Abstract: In the last years, the crashworthiness of an automotive body structure can be improved, since the beginning of the design stage, thanks to the development of specific optimization tools. It is well known how the finite element codes can help the designer to investigate the crashing performance of structures under dynamic impact. Therefore, by coupling nonlinear mathematical programming procedure and statistical techniques with FE simulations, it is possible to optimize the design with reduced number of analytical evaluations. In engineering applications, many optimization methods which are based on statistical techniques and utilize estimated models, called meta-models, are quickly spreading. A meta-model is an approximation of a detailed simulation model based on a dataset of input, identified by the design of experiments (DOE); the number of simulations needed to build it depends on the number of variables. Among the various types of meta-modeling techniques, Kriging method seems to be excellent in accuracy, robustness and efficiency compared to other ones when applied to crashworthiness optimization. Therefore the application of such meta-model was used in this work, in order to improve the structural optimization of a bumper for a racing car in composite material subjected to frontal impact. The specific energy absorption represents the objective function to maximize and the geometrical parameters subjected to some design constraints are the design variables. LS-DYNA codes were interfaced with LS-OPT tool in order to find the optimized solution, through the use of a domain reduction strategy. With the use of the Kriging meta-model the crashworthiness characteristic of the composite bumper was improved.
Abstract: The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.
Abstract: Fuzzy regression models are useful for investigating
the relationship between explanatory variables and responses in fuzzy
environments. To overcome the deficiencies of previous models and
increase the explanatory power of fuzzy data, the graded mean
integration (GMI) representation is applied to determine
representative crisp regression coefficients. A fuzzy regression model
is constructed based on the modified dissemblance index (MDI),
which can precisely measure the actual total error. Compared with
previous studies based on the proposed MDI and distance criterion, the
results from commonly used test examples show that the proposed
fuzzy linear regression model has higher explanatory power and
forecasting accuracy.
Abstract: This work proposed a multi-objective mathematical programming approach to select the appropriate supply network elements. The multi-item multi-objective production-distribution inventory model is formulated with possible constraints under fuzzy environment. The unit cost has taken under fuzzy environment. The inventory model and warehouse location model has combined to formulate the production-distribution inventory model. Warehouse location is important in supply chain network. Particularly, if a company maintains more selling stores it cannot maintain individual secondary warehouse near to each selling store. Hence, maintaining the optimum number of secondary warehouses is important. Hence, the combined mathematical model is formulated to reduce the total expenditure of the organization by arranging the network of minimum number of secondary warehouses. Numerical example has been taken to illustrate the proposed model.
Abstract: Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.
Abstract: Water resource systems modeling has constantly been
a challenge through history for human beings. As the innovative
methodological development is evolving alongside computer sciences
on one hand, researches are likely to confront more complex and
larger water resources systems due to new challenges regarding
increased water demands, climate change and human interventions,
socio-economic concerns, and environment protection and
sustainability. In this research, an automatic calibration scheme has
been applied on the Gilan’s large-scale water resource model using
mathematical programming. The water resource model’s calibration
is developed in order to attune unknown water return flows from
demand sites in the complex Sefidroud irrigation network and other
related areas. The calibration procedure is validated by comparing
several gauged river outflows from the system in the past with model
results. The calibration results are pleasantly reasonable presenting a
rational insight of the system. Subsequently, the unknown optimized
parameters were used in a basin-scale linear optimization model with
the ability to evaluate the system’s performance against a reduced
inflow scenario in future. Results showed an acceptable match
between predicted and observed outflows from the system at selected
hydrometric stations. Moreover, an efficient operating policy was
determined for Sefidroud dam leading to a minimum water shortage
in the reduced inflow scenario.
Abstract: This paper reviews the model-based qualitative and
quantitative Operations Management research in the context of
Construction Supply Chain Management (CSCM). Construction
industry has been traditionally blamed for low productivity, cost and
time overruns, waste, high fragmentation and adversarial
relationships. The construction industry has been slower than other
industries to employ the Supply Chain Management (SCM) concept
and develop models that support the decision-making and planning.
