Mathematical optimization

Optimal Product Line Selection Problem with Price Discrimination. (Schön, C. , 2010) The article extends the fractional programming properties of a stylized model for the product line and price provided by Chen and Hausman (2000) by utilizing mathematical properties of the optimal product line selection problem using choice-based conjoint analysis to evaluate the profitability of design. 1. This model allows for various customer choice behavior and can flexibly cope with different…

CHAPTER 1 INTRODUCTION 1.1 Background To overcome the problems interconnected with manual involvement in production operations, it is essential to step towards automation. One such sector where manufacturer is focusing is on programmable robots. Robot is an electromechanical device which is used to do the specified work prescribed by the human beings. First robot was invented by George devol in 1954. Robots are controlled with the help of computers; the desired work is programmed with the…

Introduction to Numerical Linear Algebra and Optimisation. Cambridge [England] ; New York: Cambridge University Press, 1989. -Gockenbach, Mark, and Chang Liu. "Local Convergence of Newton 's Method in the Classical Calculus of Variations." Optimization, 64.4 (2015): 957-980. -Meza, Juan C. "Newton 's Method." Wiley Interdisciplinary Reviews: Computational Statistics, 3.1 (2011): 75-78. -"Newton 's Method." Newton 's Method. University of British Columbia Department of Mathematics., n.d. Web…

The mathematical genius Alan Turing is famously known for proposing that if a machine behaves as intelligently as a human being, then it is as intelligent as a human being. This assertion was widely unsupported in the mid twentieth century when it was first declared by Turing. At this point in time intelligent machines and computer science were new inventions, recognised by very few individuals, and understood by fewer. Since the invention of computer processors, their speeds have been…

different approaches into different domains which researchers have worked upon to produce an optimal solution for providing the architect with multiple designs. We have identified four different domains: Building the design, Analysis of the design, Optimization of designs and Computer Aided Tools for creating…

As discussed SIMP is the first highly modifiable software based amortization model. The demo we are about to review was optimized with to consider borrowers will either sell or refinance their homes within 10 years. In this example we have optimized SIMP to reduce principal at approximately the same pace as the 15 year show them please refer to column X . 15 year mortgage reduces the principal balance of a loan by 10 % in just over 2 years, now lets take a look at SIMP please go to column…

function, especially for the industries involving distribution. The Operational Research literature has addressed this problem by calling it as the vehicle routing problem (VRP). Vehicle scheduling or vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem. The Travelling Salesman Problem (TSP) was introduced much before the Vehicle Routing Problem(VRP). In a way, VRP generalises the TSP. VRP first appeared in a paper by George Dantzig and John Ramser…

overall objective in mind when determining the problem statement. For example is this a new system or process, it is more likely we are going to be concerned with characterization or factor screening, as opposed to existing systems that may focus on optimization. It is also important to note that the problem being formulated may not fully be solved by a single experiment, in which case a sequential approach may be employed that will utilize a series of small experiments each with a specific…

Another operations management technique widely used in the business world in linear programming. What is linear programming? Linear programming is a commonly used mathematical technique designed to help operations managers plan and make the decisions necessary to allocate resources (Quantitative Module B: Linear Programming). In addition, Linear Programming (“LP”) is one of the few operations management techniques that will guarantee an optimal answer, providing that all of the assumptions are…

The newsvendor problem is a mathematical model which is used to determine the optimal stock under uncertainty. In the following, the newsvendor context under cost minimization will be introduced. Let h be the unit holding cost respectively the unit overage cost (as we regard the pure cost context) and b the unit penalty of not serving demand (or unit backorder cost) respectively the unit underage cost. Then, the target inventory B is equal to the mean demand µ plus safety stock SS. The safety…