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.
One of the main tasks in the planning of production processes is to satisfy the needs of the customers in terms of quantity, quality and time. The issue of the timely execution of production orders is becoming increasingly important. Based on the conducted studies it can be concluded that the size of the delay depends on the adopted scheduling of orders. This paper focuses on the problem of implementing a scheduling of production orders that will allow to avoid delays, and in the event such a scheduling is not possible, for minimizing the sum of delays of all the orders. A new algorithm has been proposed that allows to determine of the optimal sequence of production orders with the minimum sum of delays. The considerations have been limited to the issue of a two-machine system in which the orders are carried out in a flow.
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