The article presents a new algorithm that enables the allocation of the optimal scheduling of the production orders in the two-machine system based on the minimum cost of order delays. The formulated algorithm uses the method of branch and bounds and it is a particular generalisation of the algorithm enabling for the determination of the sequence of the production orders with the minimal sum of the delays. In order to illustrate the proposed algorithm in the best way, the article contains examples accompanied by the graphical trees of solutions. The research analysing the utility of the said algorithm was conducted. The achieved results proved the usefulness of the proposed algorithm when applied to scheduling of orders. The formulated algorithm was implemented in the Matlab programme. In addition, the studies for different sets of production orders were conducted.
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