DSpace Collection: Thesis - Mathematics
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NONLINEAR TRANSPORTATION PROBLEMS
http://etd.aau.edu.et:80/dspace/handle/123456789/376
Title: NONLINEAR TRANSPORTATION PROBLEMS
<br/>
<br/>Authors: Kidist, Terefe
<br/>
<br/>Description: A THESIS
SUBMITTED TO THE DEPARTMENT OF MATHEMATICS OF
ADDIS ABABA UNIVERSITY IN PARTIAL FULFILMENT
OF THE REQUIREMENTS FOR MASTER OF SCIENCE
DEGREE IN MATHEMATICSLINEAR THREE-LEVEL PROGRAMMING PROBLEM WITH THE APPLICATION TO HIERARCHICAL ORGANIZATIONS
http://etd.aau.edu.et:80/dspace/handle/123456789/375
Title: LINEAR THREE-LEVEL PROGRAMMING PROBLEM WITH THE APPLICATION TO HIERARCHICAL ORGANIZATIONS
<br/>
<br/>Authors: Esubalew, Lakie
<br/>
<br/>Abstract: In many decision processes there is an hierarchy of decision-makers and deci-
sions are taken at di®erent levels in this hierarchy. The decentralized planning
problem has long been recognized as an important decision-making problem.
In many practical decision making activities, decision making structure has
changed in the last few decades, from a single person (or decision maker) and
single criterion (or constraint factor) to multi-person (or decision maker) and
multi-criteria and even to hierarchical (or multi-level) situations. In any or-
ganization with hierarchical decision systems, the sequential and preemptive
nature of the decision process makes the problem of making an optimal de-
cision, and it is di®erent from the usual operations research methods.
In hierarchical decision process decision-makers are often arranged within a
hierarchical administrative structure, each with his/her objective (perhaps
con°icting). A planner at one level of the hierarchy may have an objec-
tive and a set of feasible decision space determined, in part, by other levels.
However, his control instruments may allow him/her to in°uence the policies
at other levels and in this manner improve his/her own objective function.
Therefore a multilevel programming problem approach is developed for mod-
elling such type of decentralized planning problems.
A multilevel programming problem is a nested optimization problem over a
single feasible region. This approach partitions control of the decision vari-
ables among several decision makers,in the hierarchy. Each decision-maker in
the hierarchy acting in a sequence to maximize his/her own objective func-
tion. These decision-makers interact through a set of \corporate" constraints
involving the decision variables of all divisions. The general structure of the
multilevel programming problem method will be discussed in detail and we
will focus on three level linear programming problems.
<br/>
<br/>Description: A THESIS
SUBMITTED TO THE DEPARTMENT OF MATHEMATICS OF
ADDIS ABABA UNIVERSITY IN PARTIAL FULFILMENT OF
THE REQUIREMENTS FOR MASTER OF SCIENCE
DEGREE IN MATHEMATICSTHREE-PERSON COOPERATIVE GAME AND ITS APPLICATION IN DECISION MAKING PROCESS OF HIERARCHICAL ORGANIZATIONS
http://etd.aau.edu.et:80/dspace/handle/123456789/374
Title: THREE-PERSON COOPERATIVE GAME AND ITS APPLICATION IN DECISION MAKING PROCESS OF HIERARCHICAL ORGANIZATIONS
<br/>
<br/>Authors: Abiy, Dejenee
<br/>
<br/>Abstract: The solution of an n-level linear problem, when the levels make decisions se-
quentially and independently, is not necessarily pareto-optimal, i.e.there exist
feasible points which o®er increased payo®s to some levels without diminish-
ing the payo®s to other levels. These increased payo®s may be obtained if
the levels coalesce.
In particular if the number of decision makers on each level form coalition to
work cooperatively they can get a better payo®. A game theoretic methodol-
ogy for predicting coalition formation in the decision makers on each level is
presented. The problem is modeled as an abstract game. If a core exists for
the characteristic function game, then there exists a set of enforceable points
which o®er the increased payo®s available to the system, but a core may not
exist. When the core exist, for games with non-empty cores, it would be an
advantageous property for a power index to assign values to the players that
comprise a solution in the core. We use Shapley value, as a solution concept,
which has got a drawback that it might not always been an element of the
core. So we take the Willick's power index as a best solution concept, which
has got a better relation with the core than Shapley.
The n-level Stackleberg problem, which represent a class of n-level linear
problem, as a special case the 3-level Stackleberg problem, is de¯ned. In the
university budget allocation system coalition among decision makers in each
level, science faculty, is used to demonstrate the suggested methodology.
<br/>
<br/>Description: A THESIS
SUBMITTED TO THE SCHOOL OF GRADUATE STUDIES,
ADDIS ABABA UNIVERSITY IN PARTIAL FULFILMENT
FOR THE DEGREE OF MASTER OF SCIENCE
IN MATHEMATICS