A Scalar Dependent Variable - Assignment Example

IB) critically assess the strength and limitations of using linear regression as a means of evaluating the relationship between variables Linear regression is a statistical method used in analyzing the relation between one or more independent variable and a dependent variable. It can be described as a method, where modeling the relation between a scalar dependent variable y and another explanatory variable denoted X. For this to occur the dependent variable should be able to take any value or continuous.(Wiley 2013) Strengths of Linear regression Predicting the Future It is important in predicting the future. This can be used in business trying to understand the future market. Predicting the next business quarter or the next year.(Wiley 2013) Concluding decisions Linear regression can be used in making business decisions regarding what action to take with minimal risk. This is very helpful when organizations have to make a choice between two competing decisions. Correcting errors Through linear regression managers can be able to correct errors or even find better ways of doing business.(Nichols 2007) New insights Linear regression can be very helpful during the research and development of a new product and its good for cost minimization. (Thiery, C., Bel, G. and Thomas, A. (2010) Limitations of Linear Regression Focuses on the Mean of the Dependent Variable Linear regression looks at a relation between the mean of the dependent and the independent variables. In a scenario, if you take the relationship between the weight of an infant and some maternal characteristics like age; linear regression looks at the average weight of babies. Though, at certain times, one needs to look at the limits of the dependent variable, e.g., an infant is at risk when its weight is low, so one should look at the extremes here (Aivaz 2003). Linear regression is not a comprehensive description of the relationship between the variables. You can solve this issue by using quantile regression. Linear regression assumes that data has to be independent. For an event to have data that is independent is very slim. That the result of one score on a particular subject have nothing to do with the other.(Aivaz 2003) 2c) Critically evaluate at least three disadvantages of using linear programming as a decision solving technique in logistics transportation or supply chain context. A linear programming is a mathematical formula that is used in finding a means to realize the best outcome (like the maximum profit or the lowest cost) in a particular mathematical model for a list of necessities that are represented in a linear relationship.(Vanderbei 2003) Linear programming can be applied in various fields in business and the objective of it could be either to maximize on the profit of business or also to minimize the cost and work with the limited scarce resources to get the maximum output. It was broadly used in World War 2 to help in ease with logistics, scheduling and resource allocation under constraints like cost and lab our which people though it was the effect of post war era. The number of variables and solutions required to model the real life situations precisely is huge, and the solving process is time consuming[ CITATION Lin11 \l 1033 ]. i) Single Objectivity One of the limitations of linear programming is that it is only functional when finding a single objective probably profit maximization or cost minimization. The problem with this is that organizations tend to have more than one goal to achieve. It is also the reason why goal programming is more viable.(Rusell &Taylor 2013) ii) Parameters are assumed to be constant. The parameters that appear in linear programming are assumed to be constant but working under this assumptions in business could be challenging as nothing is permanent a vehicle may break down, a plane may crash, violence may erupt in countries where goods are delivered in such situations its inevitable to have variables that are constant. In the world of today no situation is constant and things keep changing on a day to day so for one to assume that parameters are constant is not realistic and does not stand in the world of business.(Nichols 2007) In the linear programming, decision variables take non-negative integers and fractional values. Nonetheless, there are quite situations where the planning models have integer variables. For example, vehicles in a convoy, generators in an organization, equipment, investment options. Rounding off the answer to the nearest figure will not result an optimal solution. In these scenarios, linear programming techniques cannot be essential.(Aivaz 2003) Fractional solutions in linear programming have no solution. This is another limitation in that any result has to be a rounded figure this causes as in supply when one is trying to find the maximum boxes to be stored the result has to be a rounded whole figure of the document.