Quantitative Techniques in Management

The complexity of today’s business operations, high cost of technology, materials, manpower and competitive pressures, contribute to the difficulty of making effective decisions. An effective decision depends on different economic, social and political factors and the view points. The primary objective of quantitative methods or techniques is to help decision-makers make better decisions by solving problems more effectively. Thus, an understanding of the applicability of quantitative methods to business decision-making is important for any decision-maker.

Linear programming (LP) is a widely used mathematical modelling technique developed to help decision-makers in planning and decision-making regarding optimal use of scarce resources. This chapter is devoted to illustrate the applications of LP programming in different functional areas of management and how LP models are formulated.

This chapter presents graphical solution method for solving any LP problem with only two decision variables. This method provides a conceptual basis for solving large and complex LP problems.

The purpose of this chapter is to help you gain an understanding of how the simplex method works. Understanding the underlying principles help to interpret and analyze solution of any LP problem.

The chapter deals with how to find the marginal value (also known as shadow price) of each resource. This value reflects an additional cost to be paid to obtain one additional unit of the resource to get the optimal value of objective function under resource constraints.

The purpose of sensitivity analysis is to evaluate the effect on the optimal solution of an LP problem due to variations in the input coefficients (also called parameters), one at a time

In this chapter, Gomory’s cutting plane method, and Branch and Bound method have been discussed for solving an extension of LP model called linear integer LP model. In a linear integer LP model one or more of the variables must be integer due to certain managerial considerations.

Goal programming is an approach used for solving any multi-objective optimization problem that balances trade-off in multiple and often conflicting in commensurable goals at different priority levels.

The structure of transportation problem involves a large number of shipping routes from several supply centres to several demand centres. The objective is to determine the number of units of an item (commodity or product) that should be shipped from an origin to a destination in order to satisfy the required quantity of goods or services at each destination centre.

An assignment problem is a particular case of a transportation problem where the given resources are allocated to an equal number of activities with an aim of either minimizing total cost, distance, time or maximizing profit. Travelling salesman is a specific application of assignment model

A game is a contest involving two or more competitors each of whom wants to win. A theory of games provides a series of mathematical models that may be useful in explaining interactive decision-making concepts, where two or more competitors are involved under conditions of conflict and competition.

The decision theory is a technique used for decision making in an uncertain condition. It provides a framework and methodology for rational decision making when the outcomes are uncertain. The problems involving a sequence of decisions (including perhaps a decision on whether to obtain more information), a decision tree is used to graphically display the progression of decisions and random events. The problems involving the probability of uncomfortable large losses, utilities provide way for incorporating the decision maker's attitude towards risk into the analysis.

The objective of project management study is to schedule activities associated with any project in an efficient manner so as to complete the project on or before a specified time limit and at the minimum cost with specified quality standard. Two project management techniques – PERT and CPM are commonly used to show the logical sequence of activities to be performed in any project in order to achieve project objectives.

The word inventory refers to any kind of resource that has economic value and is maintained to fulfil the present and future needs of an organization. Inventory of resources is held to provide desirable service to customers (users) and to achieve sales turnover target. Investment in large inventories adversely affect an organization’s cash flow. Working capital as investment in inventory represents substantial portion of the total capital investment in any business. It is, therefore, essential to balance the advantage of having inventory of resources and the cost of maintaining it so as to determine an optimal level of inventory of each resource. This would ensure that the total inventory cost is minimum.

A queue, in general, is formed at any place when a customer (human beings or physical entities) that requires service is made to wait due to the fact that the number of customers exceeds the number of service facilities or when service facilities do not work efficiently and take more time than prescribed to serve a customer

Markov chain models (also known as stochastic processes) are useful to study a system in which the system’s current state depends on all of its previous states. Markov chains are classified by their order. The case in which probability occurrence of each state depends only upon the immediate preceding state, is said to be first order Markov chain. In second order Markov chains, it is assumed that the probability of occurrence in the forthcoming period depends upon the state in its last two periods. Similarly, in the third order Markov chains, it is assumed that the probability of a state in the forthcoming period depends upon the states in its last three periods

Simulation is one of the widely used technique by corporate managers as an aid for decision-making. This technique uses a computer to simulate (imitate) the operation of any system or process. It is also used to analyse systems that operate indefinitely. In such a case, the computer randomly generates and records the occurrence of the events that drive the system as if it was physically operating. Recording the performance of the simulated operation of the system for a number of alternative options of operating procedures enables us to evaluate and compare these alternatives to choose the most desired one.

The financial decision area is a veritable manifold in the real-world hedged as it is with tax implications, depreciation, investment and capital allowances, etc. The principles of such financial decision-making are established through the concepts of interest and present value of money. This chapter introduces a number of techniques to the evaluation of such financial information.

Increasing complexity of business environment, together with changing demands and expectations of consumers, forces any organization to know the future values of its key decision variables. Forecasting methods take historical data into consideration to predict the occurrence of uncertain events, and hence help to evaluate outcomes of various alternative decisions or strategies. The additional information generated through the use of any forecasting method may be used to redesign the strategy formulation as well as to establish a monitoring system to compare planned performance with the actual performance

Decision makers often come across some degree of risk while selecting a particular course of action or strategy to solve a decision problem involving uncertainty. It is because each strategy can lead to a number of different possible outcomes (or results). Thus, it is necessary for the decision makers to gain knowledge of the concepts of probability, and probability distributions to choose a course of action to arrive at an optimal decision.

In any probabilistic situation, choosing a strategy (course of action) may lead to a number of different possible outcomes. In such a situation, the decision-maker may like to know the average value (payoff) of the random variable. The list of all possible outcomes of a random variable along with their probabilities of occurrence is called probability distribution. The numerical value of a random variable may be different in different trials of any random experiment conducted under similar conditions.