Research Reports from the Department of Operations
Document Type
Dissertation
Publication Date
8-1-1983
Abstract
In this study the mathematical formulation of the hierarchical holographic modeling and solution methodology are explored. The hierarchical multiobjective optimization (HMO) methods that have been developed so far are useful mostly for the analysis of large scale systems which are controlled and managed by one planning group only. However, there does exist cases in the real world where the complex system is analyzed, planned and controlled by a multiple of constituencies, each with distinct and overlapping goals and perspectives. One decade ago, a modeling scheme termed as hierarchical overlapping coordination (HOC) scheme was introduced as a means of coordinating the different decompositions arising from the pluriconstituencies. In this HOC scheme, the multiobjective vector, decision vector, and constraint vector of each constituent are assumed to be identical, which may not be realistic. The hierarchical holographic modeling (HHM) which combines the characteristics of the HMO scheme and the HOC scheme can bring a much more precise and comprehensive approach to the analysis of the large scale systems that have both distinct and overlapping structure. First, the mathematical representation of the HHM in a generic case and the effects of multiple decompositions on the decision vectors, multiobjective vectors and constraint vectors in three HHSubmodel case are explored. Second, the solution methodology of two hierarchical holographic submodels (HHS) is considered. Two algorithms, namely the Hierarchical Holographic Overlapping Coordination algorithm and the Hierarchical Holographic Feasible scheme are proposed for generating pareto optimal solutions of the HHS. The choice of these two schemes will depend on the constraint structures in the HHS. These schemes provide flexibility to each planning group to decompose and solve their own HHS according to their own hierarchical structures, aspects and needs. Third, the coupling resource allocation problem faced by the upper level group, between two HHS is addressed. We discussed how the ranks assigned by the multiple decision makers of both HHS, to their own pareto optimal solutions can be used, in moving from trans-client to compromise solutions in an iterative manner. Finally, the applicability of the HHM scheme to a hypothetical river basin related land and resource management problem is explored.
Keywords
Operations research, Multiple criteria decision making, Decision support systems, Programming (Mathematics), System analysis--Mathematical models, Decision making--Mathematical models
Publication Title
Dissertation/Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 528 ; Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy.
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Thadathil, Jacob, "Optimization Methods in Hierarchical Holographic Modeling" (1983). Research Reports from the Department of Operations. 402.
https://commons.case.edu/wsom-ops-reports/402