(Gosavi 2003) 3ai) Analyze how Monte Carlo simulation could be used for planning purposes within an organization in areas relates to logistics, transportation or supply chains Monte Carlo simulation is an advanced mathematical technique that helps organization or people to be able to mitigate risk in quantitative analysis and be able to make noble decisions. It is used by experts in such different fields such as Transport, supply chain and warehousing. In biology field’s different molecular simulations, Monte Carlo dynamic simulations are independent from the restrictions of applying Newton’s equations of motion. This dependence allows for the possibilities that the proposal of simulations generate trial calculations within the statistical mechanics ensemble of decisions. Moreover these moves may be no small; they might lead to huge difference in speedups of up to 1010 or higher in the sampling and analyzing of equilibrium properties. Monte Carlo moves can also be adjusted or put together in a simulation allowing the analyst enough flexibility in the approach to a specific problem. [ CITATION Rus11 \l 1033 ] However Monte Carlo simulations and configurations are simple and easy to parallelize, with other techniques being conducive for use with large CPU clusters Monte Carlo simulation equips the analyst with different of possible results and the consequence that will result for any decision undertaken. It shows the worst scenarios—the possibility outcomes of going for most radical, unpopular decision together with all possible results for the most neutral.(Stocker,2006) The technique was initially used by some scientists operating an atom bomb and it was named after Monte Carlo, the Monaco resort town renowned for its casinos. Subsequently from its introduction in World War 2, the model has been applied to model a variety of physical systems. Monte Carlo or probability sampling is a technique useful in understanding the effect of uncertainties in financial, cost, and project management (Cassandras &Lafortune 1999).Consider scenario in supply chain where an organization needs raw materials to be imported from different countries Consider a scenario of another organization trying to project its inventory demand based on future sales of a new item in a new market in order to exploit its potential profitability. An old model technique would have only considered single-point view, or in a better case, an analysis of three scenarios - the "good", "better" and "best" cases. With MCS, however, the analyst can choose a single probability distribution function analyzed in an Excel-based model to find the best of all possible solutions for inventory (Fu and Hu 1997). Probability distributions include Normal – Or “bell curve.” The analyst simply has to identify that there are chances of natural catastrophe such as bad weather can cause delays in the raw materials with this they can try and understand the best option to take and with the least cost available. Cases of variables defined by regular distributions include energy prices and inflation rates. Uniform – All possibilities have the same chance of happening; the user merely defines the maximum and minimum. Such variables that can be consistently distributed include sales revenues from a new produce (Law, A. M. and Kelton, W. D. (2000) Monte Carlo simulation provides a number of benefits over deterministic, or “single-point estimate” analysis: Probabilistic Results-Results do not show only what should occur, but also how its impact could be. Graphs.- With its results of the data a Monte Carlo simulation generates, it’s simple to present it in graphs with all different scenarios this will enable the business leader in the different industry be able to present it to the key stakeholders of the business i.e. the employee, shareholders or even the government. Sensitivity Analysis- With just a little example, deterministic control it’s not possible to see which variables affects the result the most. In Monte Carlo simulation, it’s easy to understand which inputs had the largest impact on final-line results. Scenario Analysis: In transport models, it’s very difficult to understand; which is the best available route to use to ensure that the optimal time has been used. Using Monte Carlo simulation, experts can understand exactly which inputs had which variable together what was the final outcome. This is invaluable for pursuing further analysis. (Banks, J. (ed.) (1998) Inputs correlation- In Monte Carlo simulation, it’s simpler to model interdependent relationships between input variables. It’s is also accurate to view how, in reality, when some factors do not go as planned. Another advantage to