Quantitative Decisions in Business - Essay Example

Introduction Spreadsheet modeling is very necessary in analyzing business problems that is why most managers are required to learn the skills of modeling. Learning the spreadsheet-based modeling is really an art for it only requires a basic familiarity with spreadsheets. The process of modeling will be followed by a what-if analysis of the result to find out the different outcomes from different assumptions. On the other hand, network optimization problems will talk about the supply-demand and the source-destination that are present in a distribution network. Aside from the linear programming is the binary integer programming (BIP) that represents the “yes-or-no” decisions. All of these topics are related to quantitative decisions in business. The main purpose of this paper is to improve situational understanding and the basic managerial skills in order to come up with better decisions. General Process of Modeling with Spreadsheets (Long Version w/ Explanations) Plan. Problems are the groundwork of modeling that is why understanding and identifying problems are necessary before commencing with a plan. If problems are already at hand, then relevant data should also be gathered together. These two elements are needed in the formulation of spreadsheets model and in doing some calculations by hand. This initial calculation will give a background of results to be followed by second hand calculations for a checking of results, and finally the sketching of spreadsheets layout before entering the various elements. Build. After the planning stage is the building of spreadsheet model, wherein the sketch layout is moved into the new worksheet in Excel for finalization. Always start with a small version and thoroughly examined the model if the logic are working accurately before expanding to a full-scale model. Test. The manageable version of the model is being tested to determine the accuracy of results. If ever there are major problems along the way like the giving of unexpected results or the changing of values, all of these can be easily corrected because of the model’s manageable size. Build. The process of building and testing often moves back and forth especially if errors occur several times. If the testing of the small version of model verifies accuracy then it is time to build a much larger spreadsheet. There could only be a full-scale version of the model if satisfaction has already been attained. Analyze. It is not impossible to encounter problems at the evaluation stage even if the model has been into several tests. At this stage, the results of the tests in the small version and full-scale version are thoroughly examined. This is to make sure that the output cells give the accurate answers and inadequacies are being revealed. If this might happened, the process may return to the very first step which is the planning stage. Building a Good Spreadsheets Models Creating a spreadsheet model is made possible through the use of the Excel’s different features. However, the features need to be properly set up because instead of creating a good spreadsheet model, it will likely create a bad spreadsheets model (Hillier & Hillier, 2007). Data are always the forefront player in creating spreadsheets that is why it needs to be identified first. After the data are identified and entered into the spreadsheet, it must be labeled so that it can be easily distinguished. It is more suitable if the data are entered only in one cell so that in terms of modifying and searching, the entire data cells will not be affected. Furthermore, model interpretation is easier if the data are visible in the worksheet because if the data and formulas are not separated there is a big tendency that some changes in the value of the data cells are extended to the corresponding formulas. The many functions in the Excel are all useful; however, avoid using complicated formulas. A good spreadsheet model is easier to test and debug, and this will only happen if the functions that are being used are easier to interpret. On the other hand, different cells need to be distinguished from each other by using different borders, shadings, and colors with consistency for it will serve as a guide in examining the type of cells. Lastly, it is “strongly recommended that every element of the model be displayed on the spreadsheet” for easy interpretation (Hillier & Hillier, 2007). Benefits of the What-if Analysis to the Managers Through the what-if analysis, a new optimal solution will be considered in case there are changes in the values of the data with a careful estimation that the values cannot be changed into an erroneous solution (Bazaraa, Jarvis & Sherali, 2010, p. 295). Because assumptions of values are made by estimates, the what-if analysis will be used when decision-makers decide to change the values of the variables. Every changes will “help managers understand the impact of various revenue levels on the other factors involved in decisions being considered” (Sen, 2010, p. 20). Networks Optimization Problems A network is consists of set of points called nodes or vertices, and a set of lines which is also called an arc connecting certain pairs of nodes (“Network Optimization,” n.d.). A network could either be a directed or undirected wherein the basis of the structure lies in the direction of the arcs. Network in network optimization is rapidly used in various applications like real-time decision making and problem solving (Trick, 1998). Problems also arise in the areas of applications such as “telecommunications, transport systems, distribution and logistics” (Minoux, 2001). Phone network is one of the examples that deal with a set of nodes, communication links, and a path of travel that will send the message from the source node to the destination node. The transport of the voice signal must reach the destination node without delays and the shortest time possible. Another example is a distribution network that talks about the capacity of the network and the flow. The maximum flow must correspond to the number of capacity so that there would be a greater amount of material to be transported from the source to the destination node. The problem in terms of supply and demand is related to a transportation network wherein the supplies are transported from the source to the destination nodes at a minimum cost plan in order to meet the demands. 