31-08-2013, 04:58 PM
USING FUZZY MATHEMATICAL MODELS FOR CONSTRUCTION PROJECT SCHEDULING WITH TIME, COST, AND MATERIAL RESTRICTIONS
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ABSTRACT
This research investigation evaluated the viability of using fuzzy mathematical
models for determining the duration of construction schedules and for evaluating the
contingencies created by schedule compression and delays due to unforeseen material
shortages. The research also used heuristic material allocation and sensitivity analysis to
test five cases of material constraints. Material constraints increase the cost of
construction and delay the finish of projects. Mathematical models allow the
multiobjective optimization of project schedules, considering constraints such as time and
cost defined in the project, and unexpected materials shortages to determine the fuzzy
aspiration levels of Decision Makers.
INTRODUCTION
Construction management decisions are made based on schedules that are
developed during the early planning stage of projects yet many possible scenarios need to
be considered during actual construction. Decisions could be made that rely solely on the
expertise of Decision Makers (DM) that use commercial software such as: Primavera
Project Planner (P3), Primavera Project Management (P5), and Microsoft Project, but
sometimes the assumptions that are made during the planning stage of a project could
change during actual construction processes. For instance, in a pavement facility suppose
that the raw material that is coming from a particular quarry is unexpectedly insufficient,
or that abnormal weather makes it too difficult to perform any task outdoors. These, and
many other unpredictable events, constantly affect project schedules. In many cases DMs
are required to make decisions quickly during construction.
CHAPTER TWO: DEFINITIONS
This Chapter includes explanations of the words, phrases, and concepts that were
used to conduct the research investigation. The definitions and concepts are organized
into five sections (1) Construction Management, (2) Mathematical Models, (3) Fuzzy
Mathematical Models, (4) Mathematical Models used in Construction, (5) and Material
Restrictions.
Construction Materials Management
In a construction process, project managers have to make decisions about the
methods that need to be implemented to achieve planned goals. The types of technology,
or methods, used differ from project to project. Practitioners usually choose to use
technologies, or methods, that have worked best for them in the past. Decisions are made
taking into account the advantages and disadvantages that each technique offers to a
specific project. In order to make efficient decisions it is wise to include all of the
participants affected in the decision process. Therefore, final decisions will include
different positions and the experience of everyone involved, which will make the
decisions more realistic. In addition, participants will understand and incorporate the
decision process into their work (Halpin and Woodhead, 1998).
Concrete Mixing Problem (LP example)
Company XYZ uses two Fiber Reinforcing and Aggregate Materials (FRAM) to
produce concrete A and B. Industrial specifications require concrete type A to have at
least 70% of FRAM 1, and concrete B must have a least 60% of FRAM 2. The demand
for concrete A is 360 Cubic Yard (C.Y.) per day and for concrete B it is 400 C.Y. per
day. Up to 350 C.Y. of FRAM 1 at $70 per C.Y. and 410 C.Y. at $20 per C.Y. of
FRAM2 can be purchased per day (supplies). Concrete A could be sold for $80 C.Y. and
concrete B for $70 per C.Y.
Fuzzy Mathematical Programming Models
The formulation of Fuzzy Linear Programming Models (FLPM) is the same as the
formulation of Linear Programming (LP) models. In the case of FLPM, the DM has the
opportunity to define a set of possible values and create a curve of satisfaction level or
membership function. For instance, using LP one objective at a time can be optimized
such as completion time or cost. By using goal programming two objectives may be
addressed giving priority to only one of the two objectives. Using FLPM, two objectives
may be addressed at the same time. In addition, the use of membership functions gives a
more realistic approach.