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Objectives

- Define management science
- Define decision model and describe its importance
- Classify decision models
- List and explain steps involved in developing decision models in practice
- Remind breakeven analysis with computer applications
- Make a classification of management science modeling techniques
- Give examples of management science applications
- Discuss possible problems in developing decision models

Management Science is the scientific approach to executive decision making, which consists of:1. The artof mathematical modeling of complex situations,2. The scienceof the development of solution techniques used to solve these models,3. The ability to effectively communicate the results to the decision maker

What is Management Science?

- Management science uses a scientific approach to solving management problems.
- It is used in a variety of organizations to solve many different types of problems.
- It encompasses a logical mathematical approach to problem solving.
- It is also referred to as: Decision Modeling

QuantitativeAnalysis

Operations Research

Uses of Decision Models (1 of 2)

- They can solve complex problems.
- They provide analytical framework for evaluating modern business problems
- They are subject to limitations
- They provide techniques applicable in many areas such as:
- Accounting, Economics, and Finance
- Logistics, Management, and Marketing
- Production, Operations, and Transportation

Uses of Decision Models (2 of 2)

They can be applied when:

- designing and implementing new operations or procedures
- evaluating an ongoing set of operations or procedures
- determining and recommending corrective action for operations and procedures that are producing unsatisfactory results

- Quantitative data - numeric values that indicate how much or how many.
- Rate of return.
- Financial ratios.
- Cash flows.
- Qualitative data - labels or names used to identify an attribute -
- Outcome of an upcoming election.
- New technological breakthrough.

Role of Spreadsheets in Decision Modeling

- Computers are an integral part of decision making.
- Spreadsheet packages -
- Are capable of handling management decision modeling techniques.
- Have built-in functions and procedures

Optimization Models seek to maximize a quantity (eg. profit) or minimize a quantity (eg. cost, time, etc.) that may be restricted by a set of constraints (limitations on the availability of capital, workers, supplies, machines etc.)

Optimization Models

At times however, the function of a model is not to maximize or minimize any particular quantity, but to describe or predict events given certain conditions These models are known as Predictive Models. These techniques do not generate an answer or a recommended decision. Instead they provide descriptive results: results that describe the system being modeled. They usually provide important input to optimization models

(by the degree of certainty of the data)

Decision

Models

Deterministic Models

Probabilistic Models

Deterministic Models

- Deterministic models assume:
- Complete certainty.
- All information needed is available with fixed and known values.
- Most commonly used deterministic modeling technique is Linear Programming.

Probabilistic Models

- Probabilistic models are also called stochastic models.
- Probabilistic models -
- assume some of data is not known with certainty.
- take into account that information will be available after the decision is made.

Steps Involved in Decision Modeling(Management Science Approach)

1. Formulation.

2. Solution.

3. Interpretation.

Management Science Process (1 of 3)

- Observation - Identification of a problem that exists in the system or organization.
- Definition of the Problem - problem must be clearly and consistently defined showing its boundaries and interaction with the objectives of the organization.
- Developing a clear and concise problem statement

Management Science Process (2 of 3)

- Developing a model – Development of the functional mathematical relationships that describe the decision variables, objective function and constraints of the problem.
- Amanagement science modelis an abstract representation of an existing problem situation. It can be in the form of a graph or chart, but most frequently a Management Science model consists of a set of mathematical relationships that are made up of numbers and symbols.

Management Science Process (3 of 3)

- Model Solution- Models solved using management science techniques.
- Model Implementation - Actual use of the model or its solution.

Step 1: Model Formulation (1 of 2)

Developing a model requires to:

- identify the decision variables
- develop the decision model by quantifying the objective (function to be optimized-profit, cost, etc) and constraints (restrictions on resource availability etc.), ie. develop relevant mathematical relations for consideration and evaluation.