Monte Carlo simulation is the use of Latin Hypercube sampling, this samples more accurately from the all the possible range of distribution functions. MCS would then analyze the resulting profitability over a period of time, using different set of random values from the input probability functions, the pert distribution for stock and inventory levels. Depending upon the uncertainties’ and the ranges specified for them, an MCS could involve hundreds of calculations before it is finished (Arsham, 1998), Consider a scenario in which the analyst has included uncertainty into a relatively large quantity of variables. Variables such as sales demands, investment outlays, logistics and processing times, inventory and, calamity can be recorded into a spreadsheet that identifies both independent and dependent variables. By using the probability distributions, variables have different probabilities for different outcomes happening, thus significantly boosting model accuracy (Robert and Casella 2004). This method allows key stakeholders to use trade-off analysis among expected different costs, quality levels and just in time delivery distributions. Also it provides other tools to analyze and access supplier selection decisions in times of uncertainty in the supply chain environment industry. Risk monitoring analysis review utilizing Monte Carlo simulation enables companies that depend heavily on supply chain best practices to project any potential obstacles that could bring out a break down in continuity. Moreover, experience of the probability that risks may occur helps in empowering policy-makers to set contingency plans, meet rise in demand at the right time, and finally maximize profitability (Hernandez, 2012). Another way MCS can be important for The Supply Chain Operations Reference model (SCOR) is that it provides a process point of view of supply chain management. SCOR is a Cross industry typical for source chain management that has been sanctioned by the Supply Chain Council. It an emphasis on a specific company (Thiery, C., Bel, G. and Thomas, A. (2010) The reason why MCS would be difficult to use in cases such as is due to its equations of motion, no dynamical information can be gathered from a traditional Monte Carlo simulation REFERENCES 1)Introduction to Operation Management. (2013). Innovation: Essentials of an Organization. Hoboken: Wiley. 2) Dimensions of linear regression 2008, Information technology research,innovation. Operations Management 3) Nichols, DS 2007, Importance of linear programming to the world today. 4) Stocker, G 2006, Linear programming: Why goal programming offer more, Milwaukee, Wis: ASQ Quality Press. 5) Arsham, H. (1998), “Techniques for Monte Carlo Optimizing,” Monte Carlo Methods and Applications, vol. 4, pp. 181229. 6)Banks, J. (ed.) (1998), Handbook of Simulation: Principles, Methodology, Advances, Applications, and Practice, Wiley, New York. 7)Cassandras, C. G. and Lafortune, S. (1999), Introduction to Discrete Event Systems, Kluwer, Boston. 8)Fu, M. C. (2002), “Optimization for Simulation: Theory vs. Practice” (with discussion by S. Andradóttir, P. Glynn, and J. P. Kelly), INFORMS Journal on Computing, vol. 14, pp. 192227. 9)Fu, M. C. and Hu, J.-Q. (1997), Conditional Monte Carlo: Gradient Estimation and Optimization Applications, Kluwer, Boston. 10)Gosavi, A. (2003), Simulation-Based Optimization: Parametric Optimization Techniques and Reinforcement Learning, Kluwer, Boston. 11)Hernandez, F. (2012). Monte Carlo Simulation Means Quantifying Logistics Risks Doesn't Have to Be a Gamble. Supply chain brain, [online] p.4. Available at: http://www.supplychainbrain.com/content/nc/general-scm/sc-security-risk-mgmt/single-article-pa [Accessed 16 Nov. 2014]. 12)Law, A. M. and Kelton, W. D. (2000), Simulation [ CITATION Lin11 \l 1033 ]Modeling and Analysis (3rd ed.), McGraw-Hill, New York. 13)Liu, J. S. (2008), Monte Carlo Strategies in Scientific Computing, Springer-Verlag, New York. 14)Robert, C. P. and Casella, G. (2004), Monte Carlo Statistical Methods (2nd ed.), Springer-Verlag, New York. 15)Thiery, C., Bel, G. and Thomas, A. (2010). SCS M&S Magazine – 2010 / n4 (Oct) Thierry /Bel/Thomas – Page 1 of 8 The Role of Modeling and Simulation in Supply Chain Management. http://www.scs.org/magazines/2010-10/index_ file/Files/Thierry.pdf, 4(2010/4), p.8. 16) Taylor III, B. w. (2013). Introduction to Management science. Newyork: Prentice hall 17) (Brennan, 2011) Modeling and Analysis (3rd ed.), McGraw-Hill, New York. 18)[ CITATION Rus11 \l 1033 ] . Operations management. New york: Thomson Dickson. CITATION Lin11 \l 1033 : , (Brennan, 2011), CITATION Rus11 \l 1033 : , (Russell & Taylor, 2011), CITATION Lin11 \l 1033 : , (Brennan, 2011), 21)Errors and limitations associated withregression and correlation analysis By Aivaz Kaimer-Ainur 2003 Read More