1 Slide

Slides byJOHN

LOUCKSSt. Edward’sUniversity

INTRODUCTION TO MANAGEMENT SCIENCE, 13e

AndersonSweeneyWilliams

Martin

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Chapter 1Introduction

Body of Knowledge Problem Solving and Decision Making Quantitative Analysis and Decision Making Quantitative Analysis Models of Cost, Revenue, and Profit Management Science Techniques

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Body of Knowledge The body of knowledge involving quantitative

approaches to decision making is referred to as • Management Science• Operations Research• Decision Science

It had its early roots in World War II and is flourishing in business and industry due, in part, to:• numerous methodological developments (e.g.

simplex method for solving linear programming problems)

• a virtual explosion in computing power

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7 Steps of Problem Solving(First 5 steps are the process of decision

making)1. Identify and define the problem.2. Determine the set of alternative solutions.3. Determine the criteria for evaluating

alternatives.4. Evaluate the alternatives.5. Choose an alternative (make a decision).

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6. Implement the selected alternative.7. Evaluate the results.

Problem Solving and Decision Making

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Quantitative Analysis and Decision Making

Definethe

Problem

Identifythe

Alternatives

Determinethe

Criteria

Identifythe

Alternatives

Choosean

Alternative

Structuring the Problem Analyzing the Problem

Decision-Making Process

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Analysis Phase of Decision-Making Process Qualitative Analysis

• based largely on the manager’s judgment and experience

• includes the manager’s intuitive “feel” for the problem

• is more of an art than a science

Quantitative Analysis and Decision Making

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Analysis Phase of Decision-Making Process Quantitative Analysis

• analyst will concentrate on the quantitative facts or data associated with the problem

• analyst will develop mathematical expressions that describe the objectives, constraints, and other relationships that exist in the problem

• analyst will use one or more quantitative methods to make a recommendation

Quantitative Analysis and Decision Making

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Quantitative Analysis and Decision Making

Potential Reasons for a Quantitative Analysis Approach to Decision Making• The problem is complex.• The problem is very important.• The problem is new.• The problem is repetitive.

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Quantitative Analysis

Quantitative Analysis Process• Model Development• Data Preparation• Model Solution• Report Generation

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Model Development Models are representations of real objects or

situations Three forms of models are:

• Iconic models - physical replicas (scalar representations) of real objects

• Analog models - physical in form, but do not physically resemble the object being modeled

• Mathematical models - represent real world problems through a system of mathematical formulas and expressions based on key assumptions, estimates, or statistical analyses

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Advantages of Models

Generally, experimenting with models (compared to experimenting with the real situation):• requires less time• is less expensive• involves less risk

The more closely the model represents the real situation, the accurate the conclusions and predictions will be.

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Mathematical Models Objective Function – a mathematical expression

that describes the problem’s objective, such as maximizing profit or minimizing cost

Constraints – a set of restrictions or limitations, such as production capacities

Uncontrollable Inputs – environmental factors that are not under the control of the decision maker

Decision Variables – controllable inputs; decision alternatives specified by the decision maker, such as the number of units of Product X to produce

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Mathematical Models Deterministic Model – if all uncontrollable inputs to

the model are known and cannot vary Stochastic (or Probabilistic) Model – if any

uncontrollable are uncertain and subject to variation

Stochastic models are often more difficult to analyze.

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Mathematical Models Cost/benefit considerations must be made in

selecting an appropriate mathematical model. Frequently a less complicated (and perhaps less

precise) model is more appropriate than a more complex and accurate one due to cost and ease of solution considerations.

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Transforming Model Inputs into Output

Uncontrollable Inputs(Environmental Factors)

ControllableInputs

(DecisionVariables)

Output(Projected Results)

MathematicalModel

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Example: Project Scheduling

Consider the construction of a 250-unit apartmentcomplex. The project consists of hundreds of activitiesinvolving excavating, framing,wiring, plastering, painting, land-scaping, and more. Some of theactivities must be done sequentiallyand others can be done at the sametime. Also, some of the activitiescan be completed faster than normalby purchasing additional resources (workers, equipment, etc.).

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Example: Project Scheduling

Question: What is the best schedule for the

activities and for which activities should additional resources be purchased? How could management science be used to solve this problem?

Answer:Management science can provide a

structured, quantitative approach for determining the minimum project completion time based on the activities' normal times and then based on the activities' expedited (reduced) times.

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Example: Project Scheduling

Question: What would be the uncontrollable inputs?

Answer:• Normal and expedited activity completion

times• Activity expediting costs• Funds available for expediting• Precedence relationships of the activities

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Example: Project Scheduling

Question:What would be the decision variables of

the mathematical model? The objective function? The constraints?

Answer:• Decision variables: which activities to

expedite and by how much, and when to start each activity

• Objective function: minimize project completion time

• Constraints: do not violate any activity precedence relationships and do not expedite in excess of the funds available.

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Example: Project Scheduling

Question: Is the model deterministic or stochastic?

Answer:Stochastic. Activity completion times,

both normal and expedited, are uncertain and subject to variation. Activity expediting costs are uncertain. The number of activities and their precedence relationships might change before the project is completed due to a project design change.

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Example: Project Scheduling

Question: Suggest assumptions that could be made

to simplify the model. Answer:

Make the model deterministic by assuming normal and expedited activity times are known with certainty and are constant. The same assumption might be made about the other stochastic, uncontrollable inputs.