Management Science and Managerial Decision Making - Coursework Example

Running head: management science Management Science Introduction to Management Science: As a logical approach to problem solving, management science(MS) has been widely accepted and implemented in all kinds of organizations. Hillier and Hillier describe MS as the discipline that attempts to aid managerial decision making by applying a scientific approach to managerial problems that involve quantitative factors (2010, p.2). MS uses quantitative analysis and calculations, mathematics theories and techniques, data collection, data analysis and data assessment. MS is applied in variety of areas such as logistics, supply chain management, production and inventory management, decision analysis, optimization, simulation, forecasting, game theory, network/transportation forecasting models, mathematical modeling, data mining, probability and statistics, resource allocation, project management, engineering as well as many others. In short, MS uses data, makes suitable model and provides solutions to the problems in a variety of ways. Wider applicability of this approach is seen in planning for the future, and the most common tool used is the linear programming model. This discussion explores the relationship between management science approach and managerial decision making with the applicability of specific tools, such as the linear programming model. In the process, it includes an understanding of components of linear programming and associated inferences such as break-even point and sensitivity analysis. Further, the main functional constraints in linear programming problems have been outlined. MS and managerial decision making: Management Science aids in managerial decision making’ (Hillier & Hillier 2010, 3) Management science provides a holistic view of operational performance including a fair idea of potential issues, factors hindering performance, and performance analysis; it also helps in highlighting existing gaps in the system or process. In order to manage effectively, such information helps managers in appropriate decision making either by effecting changes to the system/process or adopting new approaches. MS also provides managers with tools and techniques to implement new processes and to look at existing issues from quantitative, mathematical and graphical views. These are accomplished in five steps. Firstly, manager or the MS team identifies the problem and gathers data relevant to the problem over sufficient period of time. Next, a model is formulated to represent the problem, either in the form of scientific structures or mathematical models. Thirdly, computer-based procedures for deriving solutions to the problem defined in the model are developed. Then these procedures are checked for their effectiveness in solving the problem in a variety of ways. Finally, these procedures are recommended to the managers who can then decide which approach gives best solution for their problems. If managers decide to choose any of these approaches on an ongoing basis, then a decision support system is developed, which is further used to solve similar problems using updated data. Further, management science team helps the managers in implementing the new procedures; check consistency of results and monitors the new performance. Break-even point and sensitivity analysis: Based on the mathematical model identified for a specific problem, the point at which there is no loss or profit in the outcome in relation to the quantity or cost of input is referred to as the break-even point. For instance, in production process, the point at which the cost of production of specific number of products equals the revenue generation, that point is break-even point of that production model. When the estimates or quantification of variables included in a measurement change, then the outcome also changes. MS concepts are used to study this changing behavior in order to assess effectiveness of a specific model, which is referred to as sensitivity analysis. Hillier and Hillier (2010) relate sensitivity analysis to incorrect estimation of quantifiable inputs and targets. Assessment of break-even point is useful in identifying the effort required (in terms of costs, resources and time) to produce a specific product with no loss. Sensitivity analysis helps in understanding how the effort can be modified to improve the outcome that may be in the form of profits or minimizing losses. To achieve these, a mathematical model forms the precursor, which can be obtained by scientific approach described in management science. Linear Programming: Model and Components Linear programming is a powerful problem solving tool that aids management in making such decisions as how to allocate resources of an organization to various activities to best meet organizational objectives (Hillier & Hillier 2010, 17). Linear programming is applicable to situations with multiple variables. The main objective of linear programming is to maximize return on investments, process effectiveness or minimize costs, resources or inputs. A second component of linear programming model is the constraints that decide effectiveness or level of attainable objective. Thirdly, decision variables in the form of mathematical symbols indicative of desired objectives and constraints are included. Lastly, the numerical coefficients to represent the parameters of objectives and constraint equations are required (Shah, Gor & Soni, 2007). While formulating a linear programming model, firstly the decision variables are to be identified in the problem. As the decision variables are directly linked to the objective, it is important to select right decision variables, which could be difficult in complex processes; in such cases, variables that directly impact the end objective and/or controllable inputs may be chosen. Next, these decision variables are linked to the objective of the problem by defining the objective, which could be either to maximize or minimize intended outcome. Further, constraints need to be identified and described individually. In most cases, these are usually the resources, cost and time limitations and impact of other variables. These constraints are formulated into linear equations as non-negative decision variables. It is important to note much data collection and analysis is required to decide upon decision variables. In cases like staff scheduling, for example, a constant number of staff required on a given day is to be decided based on historical workflow pattern. Further, sensitivity analysis according to workflow pattern needs to be done. Here information could change on daily, weekly or monthly basis. Decision variables are derived based on these derivations need to be considered. Very often, linear programming