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JQP2023 Management Science 1
Chapter 1: Introduction to Management Science
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Management science uses a scientific approach tosolving
management problems.
It is used in a variety of organizations to solve manydifferent
types of problems.
It encompasses a logical mathematical approach toproblem
solving.
Management Science, also known as OperationsResearch, Decision
Sciences, etc., involves a philosophyof problem solving in a
logical manner.
The Management ScienceApproach
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The Management ScienceProcess
Figure 1.1The Management Science Process
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Observation - Identification of a problem that exists (ormay
occur soon) in a system or organization.
Definition of the Problem - problem must be clearlyand
consistently defined, showing its boundaries andinteractions with
the objectives of the organization.
Model Construction - Development of the functionalmathematical
relationships that describe the decisionvariables, objective
function and constraints of theproblem.
Model Solution - Models solved using managementscience
techniques.
Model Implementation - Actual use of the model or
itssolution.
Steps in the ManagementScience Process
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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 themost profit,
given the limited amount of steel available.
Example of ModelConstruction (1 of 3)
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Variables: X = number of units to produce (decisionvariable)
Z = total profit (in $)
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 - $5Xsubject to
4X = 100
Example of ModelConstruction (2 of 3)
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JQP2023 Management Science 7
Consider the constraint equation:
4x = 100or x = 25 units
Substitute this value into the profit function:
Z = $20x - $5x= (20)(25) (5)(25)= $375
(Produce 25 units, to yield a profit of $375)
Model Solution
Example of ModelConstruction (3 of 3)
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Used to determine the number of units of aproduct to sell or
produce (i.e. volume) that willequate total revenue with total
cost.
The volume at which total revenue equals totalcost is called the
break-even point.
Profit at break-even point is zero.
Model Building:Break-Even Analysis (1 of 8)
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Model Components Fixed Costs (cf) - costs that remain constant
regardless
of number of units produced. Variable Cost (cv) - unit
production cost of product.
Total variable cost (vcv) - function of volume (v) andunit
variable cost. Total Cost (TC) - total fixed cost plus total
variable cost. Profit (Z) - difference between total revenue vp (p
= unit
price) and total cost, i.e.Z = vp - cf - vcv
Model Building:Break-Even Analysis (2 of 8)
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JQP2023 Management Science 10
Computing the Break-Even Point
The break-even point is that volume atwhich total revenue equals
total cost andprofit is zero:
vp - cf vcv = 0
or v = cf/(p - cv)
(Break-Even Point)
Model Building:Break-Even Analysis (3 of 8)
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Example: Western Clothing Company
Fixed Costs: cf = $10000Variable Costs: cv = $8 per pairPrice :
p = $23 per pair
The Break-Even Point is:
v = (10,000)/(23 -8)= 666.7 pairs
Model Building:Break-Even Analysis (4 of 8)
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Model Building: Break-EvenAnalysis (5 of 8)
Figure 1.2 Break-Even Model
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JQP2023 Management Science 13
Figure 1.3Sensitivity Analysis - Break-even Model with a Change
in Price
Model Building: Break-EvenAnalysis (6 of 8)
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Figure 1.4Sensitivity Analysis - Break-Even Model with a Change
in Variable Cost
Model Building: Break-EvenAnalysis (7 of 8)
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Model Building: Break-EvenAnalysis (8 of 8)
Figure 1.5Sensitivity Analysis - Break-Even Model with a Change
in Fixed Cost
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JQP2023 Management Science 19
Break-Even Analysis: QMSolution (5 of 5)
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Classification of ManagementScience Techniques
