Abstract:
Effects of stochastic variations of parameters in the planning
and design of a particleboard production system are studied. The
solution obtained from a linear deterministic optimization model is
compared against both the solution derived from the traditional
stochastic programming techniques and the distribution of optimal
objective function values obtained from models whose parameters
were Monte Carlo generated.
Resource Planning and Management System was used to produce
a network representation of a particleboard operation that is planned
in the Yucatan region of Mexico. The plant will use the cactus plants
that naturally grow in the area and produce particleboards for housing
construction. The stochastic elements are introduced in the process
variability, risks associated with the quality and the quantity of
supply of materials and labor, and the market demand where the
products must compete against imported particleboards. The network
model included the risk elements as triangular distributions
using the three parameters (L = minimum, M = most likely, U =
maximum) similar to the beta distribution assumption commonly made
in Program Evaluation and Review Technique.
Three major goals are pursued in this thesis: (1) practical
contribution: to ascertain the viability of constructing and operating
a particleboard production facility in Mexico; (2) theoretical contribution:
to determine the effects of risk upon optimal solutions;
and (3) industrial engineering contribution: to develop a practical
approach to planning, scheduling and control of production systems
under stochastic considerations. Four hypotheses were proposed for
testing: (1) though only a few empirical applications of stochastic
programming are now available, a practical industrial model can be
constructed by modifying a linear programming model to incorporate
the stochastic features; (2) Monte Carlo simulation provides more
objective and meaningful data to management than the use of expected
values in the linear programming techniques; (3) variations in
objective function are proportional to the variations in the parameters;
and (4) the problem of estimating parameters in the modeling phase,
in terms of suitable sample functions, are nontrivial and practically
insurmountable.
The first goal and the first two hypotheses were achieved through
RPMS and Monte Carlo simulation by graphical representation of
decision processes involved. The second and third goals and the
third hypothesis were achieved by interpreting the results in such a
way as to be useful and meaningful to management. Finally, by the
use of management experience, machine tolerances and direct
estimate methods, the fourth hypothesis was rejected.
Two major models were constructed and experimented by utilizing
RPM1 (linear programming) and RPM2 (simulation) packages
developed by Steve Shu-Kang Chou. The first model, containing 35
activity processes and 41 resource constraints, was used, first to
validate selected activity levels observed from LP against historical
records, and second to obtain the expected effects of risk in three
phases of management consideration: (1) variations only in costs and
prices: two stage programming simulation); (2) consideration of process
variability: chance-constrained programming simulation; and
(3) combination of the above two: stochastic programming simulation.
The second model was used to prove and remedy the drop in production
output and profit due to stochasticity. This was made possible by
bounding the processes with the solutions depicted from the deterministic
linear programming run. This model contained 35 activity
processes and 71 resource constraints.
Following is a summary of the conclusions drawn from this
study: (1) computer simulation facilities for stochastic programming
are now available and can be used at a relatively low cost ($450.00
for this entire project); (2) the manner in which the models and
techniques were utilized would constitute a viable tool for planning
production systems; (3) no consideration of risk in production planning
could result in underachievement of profit of, say, 28.28%, and of
production yields of, say, 7.18% as in the case of stochastic programming
simulation. However, the resulting payback resulted to be
7.83 years that, in comparison with the deterministic LP, is 2.21
years higher; and (4) the resulting drop in profit was found practically
solved by increasing the resource availability by the same percentage
of underachievement of profit.