BUSINESS PERFORMANCE MEASUREMENT AND MANAGEMENT, Editors: Vincent Charles and Mukesh Kumar, Cambridge Scholars Publishing, UK, Chapter 13, 2014, Jun 7, 2014
Simulation continues to be the primary method by which performance designers obtain information a... more Simulation continues to be the primary method by which performance designers obtain information about analysis of complex stochastic systems. Descriptive simulation measures the performance of a system, given a particular value for the input parameters. Most systems performance designs, such as product, process, and service design, involve a framework for arriving at a target value by performing a set of experiments. This approach is certainly a time consuming and costly way to determine design parameters. This paper proposes using stochastic approximation to estimate the necessary design parameters within a range of desired accuracy for a given target value for the performance function. The proposed solution algorithm is based on Newton’s methods using a single-run simulation to minimize a loss function that measures the deviation from a target value. The properties of the solution algorithm and the validity of the estimates are examined by applying them to reliability and queuing systems with a known analytical solution.
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Papers by Hossein Arsham
phases. The initialisation phase provides the initial tableau that may not have a full set of basis. The push phase uses a full gradient vector of the objective function to obtain a feasible vertex. This is then followed by a series of pivotal
steps using the sub-gradient, which leads to an optimal solution (if exists) in the
final iteration phase. At each of these iterations, the sub-gradient provides the desired direction of motion within the feasible region. The algorithm hits and/or moves on the constraint hyper-planes and their intersections to reach an optimal vertex (if exists). The algorithm works in the original decision variables and
slack/surplus space, therefore, there is no need to introduce any new extra variables such as artificial variables. The simplex solution algorithm can be considered as a sub-more efficient.
Given a linear program me has a known unique non-degenerate primal/dual solution; we develop the largest sensitivity region for linear programming models-based only the optimal solution rather than the final tableau. It allows for simultaneous, dependent/independent changes on the cost coefficients and
the right-hand side of constraint. Numerical illustrative examples are given."
For teaching purposes you may try:
Refined Simplex Algorithm for the Classical Transportation Problem with
Application to Parametric Analysis, Mathematical and Computer Modelling,
12(8), 1035-1044, 1989.
http://home.ubalt.edu/ntsbarsh/KahnRefine.pdf
pears within various areas of research and applications. Of particular
importance is the sparse simplex, where A is the basis matrix. In
the paper a procedure for computing of the inverse matrix (A+D)¡1
is presented and discussed, where A 2 Rn£n is a given non-singular
matrix, A¡1 is already calculated, and A + D is a perturbed matrix
of A by D, where D is sparse. The non-singularity requirement for D
is removed.
analytical solution.
are completely insensitive to both tails it is difficult in a particular application
to detect departure from whiteness. A modified version of the widely used (K-
S) test of null hypothesis is constructed, that a given time series is Gaussian
white noise, against the alternative hypothesis that the time series contains
an added or multiplicative deterministic periodic component of unspecified fre-
quency. The usual K-S test is treated as a special case. The proposed test is
more powerful than the ordinary K-S test in detecting extreme (low or high)
hidden periodicities. Computational procedures necessary for implementation
are given."
service design, involve a framework for arriving at a target value
for a set of experiments. This paper considers a stochastic approximation
algorithm for estimating the controllable input parameter
within a desired accuracy, given a target value for the performance
function. Two different problems, what-if and goal-seeking problems,
are explained and defined in an auxiliary simulation model,
which represents a local response surface model in terms of a polynomial.
A method of constructing this polynomial by a single run
simulation is explained. An algorithm is given to select the design
parameter for the local response surface model. Finally, the mean
time to failure (MTTF) of a reliability subsystem is computed and
compared with its known analytical MTTF value for validation
purposes.