Quantitative Analysis Lecture Notes

Flashcards on Quantitative Analysis, Network Models, Probability Analysis, and Learning Curve.

Quantitative Analysis

Refers to the application at mathematics in actual business operations; also known as quantitative methods.

Network Models

• Involves project scheduling techniques that are designed to aid the planning and control of largescale projects that have many interrelated activities.

• These models aid management in predicting and controlling costs that pertain to certain projects or business activities.

Gantt or Bar Chart

• This is a graphical illustration of a scheduling technique in the form of a horizontal bar chart. The project is divided into different sub-projects called activities or tasks (also call ‘milestones’).

• The starting and completion time of activity is estimated and a bar chart prepared showing each activity as a horizontal bar along a time scale.

Program Evaluation and Review Technique (PERT)

Developed to aid managers in controlling large-scale, complex problems.

PERT Diagram

A probabilistic diagram of the interrelationship of a complex series of activities; it is a free-form network showing each activity as line between events.

Events (in PERT)

Discrete moment in time representing the start or finish of an activity; they consume no resources.

Activities (in PERT)

Tasks to be accomplished; they consume resources (including time).

Series Activity

An activity that cannot be done unless another activity is undertaken first.

Parallel Activity

An activity that can be performed simultaneously with another activity.

Critical Path Method (CPM)

Network technique that uses deterministic time and cost estimates, among its advantages include cost estimates plus the concept of crash efforts and costs.

Critical Path

The longest path through the PERT network.

Expected Time

The average time an activity would require if it were repeated several times.

Slack Time

Amount of time that can be added to an activity without increasing the total time required on the critical path; the length of time an activity can be delayed without forcing a delay for the entire project

Crash Time

Amount of time to complete an activity assuming that, under rush conditions, all available resources were devoted to the task (e.g., overtime, extra labor, etc.); any crash time spend in an activity normally would incur crash cost.

Probability Analysis

Important to decision-making because of the unpredictability of future events.

Risk

Occurs when the probability distribution of the possible future state of nature is known.

Uncertainty

Occurs when the probability distribution of possible future state of nature is not known and must be subjectively determined.

Objective probabilities

Calculated from either logic or actual experience.

Subjective probabilities

Estimates, based on judgments of the likelihood of future events.

Mutually exclusive events

Two events that cannot occur simultaneously.

Independent events

Two events where the occurrence of one has no effect on the probability of another.

Joint probability

The probability that both events will occur.

Conditional probability

The probability that one event will occur given that the other has already occurred.

Learning Curve

Describes the efficiencies arising from experience, because with experience comes increased productivity.

Linear Programming

Mathematical technique that helps managers to determine the volume of various products to produce when resources are limited or scarce in order to maximize net income. It is a technique used to optimize an objective function (maximize revenue of profit function, or minimize a cost function), subject to constraints (such as scarce resources, minimum/maximum levels of production, performance, etc.).

Typical Quantitative methods applications

• Corporate planning models

• Forecasting mechanism

• Productivity and efficiency measure

• Inventory planning and control

• Resource allocation

Use of Network Models

• Planning

• Measuring progress to schedule

• Evaluating changes to schedule

• Forecasting future progress

• Practicing and controlling costs

Common Project Scheduling Techniques

1. Gantt or Bar Chart

2. Program Evaluation and Review Technique (PERT)

3. Critical Path Method (CPM)

Types of Activities in Program Evaluation and Review Technique (PERT) – Critical Path Method (CPM)

• Series

• Parallel

Probability of an event

Varies from 0 to 1 (0% to 100%). 100% or probability of 1.0 means that event is certain to occur while zero probability means the event cannot occur under any circumstances.

Expected value of an action

Found by multiplying the probability of each outcome by its pay-off and summing up the products.

Decision tree diagram

Normally devised to show several possible decisions or acts and the possible consequences (outcome or events) of each act.

Types of Subjective probabilities

• Mutually exclusive

• Independent

• Joint probability

• Conditional probability

Cumulative average time per unit

Reduced by a certain percentage each time production doubles

Limited resources

Must be allocated to the company’s most profitable products so that net income is maximized.

Linear programming models

Extremely helpful in the analysis and solution of resource allocation problems.

Simplex method

A much detailed linear programming technique especially useful if there are more than two variables in a linear programming problem.

Incremental unit time (time to produce the last unit)

Reduced when production doubles