Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
An improved branch and bound algorithm for mixed integer nonlinear programs
Computers and Operations Research
Integrating SQP and Branch-and-Bound for Mixed Integer Nonlinear Programming
Computational Optimization and Applications
Numerical Experience with Lower Bounds for MIQP Branch-And-Bound
SIAM Journal on Optimization
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Label printing finds many applications in industry. However, this task is still labor intensive in many printing factories. Since each template can only accommodate a fixed number of labels, an important task is to work out the compositions of templates by allocating suitable labels to each template in order to fulfill the order requirements effectively. The template design could be rather arbitrary, which usually ends up with a lot of excessive printed labels. Enhancing the template design will significantly improve the efficiency of the printing process, and, at the same time, reduce the waste of resources. This motivates the study of more automatic design methods. In this paper, the problem is first formulated as a nonlinear integer programming problem. The main variables in the formulation are the compositions and the printing frequencies of templates. For practical purpose, each type of label is confined to one template only which allows automated packing and handling. The structure of the problems is carefully analyzed and a new algorithm is proposed. Numerical results show that the proposed method is a simple but effective way of generating good template designs.