models based on spreadsheet models are being used in organizations. In this, all decision variables must be related with appropriate cell formulae. Firstly, the inputs constitute all numerical information; second are the changing cells in which the decision variables may be modified to obtain optimum values for the objective. Thirdly, the target or objective cell depicts optimum value of the objective obtained upon testing different decision variables in the changing cells. In a spreadsheet, constraints are usually indicated with conditional formula that indicates constraints with respect to ultimate objective. Mathematical/Algebraic model: Although spreadsheet models are most extensively used in contemporary management systems, their origin is traced to the mathematical and graphical models. The mathematical model uses algebraic expressions. Even this method requires relevant data and identification of decision variables. Further, constraints need to be defined for the chosen decision variables. Then, overall measure of performance/outcome is measured. This measure of performance is related with verbal description of the constraints in an algebraic expression. In this model too, constraints need to be defined by nonnegativity. Other constraints are referred to as functional constraints. A solution or equation that satisfies all constraints is referred to as feasible solution, and the one that is incongruent with even one constraint is infeasible constraint. The best feasible solution, or the one that is close to the equation is the best or optimal solution. Graphical model: The graphical models are used when decision variables are very less. Here, the two most important indications are the constraint boundary lines and objective function lines. For instance, in situations with two decision variables, the constraint boundary lines are plotted for each functional constraints and permissible region/point of constraint is marked using the origin. The feasible region is represented by the area where all constraints are satisfied at once. Here the optimal solution may be determined. For plotting the constraints, firstly nonnegative constraints are plotted followed by other constraints. If any two points fall in line, a straight line is drawn. The boundary of the permissible region is the feasible region, which is then shaded. Feasible point is located on this boundary function line. Functional Constraints: Identifying situations where linear programming can be applied to solve management problems is important to bring about improvements in the system. The most common functional constraints in management include resource constraints, benefit constraints and fixed-requirement constraints. Firstly, resource constraint refers to the resource allocation problem within linear programming and is represented by the equation between resource available and resource used. This is represented by amount used ­≤ amount available. For resource allocation problems, the functional constraint is represented by ≤. The second constraint is the benefit constraint, which identifies the amount of benefit to be achieved, irrespective of the resource usage. Here, the focus is to achieve maximum benefit with minimum costs. For this, minimum acceptable levels of all possible benefits are decided, and costs related to each of these benefits are minimized to the possible extent. An appropriate limit where maximum benefit with minimum costs is achievable is then decided. The benefit constraint is represented by Level Achieved ≥Minimum Accepted Level. The third constraint is the fixed-requirement constraint, identified by amount provided = amount required; or, output = input. Importantly, fixed requirement constraints constitute the functional constraints in this kind of problem. Often, mixed problems comprise of fixed-requirement constraints, the most common types being transportation, transshipment and assignment problems (Stevenson, 2006). Transportation problems are applied to distribution-type in which supplies of goods to various locations are to be shipped at minimum costs. In case of transportation problems, the fixed requirements include amount of output must be equal to amount of output shipped to customers and amount received by the customer should equal amount ordered (Hillier & Hillier, 2010). In transshipment, intermediate destinations are involved for temporary storage of products; a linear programming model would be aimed to minimize total transshipment costs (Stevenson, 2006). Assignment problems are applied to assignment of work, tasks, machines etc to employees to bring optimum output and minimum wastage. The factors that determine resource constraints include amount available of each resources; amount of resource used per activity; and, outcome of each activity that used one unit of resource. In the benefit constraint, every step involved in the process of producing the output is regarded as benefit constraint. The benefit constraint or the minimum acceptable level is usually formulated as a management policy, but other influencing factors may also be involved. This is determined mainly by the minimal acceptable level of each benefit; impact of each activity on the benefit; and cost involved in each activity. Thirdly, fixed requirement problems are formulated based on fixed-requirement constraints which are modified to obtain optimum usage. Transportation and assignment of job are fixed requirement constraints in which the factors include amount of produce shipped and amount of machines/resources allocated to workers, respectively. Summary and conclusions: In summation, management science refers to the discipline of applying quantitative analytical models to organizational situations which further aid in managerial decision making process; often these decisions are related to cost, resource allocation, quality and efficiency. The break-even point and sensitivity analysis processes are very effective in managerial decision making. Linear programming is the most commonly used and effective problem solving tool applied to these situations. Method of linear programming model varies with the type of constraints; three main constraints identified include resource, benefit, and fixed-requirement constraints. In conclusion, linear programming model is an effective tool in managerial decision making as it has the potential to address any management issue. References Hillier, F.S & Hillier, M.S. (2010). Introduction to Management Science: A Modeling and Case Studies Approach with Spreadsheets, (4th Ed), New York, NY: McGraw-Hill/Irwin Publishing Company Shah, N.H, Gor, R.M & Soni, H. (2007). Operations Research. New Delhi: PHI Learning Pvt. Ltd. Stevenson, W.J & Ozgur, C. (2006). Introduction to Management Science W/Cd. New Delhi: Tata McGraw-Hill. Read More