The Data Centric Architecture of a Factory Digital Twin
perform well in a large fraction of the future possible timelines . A key function of an FDT is to provide a data-based approach for determining the right level of “ insurance ” ( Jung et al 2008 [ 11 ]).
Different FDT technologies provide a variety of means for addressing the timeline . Spreadsheets are the most popular technology for developing an FDT ( Gottfried 2005 [ 10 ]). A cell often represents a manufacturing quantity at a particular point in time . Similarly uniform discretization models ( UDMs ) represent manufacturing quantities at uniform points in time ( see below ). Discrete event simulator based FDT technology maintains a stack of interesting time points and updates the simulation from earliest to latest time ( Law 2024 [ 20 ]).
In the next section , we describe a novel technology for optimizing an FDT over the timeline that is built from the RTN .
4 INFINITE DIMENSIONAL PROGRAMMING INNOVATION FOR TIMELINE MANAGEMENT
In this section , we summarize the unique treatment of the timeline used by the VirtECS system from APCI ( www . combination . com ) for developing FDTs to enable mathematical programming optimization . VirtECS translates the RTN description to an infinite dimensional mathematical program ( Friesz 2010 [ 12 ]) that enables branch and bound of the resulting Mixed Integer Linear Program ( MILP ).
Optimizing process behavior over time involves considering the possible ways that activities could be performed over time to satisfy causality and meet all other physics constraints . Consider the planning of the extent ( e . g . batch size , processing rate , or an investment amount ) of an activity . If the activity is undertaken ( yes or no ) at a given time t then the extent must be between allowed minimum and maximum levels . As a mathematical relationship this can be written as :
E min x t ≤ E t ≤ E max x t ( 1 )
Where Emin is the minimum allowed extent of the activity , Emax is the maximum allowed extent of the activity , Et is the chosen extent of the activity , and xt is assigned a value of one if the activity occurs at a time t and zero otherwise . If the activity does not occur at time t , then xt is set to zero , the left and right hand parts of the relationship ( 1 ) are zero , and the chosen extent Et must be zero . Conversely , if the chosen extent at a given time , Et , is not going to be zero , then the activity must be chosen to occur ( xt must equal one ). More complicated process physics can be easily represented mathematically .
By introducing mathematical notation , physics concepts underlying processes can be easily represented using mathematical expressions : material balances , unit allocation constraints , resource limitations , etc . The objective to be optimized can also be specified as a mathematical relationship so that the goal of the problem to be solved becomes choosing the variable values to get the best objective value while satisfying all the constraints .
Journal of Innovation 105