## Introduction

Management science is generally regarded as the key aspect of successful business performance. In general, the science of management involves numerous aspects and tools, hence, the widest explanation of the management science will be closely related to defining the key aim of management. Even though some of the managerial aspects can not be regarded as an integral part of managerial science, most tools are used independently of the generally accepted classification. Hence, this paper aims to analyze in-depth the aspects of managerial science, give the definition, discuss the relations amongst MS, managerial decision making, and the scientific approach of managing as well as decision-making. Linear programming as one of the most reliable scientific approaches will be analyzed from the perspective of management effectiveness.

## Management Science

Management itself is a wide concept, and the number of tools and strategies that form a managerial approach would stay on the list of recommendations without proper systematization. Management science is the attempt to systematize these approaches as well as create innovative rules and principles based on the adjacent disciplines. To be more precise, these disciplines are algebra, geometry, and trigonometry in some cases. These approaches are aimed at creating the mathematical models of management science to systematize the managerial tools and approaches.

The range of problems and issues that are included in the management science competency sphere is wide. This generally involves scheduling, locating the industrial powers as well as the working places of the office employees. This involves flow management, including the principles and forecasts of resource management, defining the future development ways and processes, as well as identifying the communication processes within any organization.

Management science may be regarded as the set of tools for solving the most important business aspects and the related problems. Because some processes and principles that are used in business vary depending on the supplementary tools used, as well as the implementation principles, the key aim of the management science is to find the best management tool for any decision-making process and provide recommendations for the most effective implementation principle for any strategy required.

Considering the exact instances of management science used, it is stated that most business companies can save sufficient sums using the management science approaches. Hence, British Airways have a spare parts policy based on the principles of MS. Ford uses MS approaches to optimize design and test works for the new models. Samsung uses these approaches for producing microchips and controlling the sales rate. The instances are numerous, as well as the aspects of the solutions trusted to the MS approach. In general, the mathematical models are featured with a higher precision rate in comparison with the generally accepted management strategies, hence, the likelihood of success or failure may be accurately calculated only by resorting to Management Science.

## MS, Managerial Decision-Making, and the Scientific Approach

Decisions are regarded as the factors that define the success of organizational development, consequently, the importance of the proper decision-making process is beyond any doubt. The scientific approach towards the decision-making process creates the basis of the management science aimed at making the proper choice required for successful organizational development. As it is stated in Lynn (2004, p. 731):

Corporate investment decisions often involve substantial amounts of money. Many investment decisions are also difficult to reverse and can affect the company’s business far into the future. There are different theories on managerial decision-making. Each decision is influenced by two major factors: decision quality, and acceptance.

In the light of this statement it should be emphasized that regardless of the theoretic approach towards decision-making, it involves at least three stages:

- Definition of the problem, which helps to define the key aspects of the problem
- Collection of the information associated with the problem, definition of the possible alternatives. In general, this is required for increasing the decision-making process.
- Selection of the best alternative based on the information gathered and alternatives analyzed.

The scientific approach towards decision-making involves at least two effective analytical tools. These are break-point and sensitivity analyses. They are regarded as the basic tools of Management Science. The break-even analysis presupposes the calculation of the sales rate when the profit will be equal to zero, i.e. when incomes are equaled to expenses. The economic perspective of this analysis is closely associated with the minimal amount of goods that should be sold. The managerial aspect of this analysis is aimed at searching the sales strategy where no loss is observed. Managers who resort to scientific decision-making principles use this analysis for creating the most effective retail strategy. Additionally, it may be an effective background of the logistic activities performed by an organization.

Sensitivity analysis presupposes consideration of all the independent variables that are involved in the business process, and assessment of their influence. The frameworks of this analysis may be various, and they define the number of variables that are used. It is generally regarded as an effective way to predict the consequences of the taken decision. The mathematical model of the sensitivity analysis involves the application of the equations with variables and further analysis of the possible multitude of results. The MS approach towards defining the best alternative is based on analyzing the multitude of consequences that may be originated by various decisions. Hence, whether one-way or multi-way for sensitivity analysis is used, it is the solid basis for defining the best solution. The graphic modeling of the sensitivity analysis for business decisions is generally performed as a chart, depicting the decrease or increase of certain parameters depending on the changes of a single or several variables. Consequently, both tools may be regarded as effective decision-making instruments, while the precision of these instruments is generally defined by the variables that are used and the aims of the analysis.

## Linear Programming

Linear programming principles are close to the basics of the break-even and sensitivity analysis, as this model is aimed at defining the parameters of the required outcome (whether these are maximum sales or minimal costs). The traditional approach for implementing linear programming into the management science for improving the decision-making process is closely associated with the matters of optimization and finding the best solution. Hence, as it is pointed out in Beach (2007), the simplex method of linear programming is closely linked with constructing the polytope model which is used for finding the best alternative. The non-decreasing values of the modeled process define the required optimum. By the statement by Morishima (2007, p, 310), the following should be emphasized:

In many managerial problems, when linear programming is used, “stalling” occurs: Many pivots are made with no increase in the objective function. In rare practical problems, the usual versions of the simplex algorithm may actually “cycle”. In practice, the simplex algorithm is quite efficient and can be guaranteed to find the global optimum if certain precautions against cycling are taken. The simplex algorithm has been proved to solve “random” problems efficiently, i.e. in a cubic number of steps, which is similar to its behavior on practical problems.

