The cutting–wrapping problem in the textile industry: Optimal overlap of fabric lengths and defects for maximizing return based on quality

This paper deals with an important problem in the last phase of manufacturing in the textile industry. This involves cutting large lengths of fabric into smaller pieces, which are then wrapped around rolls. The quality of cloth rolls transported to the customer is specified by the quality of fabric pieces that make up the roll. A piece of fabric falls within a given quality category if some of its characteristics, such as piece length, the number of critical defects per metre, and the defective score per metre, are compatible with the corresponding quality specifications. Naturally, the selling price per metre of fabric is proportional to the quality category. Thus, it becomes necessary to determine an optimal cutting strategy of very long woven fabric (e.g. 2000 m) into smaller pieces (e.g. each 130 m long at most), which involves a difficult continuous assignment problem of identifying the optimal cutting locations of pieces overlapping with defects of known lengths and locations. Not only must the scrap be minimized but the overall profit per metre fabric should be maximized. The two objectives may not always support each other due to relative unit selling prices of various quality categories. The solution to this problem has an immediate impact on company profit. The mathematical formulation of the problem involves numerous binary variables as well as continuous variables. A Mutative Simulated Annealing approach is proposed here to solve this problem. The solution technique is tested both on real data obtained from a textile manufacturer and hypothetical data. Results are compared against upper bounds calculated for each objective defined, as well as with a sequential heuristic designed for this problem.