Formulation and solution of problems of tool positioning on a single machining centre

The authors extend previous work on the construction of a computer technique used to formulate and solve a tool positioning problem concerning the efficient use of a single machining centre. The problem is formulated as an integer programming model. The problem is to identify which pockets of a circular tool magazine should be used to accommodate specific tools, during machine setup, so as to minimize the makespan of a given sequence of operations. The authors now analyse the more realistic situation in which it is assumed that the given sequence of operations is to be carried out repeatedly. Consequently, the pockets of the magazine must contain the same classes of tools at the end of each cycle of operations as they did at the beginning, so that the process can be repeated in an identical fashion. The extended problem is also formulated as an integer programming model, capable of being solved using commercially available software. Problems of a realistic size can then be used to set up operating conditions for a machining centre.