However the last decade there is a distinct shift from a project-based
to a supply-based approach of construction management. CSCM
comes up as a new promising management tool of construction
operations and improves the performance of construction projects in
terms of cost, time and quality. Modeling the Construction Supply
Chain (CSC) offers the means to reap the benefits of SCM, make
informed decisions and gain competitive advantage. Different
modeling approaches and methodologies have been applied in the
multi-disciplinary and heterogeneous research field of CSCM. The
literature review reveals that a considerable percentage of the CSC
modeling research accommodates conceptual or process models
which present general management frameworks and do not relate to
acknowledged soft Operations Research methods. We particularly
focus on the model-based quantitative research and categorize the
CSCM models depending on their scope, objectives, modeling
approach, solution methods and software used. Although over the last
few years there has been clearly an increase of research papers on
quantitative CSC models, we identify that the relevant literature is
very fragmented with limited applications of simulation,
mathematical programming and simulation-based optimization. Most
applications are project-specific or study only parts of the supply
system. Thus, some complex interdependencies within construction
are neglected and the implementation of the integrated supply chain
management is hindered. We conclude this paper by giving future
research directions and emphasizing the need to develop optimization
models for integrated CSCM. We stress that CSC modeling needs a
multi-dimensional, system-wide and long-term perspective. Finally,
prior applications of SCM to other industries have to be taken into
account in order to model CSCs, but not without translating the
generic concepts to the context of construction industry.
Abstract: An efficient remanufacturing network lead to an
efficient design of sustainable manufacturing enterprise. In
remanufacturing network, products are collected from the customer
zone, disassembled and remanufactured at a suitable remanufacturing
facility. In this respect, another issue to consider is how the returned
product to be remanufactured, in other words, what is the best layout
for such facility. In order to achieve a sustainable manufacturing
system, Cellular Manufacturing System (CMS) designs are highly
recommended, CMSs combine high throughput rates of line layouts
with the flexibility offered by functional layouts (job shop).
Introducing the CMS while designing a remanufacturing network will
benefit the utilization of such a network. This paper presents and
analyzes a comprehensive mathematical model for the design of
Dynamic Cellular Remanufacturing Systems (DCRSs). In this paper,
the proposed model is the first one to date that considers CMS and
remanufacturing system simultaneously. The proposed DCRS model
considers several manufacturing attributes such as multi period
production planning, dynamic system reconfiguration, duplicate
machines, machine capacity, available time for workers, worker
assignments, and machine procurement, where the demand is totally
satisfied from a returned product. A numerical example is presented
to illustrate the proposed model.
Abstract: This work proposes a fuzzy methodology to support
the investment decisions. While choosing among competitive
investment projects, the methodology makes ranking of projects
using the new aggregation OWA operator – AsPOWA, presented in
the environment of possibility uncertainty. For numerical evaluation
of the weighting vector associated with the AsPOWA operator the
mathematical programming problem is constructed. On the basis of
the AsPOWA operator the projects’ group ranking maximum criteria
is constructed. The methodology also allows making the most
profitable investments into several of the project using the method
developed by the authors for discrete possibilistic bicriteria problems.
The article provides an example of the investment decision-making
that explains the work of the proposed methodology.
Abstract: The focus of this paper is to develop a technique
of solving a combined problem of determining Optimum Strata
Boundaries(OSB) and Optimum Sample Size (OSS) of each stratum,
when the population understudy isskewed and the study variable has
a Pareto frequency distribution. The problem of determining the OSB
isformulated as a Mathematical Programming Problem (MPP) which
is then solved by dynamic programming technique. A numerical
example is presented to illustrate the computational details of the
proposed method. The proposed technique is useful to obtain OSB
and OSS for a Pareto type skewed population, which minimizes the
variance of the estimate of population mean.
Abstract: Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.
Abstract: This research involves the design and analysis of pinch-based water/wastewater networks to minimize water utility in the petrochemical and petroleum industries. A study has been done on Tehran Oil Refinery to analyze feasibilities of regeneration, reuse and recycling of water network. COD is considered as a single key contaminant. Amount of freshwater was reduced about 149m3/h (43.8%) regarding COD. Re-design (or retrofitting) of water allocation in the networks was undertaken. The results were analyzed through graphical method and mathematical programming technique which clearly demonstrated that amount of required water would be determined by mass transfer of COD.
Abstract: An effective supplier selection process is very important to the success of any manufacturing organization. The main objective of supplier selection process is to reduce purchase risk, maximize overall value to the purchaser, and develop closeness and long-term relationships between buyers and suppliers in today’s competitive industrial scenario. The literature on supplier selection criteria and methods is full of various analytical and heuristic approaches. Some researchers have developed hybrid models by combining more than one type of selection methods. It is felt that supplier selection criteria and method is still a critical issue for the manufacturing industries therefore in the present paper the literature has been thoroughly reviewed and critically analyzed to address the issue.
