Abstract
An Augmented Makespan Assignment Problem (AMAP), which is a variation of theGeneralised Assignment Problem (GAP), is analysed in this paper. In this problem, weminimise the makespan for producing several products with each on one of several machines.The data instances are such that some of the available machines are identical, which in turnleads to mixed integer programming problems that have many optimal integer solutions.Most commercial software for mathematical programming therefore has problems provingthat the solution they find is an optimal one. Even optimisation software that does someinteger preprocessing on the system of linear relations has problems in solving a straightforwardformulation of the model. Darby-Dowman et al. investigated this model and foundit difficult to solve as an IP. We show that if more of the model structure is highlighted at themodelling stage, and these are exploited in preprocessing the formulation before the problemmatrix is produced, then we get easily solvable integer programs for the data instances underconsideration. We give computational results for five different commercial codes with andwithout our preprocessing at the modelling stage.
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Baricelli, P., Mitra, G. & Nygreen, B. Modelling of augmented makespan assignment problems(AMAPs): Computational experience of applyinginteger presolve at the modelling stage. Annals of Operations Research 82, 269–288 (1998). https://doi.org/10.1023/A:1018914820426
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DOI: https://doi.org/10.1023/A:1018914820426