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Production and Operations Management
• An area of management concerned with overseeing,
designing, and controlling the production of goods or
services
• It aims to ensure that operations and production are
performed efficiently and optimally, while meeting
customer requirements. E.g. in terms of:
• Cost
• Time
• Resources
• Capacity
• Profit
• etc.
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Production and Operations Management
• It is often viewed as the process of converting inputs
(availability of resources, materials, time, capacity, etc.)
into outputs (goods and/or services produces)
• Techniques from the areas of operations research and
management science are typically employed
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What is Operations Research?
• Operations Research (OR): A discipline that involves
using mathematical techniques in order to make decisions
• Some subdisciplines of OR:
• Optimization: choosing the best of possibly many options
• Simulation: trying out theories or approaches, and observing what
may happen
• Probability and statistics: measuring risk, computing expected
outcomes
• Utility theory: quantifying the subjective value of various options or
outcomes
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What is Management Science?
• Management Science:
• Often used interchangeably with OR
• More often viewed as the application of OR to business or
managerial decision making
• Some subdisciplines of Management Science:
• Manufacturing: deciding the optimal number of units of each type to
produce
• Scheduling: fleet for airlines, vehicles in supply chains, etc.
• Queueing theory: the field of study involving waiting lines
• Decision analysis: decision-making criteria, computation of best
options
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What is Management Science?
• The science of managerial decision-making. A systematic
approach to:
• modeling processes
• clarifying constraints and objectives
• defining the alternative strategies
• evaluating potential courses of action
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CrossChek Sporting Goods
• CrossChek Sporting Goods is a manufacturer of sporting
goods, including golf clubs, hockey equipment, bats, balls
and all things related to sports.
• A significant portion of CrossChek’s operations involve the
process of procurement of components and materials
from suppliers, through to the manufacturing of sporting
goods for distribution. CrossChek’s sporting products are
then sold direct to consumers, as well as to retail outlets.
• For the business to be profitable, a number of operations
need to be optimized:
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Manufacturing
• Consider two high-end hockey sticks, A and B. $150 and
$200 profit are earned from each sale of A and B,
respectively. Each product goes through 3 phases of
production.
• A requires 1 hour of work in phase 1, 48 min in phase 2, and 30
min in phase 3.
• B requires 40 min, 48 min and 1 hour, respectively.
• Limited manufacturing capacity:
• phase 1 1000 total hours
• phase 2 960
• phase 3 1000
• How many of each product should be produced?
• Maximize profit
• Satisfy constraints.
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New Product Lines
• Each year CrossChek decides which new baseball bats
and gloves it will market. Consider that each new bat is
expected to generate $150K for the year, while each new
glove generates $200K.
• Each new offering requires time for marketing (bats 20
hrs, gloves 30 hrs), which is limited to a total of 200 hrs.
• Each product also has storage space requirements (bats
300 sq ft, gloves 400 sq ft), which is limited to 3000 sq ft.
• How many new lines of bats and gloves should be
offered?
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Scheduling Product Production
Activity Description
Predecessor
Time (days)
A
Planning
--
5
B
Club Head Design
A
4
C
Club Head Manufacturing
B
8
D
Shaft Assembly
A
7
E
Grip Attachment
D
1
F
Club Head Assembly
C, D
4
G
Balancing
E, F
5
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Inventory Optimization
• CrossChek acts as a distributor for “Joe Buck Signature”
footballs. Demand for this particular type of football varies
from 30-60 units per day. Each unit sold yields $20 profit.
The holding and opportunity costs of each unit totals $1
per day. What is our optimal inventory level? If there is a
fixed cost of $200 associated with each order CrossChek
makes with its supplier, at what point should we place
orders? How much should we order?
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Processing Orders
• CrossChek gets requests-for-quotes at a rate of about 15
per hour. Each of these requests is individually assessed
by a sales clerk, who then answers with a quote. Each
clerk earns a wage of $17 per hour, and the average profit
earned by CrossChek is $28 per request. It takes a clerk
an average of 15 minutes to answer a request for a quote,
and it is found that the probability of a sale is 25% if a
quote is given within an hour, dropping by 5% after each
additional hour. What is the optimal number of clerks to
employ?
