Abstract
We give an interrelated description for all algorithms which implement a procedure of scheduling and operative planning on the basis of formal procedures and expert solutions. We have achieved this result sequentially solving the following problems: (1) we formalize the network representation of a technological process; develop a language which implements the dynamics of the process functioning, define a set of practical optimality criteria for the operational plan; (2) we obtain a formal representation of the technological process, adapt the general procedures of its two-level aggregation; (3) we substantiate the scheduling problem reduction to the approximating problem of the total weighted completion times minimization on a single machine with precedence relations between the tasks; (4) we formalize the procedure of the coordinated planning which defines the processing order of products (or product series) corresponding to a single basic criterion; (5) we formalize the process of an operational plan construction based on results of the coordinated planning; (6) we develop two algorithms for an operational plan adjustment; (7) we substantiate a procedure for a decision maker for the expert evaluation and adjustment both of a potential portfolio of orders and the due dates of the products (or product series) included in it, for the approval of the final operational plan on the basis of analysis of plans obtained by the formal methods. The last section describes an informational software system implementing the hierarchical model in a specific practical area: for solving the problems of scheduling and planning for small-series productions.
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Notes
- 1.
Here and after, \( \overline{a,b} \) denotes the interval of integer numbers from a to b, that is, \( \overline{a,b} \) = \( {\mathbb{Z}} \cap \left[ {a,b} \right] \) = a, a + 1, …, b.
- 2.
A product’s priority is the ratio of the product’s weight to its critical path length.
- 3.
We define an aggregated job priority as the priority of the product it belongs to. A common vertex priority is the total weight of the products the combined aggregated jobs belong to, divided by the total length of their critical paths.
References
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Zgurovsky, M.Z., Pavlov, A.A. (2019). Algorithms and Software of the Four-Level Model of Planning and Decision Making. In: Combinatorial Optimization Problems in Planning and Decision Making. Studies in Systems, Decision and Control, vol 173. Springer, Cham. https://doi.org/10.1007/978-3-319-98977-8_9
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