Abstract: In this article, a mathematical programming model
for choosing an optimum portfolio of investments is developed.
The investments are considered as investment projects. The
uncertainties of the real world are associated through fuzzy
concepts for coefficients of the proposed model (i. e. initial
investment costs, profits, resource requirement, and total available
budget). Model has been coded by using LINGO 11.0 solver. The
results of a full analysis of optimistic and pessimistic derivative
models are promising for selecting an optimum portfolio of
projects in presence of uncertainty.
Abstract: In this research, we have developed a new efficient
heuristic algorithm for the dynamic facility layout problem with
budget constraint (DFLPB). This heuristic algorithm combines two
mathematical programming methods such as discrete event
simulation and linear integer programming (IP) to obtain a near
optimum solution. In the proposed algorithm, the non-linear model
of the DFLP has been changed to a pure integer programming (PIP)
model. Then, the optimal solution of the PIP model has been used in
a simulation model that has been designed in a similar manner as the
DFLP for determining the probability of assigning a facility to a
location. After a sufficient number of runs, the simulation model
obtains near optimum solutions. Finally, to verify the performance of
the algorithm, several test problems have been solved. The results
show that the proposed algorithm is more efficient in terms of speed
and accuracy than other heuristic algorithms presented in previous
works found in the literature.
Abstract: This paper presents a hybrid algorithm for solving a timetabling problem, which is commonly encountered in many universities. The problem combines both teacher assignment and course scheduling problems simultaneously, and is presented as a mathematical programming model. However, this problem becomes intractable and it is unlikely that a proven optimal solution can be obtained by an integer programming approach, especially for large problem instances. A hybrid algorithm that combines an integer programming approach, a greedy heuristic and a modified simulated annealing algorithm collaboratively is proposed to solve the problem. Several randomly generated data sets of sizes comparable to that of an institution in Indonesia are solved using the proposed algorithm. Computational results indicate that the algorithm can overcome difficulties of large problem sizes encountered in previous related works.
Abstract: Calibration estimation is a method of adjusting the
original design weights to improve the survey estimates by using
auxiliary information such as the known population total (or mean)
of the auxiliary variables. A calibration estimator uses calibrated
weights that are determined to minimize a given distance measure to
the original design weights while satisfying a set of constraints
related to the auxiliary information. In this paper, we propose a new
multivariate calibration estimator for the population mean in the
stratified sampling design, which incorporates information available
for more than one auxiliary variable. The problem of determining the
optimum calibrated weights is formulated as a Mathematical
Programming Problem (MPP) that is solved using the Lagrange
multiplier technique.
Abstract: Mathematical programming has been applied to various
problems. For many actual problems, the assumption that the parameters
involved are deterministic known data is often unjustified. In
such cases, these data contain uncertainty and are thus represented
as random variables, since they represent information about the
future. Decision-making under uncertainty involves potential risk.
Stochastic programming is a commonly used method for optimization
under uncertainty. A stochastic programming problem with recourse
is referred to as a two-stage stochastic problem. In this study, we
consider a stochastic programming problem with simple integer
recourse in which the value of the recourse variable is restricted to a
multiple of a nonnegative integer. The algorithm of a dynamic slope
scaling procedure for solving this problem is developed by using a
property of the expected recourse function. Numerical experiments
demonstrate that the proposed algorithm is quite efficient. The
stochastic programming model defined in this paper is quite useful
for a variety of design and operational problems.
Abstract: Based on the fuzzy set theory this work develops two
adaptations of iterative methods that solve mathematical programming
problems with uncertainties in the objective function and in
the set of constraints. The first one uses the approach proposed by
Zimmermann to fuzzy linear programming problems as a basis and
the second one obtains cut levels and later maximizes the membership
function of fuzzy decision making using the bound search method.
We outline similarities between the two iterative methods studied.
Selected examples from the literature are presented to validate the
efficiency of the methods addressed.
Abstract: The optimization problem using time scales is studied.
Time scale is a model of time. The language of time scales seems to
be an ideal tool to unify the continuous-time and the discrete-time
theories. In this work we present necessary conditions for a solution
of an optimization problem on time scales. To obtain that result we
use properties and results of the partial diamond-alpha derivatives for
continuous-multivariable functions. These results are also presented
here.