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

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.