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Evolution
• Consider new products A, B and C. If CrossChek is
successful in persuading its retail partners to carry A, it
expects to make $500K profit. Otherwise, it stands to lose
about $100K. For B, make $400K or lose $50K, and for C
make $300K or break even.
• It expects A, B and C to be successful with probabilities,
of 30%, 40% and 50%, respectively.
• Also, if A is successful, it plans to roll out a “CrossChek
Special” version of the product, which will make an
additional profit of $50K with 70% probability.
• Which product should they produce?
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Multi-Criteria Decision Making
• Consider other factors, in the above scenario, such as the
extra (unpaid) time that several employees will need to
invest, as well as the possibility of low employee moral if
the new product fails. CrossChek may even need to
consider layoffs, which may damage public image. These
factors will need to be included in the analysis.
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Course Project
• Create a fictional business similar to that above, and
determine optimal processes and decisions for the
business using management science techniques learned
in class. Students will work in teams (of 4 or 5). Teams will
submit a report as well as give a presentation.
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Decision Making
• Central to management science
• Process:
• 1. Define the problem
• 2. Identify the alternatives
• 3. Determine the criteria
• 4. Evaluate the alternatives and select
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Models
• Representations of objects, situations, scenarios, etc.,
used to monitor the effects associated with various inputs
• A model car may be used to assess the effects of different
test crashes
• A mathematical model may be used to compute how
aerodynamics reduce wind resistance, and thus improve
overall gas mileage
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Models
• As a simple example, a mathematical model can be used
to compute CrossChek’s profits from sales of a particular
hockey stick:
CrossChek’s profit per hockey stick sold: $150
• We would like a mathematical model for CrossChek’s
profit from the sale of hockey sticks
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Models
• Mathematical models are constructed with the use of
variables
• Think of various profit outcomes
• What variables are being controlled?
• i.e. those whose values can be chosen/changed
• inputs
• What variables are being computed?
• outputs
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Models
• More simply a mathematical model can be used to
compute CrossChek’s profits from sales of a particular
hockey stick:
CrossChek’s profit per hockey stick sold: $150
• We would like a mathematical model for CrossChek’s
profit from the sale of hockey sticks
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Models
• More simply a mathematical model can be used to
compute CrossChek’s profits from sales of a particular
hockey stick:
CrossChek’s profit per hockey stick sold: $150
Let x represent the number of sticks sold
Let P represent the total profit
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Models
• More simply a mathematical model can be used to
compute CrossChek’s profits from sales of a particular
hockey stick:
CrossChek’s profit per hockey stick sold: $150
Let x represent the number of sticks sold
Let P represent the total profit
P = 150x
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Models
• Give the model for total profit if CrossChek also offers a
second type of stick that gives a profit of $200 per sale
• Define the necessary variables
• Represent the model in terms of the variables
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Models
• Give the model for total profit if CrossChek also offers a
second type of stick that gives a profit of $200 per sale
• Define the necessary variables
• Represent the model in terms of the variables
Let x represent the number of sticks of first type sold
Let y represent the number of second type sold
Let P represent the total profit
P = 150x + 200y
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Models – More Examples
• Give a model for the temperature in Montreal, given that it
is always 5 degrees colder than Toronto
• Give a model for Jim’s annual salary given that he makes
twice as much as Frank
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Models – More Examples
• We have a number of rules regarding the distribution of
marbles amongst a group of kids:
Jenny gets 2 more marbles than Fred
Fred gets one more marble than Sue
Sue gets twice as many marbles as Alex
• We would like a mathematical model to represent possible
distributions of marbles
• Include an expression for the total number of marbles
distributed
• What are the controllable inputs? What are the constraints?
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Models – More Examples
• CrossChek would like to examine the effect on profit of
various combinations of hockey stick production
Stick 1 provides $150 profit per unit
Stick 2 provides $200 profit per unit
Stick 1 takes 30 minutes to produce per unit
Stick 2 takes 40 minutes to produce per unit
Up to 10 hours of production time is available
• Give the mathematical model for profit given the
constraint
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Models – More Examples
• Given this model, CrossChek would like to maximize profit
• Three allocations are being considered:
11 units of stick 1, 6 units of stick 2
10 units of stick 1, 10 units of stick 2
6 units of stick 1, 9 units of stick 2
• Which allocations satisfy the constraints?
• If those that satisfy the constraints, which maximizes
profit?