Step 1: Model Formulation (2 of 2)

- Acquire input data.
- Collect accurate data for use in model.
- Possible data sources are:
- Official company reports.
- Accounting, operating, and financial information.
- Views, and opinions from knowledgeable individuals

Step 2: Model Solution (1 of 3)

- Developing a solution may involve:
- Solution of a set of mathematical expressions to arrive at best (optimal) solution, or
- Alternative trial and error iterations, or
- Complete enumeration of all possibilities or
- utilization of an algorithm.

Step 2: Model Solution (2 of 3)

An appropriate solution technique may be an optimization algorithm (series of steps repeated until the best solution is attained) or a heuristic algorithmMost algorithmsare intended to provide an optimal solution for a model. Sometimes, however, problems can prove to be too complex or time consuming to employ optimization algoritms. In such cases a heuristicprocedure may be preferred

Step 2: Model Solution (3 of 3)

- Prior to implementation of model solution, the solution is tested
- Testing of solution is accomplished by examining and evaluating:
- Datautilized in the model and
- themodelitself.

Step 3:Implementation & Interpretation (1 of 2)

- Optimal solution must be implemented carefully.
- Solution implementation usually requires making changes within the organization.
- Recommendations often require changes in data, data handling, resource mixes, systems, procedures, policies, and personnel.
- Managers and others may resist recommended solutions.

Step 3: Implementation and Interpretation (2 of 2)

- Interpretation and What-if Analysis.

Analyzing the results and sensitivity analysis.

Examine changes in optimal solution as a result of changes in input values and model parameters

- Information and Data:
- Business firm makes and sells a steel product
- Product costs $5 to produce
- Product sells for $20
- Product requires 4 pounds of steel to make
- Firm has 100 pounds of steel
- Business Problem:
- Determine the number of units to produce to make the most profit given the limited amount of steel available.

Variables: X = number of units (decision variable)

Z = total profit

Model: Z = $20X - $5X (objective function)

4X = 100 lb of steel (resource constraint)

Parameters: $20, $5, 4 lbs, 100 lbs (known values)

Formal Specification of Model:

maximize Z = $20X - $5X

subject to 4X = 100

(1 of 4)

- Used to determine the number of units of a product to sell or produce (i.e. volume) that will equate total revenue with total cost.
- The volume at which total revenue equals total cost (zero profit) is called the break-even point.
- Profit at break-even point is zero.

(2 of 4)

Model Components:

- Fixed Costs (cf) -costs that remain constant regardless of number of units produced. $’s necessary to invest in facilities
- Variable Cost (cv) - unit cost of product.
- Total variable cost (vcv) - function of volume (v) and variable per-unit cost.
- Total Cost (TC) - total fixed cost plus total variable cost.
- Profit (Z) - difference between total revenue vp (p = price) and total cost.

Profit = Total Revenue - Total Cost

Profit = Revenue - Fixed Cost - Variable Cost

Where:

Revenue= [Sales price ($/unit) x Number (units)]

Variable Cost = [Variable cost ($/unit) x Number (units)]

Fixed Cost = $ necessary to invest in facilities (buildings, equipment, processes, etc.) = constant dollar value.

(4 of 4)

Z = vp - cf – vcv

Set profit equal to 0:

vp = cf + vcv

Compute the Break-Even Point:

Break-even quantity = cf/(p - cv)

Example II: Break-Even Analysis

(1 of 10)

Example: Western Clothing Company

cf = $10000

cv = $8 per pair

p = $23 per pair

V = 666.7 pairs, break-even point

Example II: Break-Even Analysis

(3 of 10)

Sensitivity Analysis : Break-Even Model with a Change (Increase) in Price

Example II:Break-Even Analysis (4 of 10)

Sensitivity Analysis : Break-Even Model with a Change (Increase) in Variable Cost

Example II: Break-Even Analysis

(5 of 10)

Sensitivity Analysis : Break-Even Model with Changes in Fixed and Variable Costs

Example II: Break-Even Analysis-Excel QM Computer Solution (7 of 10)

Exhibit 1.2

Example II: Break-Even Analysis-QM for Windows Computer Solution (9 of 10)

Example II: Break-Even Analysis-QM for Windows Computer Solution (10of 10)

Example III: Breakeven Analysis (1 of 5)

Problem:

Bill's company, Pritchett's Precious Time Pieces, buys, sells, and repairs old clocks and clock parts. Bill sells rebuilt springs for unit price $10. Fixed cost of equipment to build springs is $1,000. Variable cost per unit is $5 for spring material.

