Minimization (PCM), under which payment costs are minimized directly. In order to solve the PCM in the dual space, the Lagrangian relaxation and surrogate optimization approach is frequently used. When standard optimization methods, such as branch-and-cut, become ineffective due to the large size of a problem, the Lagrangian relaxation and surrogate optimization approach provides a good feasible solution within a reasonable CPU time. The convergence of the standard Lagrangian relaxation and surrogate subgradient
The classical job-shop scheduling problem (JSP) is a combinatorial optimization problem, which is among the most complicated problems in the scheduling area. The JSP has been proven to be NP-hard (Zhang et al., 2008). Flexible job-shop scheduling problem (FJSP) is a generalization of the classical JSP. It takes shape when alternative production routing is allowed in the classical job-shop (Al-Hinai, 2011). FJSP is NP-hard due to; (a) assignment decisions of operations to a subset of machines and
to extend the intrinsic lifetime of piece of very expensive equipment to be systematic replaced. The objective of preventive interventions is to either reduce the effect of the system wear-out or delay the onset of these effects. Deterministic optimization models have been proposed by various authors. Yao et al (2001) presented a model with two-layer hierarchical structure that optimizes the preventive maintenance scheduling for operations in semiconductor manufacturing industry. For the higher level
This project involves optimization of materials procurement, transportation in construction projects. With the thought of operations research, designed a objective function and constrained conditions for a materials procurement and transportation optimization model. According to data, simulates the cost and the method provided can be used to analyze the rule of materials procurement and transportation cost and make a correct decision and to solve the problem of analyzing and forecasting procurement
dependency representation using causal diagrams. There are other hybrid methods which can be adopted, which combine quantitative and qualitative techniques. Step 3: Model Analysis and Interpretation – which gives the derivation of results for the mathematical equations and/or simulation of the relationships between variables, which in turn gives the solution for the particular research questions or criteria which have been set in the beginning of the process. It may take additional steps such as model
model also takes into account the covariance between all assets. For this reason, the Markowitz framework is commonly referred to as mean-variance portfolio analysis. Much of the focus has been on mathematical theories behind uncertainty set construction and reformulations resulting in optimization problems that can be solved efficiently; and, as a result, there are many formulations that can be used to build robust equity portfolios. Since 1990 there have been numerous extensions of the Markowitz’s
one after another. By 1953, he re ned this to the modern meaning, referring speci cally to nesting smaller decision problems inside larger decisions. 1Bellmans'(1957) and Bertsekas'(1976) contributions give us the mathematical theory behind it as a tool of solving dynamic optimization problems. For economists, Sargent (1987), Stokey and Lucas (1989) contributed a valuable bridge between them. 2.1 Dynamic Programming Overview Dynamic programming is used to solve complex problems by decomposing them
their proposed mathematical models could explain the performance indicators with the factors limits being examined. Vieira et al. (2013) gave a mixed integer programming formulation that lets us to make efficient, almost orthogonal, almost balanced designs for mixed factor problems. These problems call nearly orthogonal-and-balanced (NOAB) designs (Vieira et al., 2013). Generic nonlinear programming (NLP) problems hold continuous or integer variables, but mechanical design optimizations usually include
Over the past two years, I have accumulated a good knowledge of Finance. I was introduced to Bayesian Statistics, GARCH processes, and other topics of time series analysis. I also learned how to price volatility swaps and categorize different optimization tasks. While I never intended to focus solely on the practical side of finance, nearly all of my work revolves around it. For example, I have done research that forecasted assets' expected returns as well as research on a better way to execute
1950’s has been extraordinary. Today it is a standard tool used by some companies (around 56%) of even moderate size. Linear programming uses a mathematical model to describe the problem of concern. Linear programming involves the planning of activities to obtain an optimal result, i.e., a result that reaches the specified goal best (according to the mathematical model) among all feasible alternatives. Linear Programming as seen by various reports by many companies has saved them thousands to even millions