The mathematical model of linear programming is based on creating a simplex algorithm and further defining linear function subject to linear constraints. The model itself is based on the traditional values of analyzing the variants possible, and if applied to managerial issues (as in the example of chapter 3), the mathematical model helps define the best advertisement strategy. The calculations, provided for this solution are closely linked with the consequences that may take effect if one of the decisions is taken.

The algebraic model mentioned in the text is based on building the chart where curves represent the possible consequences of the decisions taken (or alternatives of these decisions). This may be either in the form of a chart, where the cross point of the lines will define the best alternative, or in the form of a spreadsheet which is used for the proper resource allocation alternative selection. Even though the graphic representation of the linear programming model is linked with the particular selection and properly defined calculation process, Pidd (2007) emphasizes that some problems and variations have their optimal solutions. Considering the problem of the resource allocation principles, the following aspect should be highlighted:

The problem of finding a feasible solution to a system of linear inequalities is a linear programming problem in which the objective function is the zero function: For this feasibility problem with the zero-function for its objective-function, if there are two distinct solutions, then every convex combination of the solutions is a solution. (Yahya-Zadeh, 2002, p. 69)

Hence, the general approach of linear programming is based on the principle of the nest solution finding, based on the data and variables available. The management science and decision-making processes may be based either on the particular aspects of linear programming or on the entire calculation process, which is featured with the algorithmic solution process.

## Functional Constraints

All the functional constraints of the linear programming in managerial aspects are closely linked with the resource constraints, as well as the principles of controlling the resource allocation strategy. The functional constraints of the mathematical model are defined by â‰Ą and â‰¤ signs that feature the functional use of the resources available. Mathematically, the constraints of the linear programming in decision-making are represented as follows:

*a*1,1×1 + *a*1,2×2 â‰¤ b1

*a*2,1×1 + *a*2,2×2 â‰¤ b2

*a*3,1×1 + *a*3,2×2 â‰¤ b3

The functional constraints of the values available are based on the functional assessment of the resource allocation alternatives. The key functional constraint of linear programming is closely associated with the fact that every problem subjected to linear programming solution falls entirely and neatly into either one type or the other. Hence, the resource allocation problems, if solved by management science approaches, originate from the pure cost-benefit-trade-off problems (Healy, 2003). However, the actual problems associated with functional constraints may predominate, especially those that are associated with the fairly common resource allocation problems.

Another two types of functional constraints are closely linked with the Non-negative variables

x1 â‰Ą 0

x2 â‰Ą 0

and Non-negative right-hand side constants

bi â‰Ą 0

The former create the function with the feasible area in the positive part of the chart, however, negative values of the variables are not accepted for these functions. Hence, the losses and expenses associated with various managerial decisions can not be considered as the reliable aspect of the analysis. The latter is closely related to the functional restriction of the use of variables, so the frameworks of this functional analysis are too narrow for most resource allocation and decision-making analyses (Lynn, 2004). However, the actual importance of the constraints is not confirmed, the lack of constraints would mean the inconsistency of mathematical modeling and managerial solutions, as decision-making always requires particular frames.

## Conclusion

Management science is generally regarded as the set of tools and instruments for the effective decision-making associated with various aspects of business activity. The regarded cases are linked with resource allocation processes, as well as scheduling, price allocation, and other related aspects. The functional opportunities that are featured for the linear programming tools have definite precision advantages associated with the consequences of decision making, however, the constraints that are also common for these methods define the frameworks of the decision-making as well as the amount of the variables that may be applied for the decision-making process.

## Reference List

Beach, L. R. (Ed.). (2007). *Decision Making in the Workplace: A Unified Perspective*. Mahwah, NJ: Lawrence Erlbaum Associates.

Healy, T. C. (2003). Ethical Decision Making: Pressure and Uncertainty as Complicating Factors. *Health and Social Work, 28*(4), 293.

Lynn, L. E. (2004). *Public Management as Art, Science, and Profession*. Chatham, NJ: Chatham House.

Morishima, M. (2007). *Equilibrium, Stability, and Growth: A Multi-Sectoral Analysis*. Oxford, England: Clarendon.

Pidd, M. (2007). *Tools for Thinking: Modelling in Management Science* (2nd ed.). Hoboken, NJ: Wiley.

Yahya-Zadeh, M. (2002). A Linear Programming Framework for Flexible Budgeting. *Issues in Accounting Education, 17*(1), 69.