Example III: Breakeven Analysis (2 of 5)

Profit = $10X - $1,000 - $5X

Break-even quantity = cf/(p - cv)

BE = $1,000 / [$10 - $5 ] = 200 springs.

Example III: BEP (3 of 5 )

- Breakeven point (BEP) in dollars can be computed:

BEP$ = Fixed cost + Variable cost per unit x BEP

- For Bill Pritchett's example, compute BEP$:

$1,000 + $5 x 200 = $2,000

Example III: Using Goal Seek to Find the Breakeven Point (5 of 5)

- Use of Goal Seek to find the BEP.

Management Science Modeling Techniques (2 of 4)

1.Linear Mathematical Programming Techniques

a. Linear Programming Models

b. Transportation Models

c. Assignment Models

d. Integer Programming Models

e. Goal Programming

Management Science Modeling Techniques (3 of 4)

2. Probabilistic Techniques

a. Decision Analysis

b. Waiting Line (Queuing) Models

c. Simulation Models

d. Forecasting Models

3. Network Techniques

a. Network Flow

b. Project Management Techniques (PERT/CPM)

Management Science Modeling Techniques (4 of 4)

4. Other Techniques

a. Non-Linear Programming Models

b. Inventory Models

Characteristics of Modeling Techniques

- Linear Mathematical Programming -clear objective; restrictions on resources and requirements; parameters known with certainty.
- Probabilistic Techniques -results contain uncertainty.
- Network Techniques - model often formulated as diagram; deterministic or probabilistic.
- Forecasting and Inventory Analysis Techniques - probabilistic and deterministic methods in demand forecasting and inventory control.
- Other Techniques - variety of deterministic and probabilistic methods for specific types of problems.

Management Science Applications-(1 of 4)

- Some application areas:

- Project Planning

- Capital Budgeting

- Inventory Analysis

- Production Planning

- Scheduling

- Interfaces -Applications journal published by Institute for Operations Research and Management Sciences

Management Science Applications (2 of 4)

- Linear Programmingwas used by Burger Kingto find how to best blend cuts of meat to minimize costs.
- Integer Linear Programming model was used byAmerican Air Linesto determine an optimal flight schedule.
- The Shortest Route Algorithmwas implemented by the Sony Corporation to develop an onboard car navigation system aimed to give directions to car drivers.

Management Science Applications( 3 of 4)

- Project Scheduling Techniqueswere used by a contractor to rebuild Interstate 10 damaged in the 1994 earthquake in the Los Angeles area.
- Decision Analysis approach was the basis for the development of a comprehensive framework for planning environmental policy in Finland.

Management Science Applications( 4 of 4)

- Queuing models are incorporated into the overall design plans for Disneyland and Disney World, which lead to the development of ‘waiting line entertainment’ in order to improve customer satisfaction.

Defining the Problem.

Conflicting Viewpoints.

Impact on Other Departments.

Beginning Assumptions.

Solution Outdated.

Developing a Model.

Fitting Textbook Models.

Understanding the Model.

Possible Problems in Developing Decision Models- (1 of 2)Acquiring Input Data.

Using Accounting Data.

Validity of Data.

Developing a Solution.

Hard-to-Understand Mathematics.

Only One Answer is Limiting.

Testing Solution.

Analyzing Results.

Possible Problems in Developing Decision Models (2 of 2)Implementation – Not Just The Final Step

- Decision models assist decision maker by providing scientific method, model, and process which is defensible and reliable.
- Overcome sole reliance upon intuition, hunches, and experience.
- A Swedish study found -
- 40% of projects suggested by decision analysts were ever implemented.
- 70% of modeling projects initiated by users, and 98% of projects suggested by top managers, were implemented.

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