulated, based on which a relax-and-fix (R&F) method is developed. Several heuristic cuts based on practical experience and observations are further integrated into the R&F method to speed up the searching. The effectiveness of the method is demonstrated through extensive computational experiments: it is able to provide near-optimal solutions with average optimality gap 1.15% with less computation time, compared to solving the MILP model directly in a commercial solver. Case studies also demonstrate that the developed R&F method can obtain high-quality solutions with average optimality gap 0.09% with much less computation time.

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