3 Types of Network Optimization Problems Minimum-Cost Flow Problem. The objective of this problem is to minimize the total cost incurred during the shipment of supply to the demand. The arcs must have the capacity to follow the arrows in one direction in order to reach the demand node with lesser cost. To reach the set of nodes with minimal cost but with maximized profit, the total supply of material on each source must be equal to the total destination that has a demand. Maximum Flow Problems. In contrast with the minimum-cost flow, the objective of maximum flow problems is to maximize the amount of flow in the shipments of supply following a set of distribution network. In this model, the cost of the flow on each arc is limited and equals to the maximum flow that is why it is usually associated with a bottleneck. Shortest Path Problems. In this problem, there is a start node called the origin and a finish node called the destination; and the objective is to find the shortest distance from the origin to the destination; “the path is said to be shortest if it has minimum length over all forward paths with the same origin and destination nodes” (Bertsekas, 1998, p. 65). “Yes-or-No” Decisions A yes-or-no decision is represented with a binary variable wherein there is only two possible choices; a value of 1 means “yes” and a value of 0 means “no” (Bosch & Trick, 2005, p. 76). The choice of action is modeled by a binary variables or zero-one in which the consequences are positive if the decision variable is 1 and negative if the decision variable is 0. Binary Variables to Binary Decision Variables “Perhaps the most type of integer variable is the binary variables: integer variable restricted to take the values of 0 to 1” (Bosch & Trick, 2005, p. 76). The binary decision variables that modeled the applications of a yes-or-no decision are called the binary decision variables in a binary integer programming (BIP) model. BIP, Pure BIP, and Mixed BIP “Binary integer programming (BIP) models either pure or mixed are among the widely used optimization models” (Hillier & Hillier, 2002, p. 11). If the problem is dealing with integer values and if the decision variables are integer-restricted variables then it is a BIP problem. If the decision variables are all assigned as binary variables and not real numbers then the model is called pure BIP (Brandimarte, 2006, p. 565). In pure BIP problems, the procedure is to find optimal solution because the given number of feasible solutions is limited to a fixed number of integer variables. The last model is called the mixed BIP model wherein not all of the decision variables are binary variables and the problems usually arise if the integer programming requires being integer-restricted variables. Conclusion Modeling with spreadsheets is really an art for although it does not follow a systematic procedure, the general process is very helpful. Basically, the steps of modeling involves planning, building, testing and analyzing the model and its result, and the guidelines of building a good spreadsheet model is very detailed. The what-if analysis is beneficial to the managers as an effective tool for managerial decision making. The benefits of this analysis are almost the same with the network models. As long as there is a supply-demand and source-destination, the three types of optimization problems will always be present. Lastly, a decision variable often takes the binary variables wherein the value of 1 represents “yes” and a value of 0 represents “no.” References Bazaraa, M. S., Jarvis, J. J. & Sherali, H. D. (2010). Linear programming and network flows. Hoboken, New Jersey: John Wiley & Sons, Inc. Bertsekas, D. (1998). Network optimization: continuous and discrete models. Belmont, Massachusetts: Athena Scientific. Bosch, R., & Trick, M. (2005). Integer programming. In E. K. Burke & G. Kendall (Eds.), Search methodologies: introductory tutorials in optimization and decision support techniques (pp. 69-90). New York, NY: Springer Science. Brandimarte, P. (2006). Numerical methods in finance and economics: A MATLAB-based introduction. 2nd ed. Hoboken, New Jersey: John Wiley & Sons, Inc. Hillier, M. S., & Hillier, F. S. (2002). Conventional optimization techniques. In R. Sarker, M. Mohammadian & X. Yao (Eds.), Evolutionary optimization (pp. 4-22). Massachusetts: Kluwer Academic Publishers. Hillier, F. S., & Hillier, M. S. (2007). Introduction to management science: A modeling and case studies approach with spreadsheets. New York, NY: The McGraw-Hill. Minoux, M. (2001). Discrete cost multicommodity network optimization problems and exact solution method. INRIA. Retrieved from http://www-sop.inria.fr/members/Frederic. Havet/Cours/minoux02.pdf Network Optimization, n.d. Michael Trick’s operations research page. Retrieved from http://mat.gsia.cmu.edu/classes/QUANT/NOTES/chap11.pdf Sen, R. P. (2010). Operations research: Algorithms and applications. New Delhi: Asoke K. Ghosh. Trick M. A. (1998). Network optimization. Michael Trick’s operations research page. Retrieved from http://mat.gsia.cmu.edu/classes/networks/node1.html#SECTION0001000 0000000000000 Read More