A. Background A. 1.The facts about food waste and hunger in Australia Australia is a great food-producing county and is truly lucky enough to feed 60 million people [1] which is almost twice as the current estimated population of about 36.24 million people.[2] However recent research shows that more than 4 million tonnes of food are disposed to landfill each year, of which food retailing accounts for 1.38 million tonnes and 2.6 million tonnes come from Australian household.[3] Every year Australian
I Wish to Pursue an MS Degree in Electrical Engineering During my senior year at Purdue University, I made a decision that has impacted the entire course of my education. While my classmates were making definite decisions about their career paths, I chose to implement a five-year plan of development and growth for myself. I designed this plan in order to examine various careers that I thought might interest me, as well as to expand upon my abilities at the time. As I was attaining a BS degree
heading angle of the car body with respect to the x-axis. In figure 2, the angle is the steering angle of the front wheels, and can be referred as a control input. The distance between the front and the rear axles is represented by l. The following mathematical model describes the kinematic relationship of the rear-wheel drive ground vehicle: [1] x ̇= v cos y ̇ = v sin (1) ̇ = v (tan φ )/l Or, in compact representation, x ̇ = f(x,u); (2) The steering angle and line velocity v are used as a
Asymptotic analysis is a key tool to study nonlinear difference equations which arise in the mathematical modelling of real-world phenomena. It is not expected that explicit solutions can be found for the solutions of nonlinear difference equations; however, some nonlinear equations can be transformed into equivalent linear equations by a change of dependent variable. In this work, we transform a discrete logistic equation, which is a nonlinear difference equation, into a linear equation and we determine
There are 10 guid... ... middle of paper ... ... type of software like CPLEX, XPRESS, OSL and GUROBI that can used solve MIP problems but not limited to MIP problems. LINGO is a simples and powerful software that can be used to solve MIP optimization problems. This software can handle tens of thousands of variables and constraints with up to few thousand integer variables (Schrage, 2006). Wong et al. (2010) and Easa and Hossain (2008) used this software to solve MIP problems to find the global
JP Molasses The analysis is divided into three sections: Part I: description of the optimization model Part II: solution to the present problem Part III: recommendations on future improvements to increase profits Part I Objective function: J.P. Molasses' goal is to maximize the profit generated from the refining of raw sugar into molasses and its byproducts and then shipping those products to customers. Decision variables: a. The amount of raw sugar shipped from eight suppliers to two
The Canny edge detection algorithm is commonly known as the optimal edge detector. During his research work, Canny's main intentions were to enhance the edge detectors which were already out at that time. Canny was successful in his objective and published a paper entitled "A Computational Approach to Edge Detection" in which he mentions a list of criteria which could improve current methods of edge detection. According to him, low error rate was one of the important criteria. Secondly, the edges
about the true state, which leads to a probability distribution over the states. So POMDP algorithms are dealing with probability distributions, while MDP algorithms are working on a finite number of discrete states. This difference changes an optimization problem over a discreate space into that defined ... ... middle of paper ... ... total discounted reward over an infinite-horizon. The expected reward for policy π initializing from belief b_o is defined as J^π (b_o )=E[∑_(t=0)^∞▒β^t r(s_t
supervisors, specialist staffs -More organization levels, autocratic style: unilateral goal setting, assignment of workers -Frequent alienation: “It’s only a job” -Less individual development opportunity and employment security STS -Joint optimization of systems -People as complements to machines -Optimal task grouping, multiple, broad skills -Internal controls: self-regulating subsystems -Fewer levels, participative style: Bilateral goal setting -Commitment: “It’s my job, group, and
B. Naïve Bayesian Classification In machine learning, Naive Bayesian Classification is a family of a simple probabilistic classifier based on the Bayes theorem (or Bayes’s rule) with Naive (Strong) independence assumption between the features. It is one of the most efficient and effective classification algorithms and represents a supervised learning method as well as a statistical method for classification. Naïve Bayesian classifiers assume that the effect of an attribute value on a given class