Scheduling in Industry 4.0 and Cloud Manufacturing by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9783030431778
Publisher: Springer International Publishing

(7.21)

(7.22)

The goals are defined as shown in Eqs. (7.23)–(7.26):

(7.23)

(7.24)

(7.25)

(7.26)

Equation (7.23) estimates uniformity of the use of the IRs and ; r, r 1 ∈ {1, …, ρ ν}. Equation (7.24) estimates amount of completed operations . Equation (7.25) takes into account losses from nonfulfilled operations. Equation (7.26) assesses total cost of ownership (TCO) for the IR .

7.4.3 Model Integration

The developed modeling complex is composed of dynamic models of IS and IR control subject to execution of material flows. It also includes elements of IR reconfiguration [e.g., in Eqs. (7.14)–(7.16) and (7.20)]. Full consideration of the reconfiguration model can be found in (Ivanov and Sokolov 2013).

The presented models M1 and M2 are interconnected with the help of Eq. (7.6) where elements from M2 are used in M1. In its turn, M1 influences M2 through Eqs. (7.14) and (7.20).

The proposed models and algorithms have been validated in a developed prototype based on C++ and XML. The OPC calculation is based on the Hamiltonian function. In integrating the main and the conjunctive equation systems, the values of variables in both of the systems can be obtained at each point of time. The maximum principle guarantees that the optimal solutions (i.e., the solution with maximal values) of the instantaneous problems (i.e., at each point of time) give the optimal solution to the overall problem. For these subproblems, optimal solutions can be found, for example, with the help of MP. Then these solutions are linked into an OPC.

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