in Wiley InterScience (www.interscience.wiley.com).New mathematical formulations of observability, redundancy, and an improved formulation for precision are provided which can be explicitly and analytically solved using mixed integer linear programming (MILP). By using the Schur complement found at the heart of both Gaussian elimination and Cholesky factorization for direct block matrix reduction and the variable classification and covariance calculations found in the reconciliation, regression, and regularization approach of Kelly, it is possible to efficiently optimize the overall instrumentation cost considering both estimability and variability as constraints during the branch-and-bound search of the MILP. Two illustrative examples are highlighted which minimize the cost of sensor placement subject to software and hardware redundancy of the measured variables, observability of the unmeasured variables, and their precision (i.e., inverse of their variance). This formulation is well suited to the problems of designing as well as retrofitting sensor locations in arbitrary networks.
This paper presents a new mixed-integer linear program (MILP) formulation for modeling sequence-dependent
switchovers for uniform discrete-time scheduling problems. The new formulation provides solutions faster
than the formulation found in the paper by Kondili et al. (Comput. Chem. Eng.
1993, 17, 211) and scales
more efficiently. The key to this formulation is the use of memory operation logic variables that track the
temporal unit-operation events occurring within the scheduling horizon for each unit. Four auxiliary dependent
binary transition variables are required for every unit-operation independent binary variable, called the mode-operation setup variable. In this paper, “dependent” means that these variables are derived from the unit-operation variables and are integral at the solution without explicitly declaring them as binary search variables
in the MILP formulation, hence reducing the computational effort. The four dependent variables are the
startup, shutdown, switchover-to-itself, and memory operation logic variables. The sequence-dependent
switchover relationships between different operations on the same unit can be derived from these variables,
whereby maintenance operations can be activated and placed between the mode operations where appropriate,
depending on the repetitive maintenance or cleaning requirements. The new formulation for sequence-dependent
switchovers can be applied to both batch- and continuous-process units. Three illustrative examples are provided
that show its advantage in terms of solution times over current state-of-the-art methods. In addition, effective
integer cuts are derived, which are based on the asymmetric traveling salesman problem with costs equal to
the sequence-dependent transition times.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.