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52:620:321 Management Science – I. Instructor: Dr. Neha Mittal Email: nmittal@camden.rutgers.edu Website: www.crab.rutgers.edu/~nmittal. Management Science - I. Book Introduction to Management Science – Anderson, Sweeney and Williams, 12 th edition Exams and Assignments Grading

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52 620 321 management science i

52:620:321Management Science – I

Instructor: Dr. Neha Mittal

Email: nmittal@camden.rutgers.edu

Website: www.crab.rutgers.edu/~nmittal

management science i
Management Science - I
  • Book
  • Introduction to Management Science – Anderson, Sweeney and Williams, 12th edition
  • Exams and Assignments
  • Grading
      • Exam 1: 25%
      • Exam 2: 25%
      • Exam 3: 25%
      • In-class Assignment: 25%
  • Course Overview
what is management science
What is Management Science?

Is the body of knowledge involving quantitative approaches to decision making. It is also referred as

Operations research

Decision science

Frederic W. Taylor of the early 1900’s provided the foundation for use of quantitative methods. MS research originated during the World War II times and flourished later on with the aid of computers.

4

what is decision making
5 Steps of Decision Making; 7 steps of Problem Solving

Define the problem.

Identify the set of alternative solutions.

Determine the criteria for evaluating alternatives.

Evaluate the alternatives.

Choose an alternative (make a decision).

---------------------------------------------------------------------

Implement the chosen alternative.

Evaluate the results.

What is Decision Making

5

slide6

Quantitative Analysis and Decision Making

Decision-Making Process

Structuring the Problem

Analyzing the Problem

Define

the

Problem

Identify

the

Alternatives

Determine

the

Criteria

Evaluate

the

Alternatives

Choose

an

Alternative

the management science approach
The Management Science Approach

Structure the problem

Analyze the problem

Implement the solution

Evaluate the results

7

slide8

Single-criterion decision analysis

      • When the objective is to find the best solutions w.r.t one criterion, problems are referred as single-criterion.
  • Multi-criterion decision analysis
      • When the objective is to find the best solutions w.r.t multiple criterion, problems are referred as multi-criterion.
slide9

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
      • concentrates on the quantitative facts or data associated with the problem
      • develops mathematical expressions/ models that describe the objectives, constraints, and other relationships that exist in the problem
model development
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
mathematical models
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/Parameters – factors that are not under the control of the decision maker

Decision Variables – an unknown quantity representing a decision that needs to be made. It is the quantity the model needs to determine.

11

model solution
Model Solution

The analyst attempts to identify the alternative (the set of decision variable values) that provides the “best” output for the model.

The “best” output is the optimal solution.

If the alternative does not satisfy all of the model constraints, it is rejected as being infeasible, regardless of the objective function value.

If the alternative satisfies all of the model constraints, it is feasible and a candidate for the “best” solution.

12

slide13

Mathematical Models

  • Deterministic Model – if all parameters to the model are known and cannot vary
  • Stochastic (or Probabilistic) Model – if any parameter is uncertain and subject to variation
example iron works inc
Example: Iron Works, Inc.

Iron Works, Inc. manufactures two

products made from steel and just received

this month's allocation of b pounds of steel.

It takes a1 pounds of steel to make a unit of product 1

and a2 pounds of steel to make a unit of product 2.

Let x1 and x2 denote this month's production level of

product 1 and product 2, respectively. Denote by p1 and

p2 the unit profits for products 1 and 2, respectively.

Iron Works has a contract calling for at least m units of

product 1 this month. The firm's facilities are such that at

most u units of product 2 may be produced monthly.

Develop a mathematical model which maximizes profit.

14

slide15
Max p1x1 + p2x2

s.t. a1x1 + a2x2<b

x1>m

x2<u

x1 , x2> 0

Constraints

Objective

Function

“Subject to”

15

slide16

Max 100x1 + 200x2

s.t. 2x1 + 3x2< 2000

x1> 60

x2< 720

x2> 0

Suppose b = 2000, a1 = 2, a2 = 3, m = 60, u = 720, p1 = 100,

p2 = 200. Rewrite the model with these specific values for the uncontrollable inputs.

The optimal solution to the current model is x1 = 60 and x2 = 626 2/3.

problem

A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day.

Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily.

To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day.

If each scientific calculator sold results in a $2 profit, and each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits?

Problem
management accounting cost volume and profit models
Management Accounting: Cost, Volume and Profit Models
  • Cost and Volume Models:
    • Cost is function of the volume produced
    • Fixed, Variable and Marginal Cost
  • Revenue and Volume Models:
    • Revenue associated with selling of units
    • Marginal Revenue
  • Profit and Volume Models:
    • Profit = Revenue – Cost
    • When revenue = cost, it is called ‘breakeven point’
example ponderosa development corp
Example: Ponderosa Development Corp.

Ponderosa Development Corporation

(PDC) is a small real estate developer that builds

only one style house. The selling price of the house is

$115,000.

Land for each house costs $55,000 and lumber,

supplies, and other materials run another $28,000 per

house. Total labor costs are approximately $20,000 per house.

Ponderosa leases office space for $2,000 per month. The cost of supplies, utilities, and leased equipment runs another $3,000 per month.

The one salesperson of PDC is paid a commission of $2,000 on the sale of each house. PDC has seven permanent office employees whose monthly salaries are given on the next slide.

19

slide20
EmployeeMonthly Salary

President $10,000

VP, Development 6,000

VP, Marketing 4,500

Project Manager 5,500

Controller 4,000

Office Manager 3,000

Receptionist 2,000

20

slide21
Question:

Identify all costs and denote the marginal cost and marginal revenue for each house.

Answer:

Fixed costs

salaries, leases, utilities

Marginal / variable costs

commission, land, materials, labor

Revenue

selling price of each house

21

slide22
Question:

Write the monthly cost function c (x), revenue function r (x), and profit function p (x).

Answer:

c (x) = variable cost + fixed cost = 105,000x + 40,000

r (x) = 115,000x

p (x) = r (x) - c (x) = 10,000x - 40,000

slide23
Question:

What is the breakeven point for monthly sales

of the houses?

Answer:

r (x ) = c (x )

x = 4

Question:

What is the monthly profit if 12 houses per month are built and sold?

Answer:

p (x) = r (x) – c (x)

p (12) = $80,000

23

example ponderosa development corp24
Example: Ponderosa Development Corp.

1200

Total Revenue =

115,000x

1000

800

600

Thousands of Dollars

Total Cost =

40,000 + 105,000x

400

200

Break-Even Point = 4 Houses

0

0

1

2

3

4

5

6

7

8

9

10

Number of Houses Sold (x)

24

assignment breakeven analysis

As part of a loan application to buy Lakeside Farm, (a property Joe hopes to develop as a bed-and-breakfast operation), the prospective owners have projected:

Monthly fixed cost (loan payment, taxes, insurance, maintenance) $6000

Variable cost per occupied room per night $ 20

Revenue per occupied room per night $ 75

Write the expression for total cost per month. Assume 30 days per month.

Write the expression for total revenue per month.

If there are 12 guest rooms available, can they break even?

Assignment: Breakeven Analysis