Operations strategy
• Operations strategy is the collective tangible movements decided, ordered, or inspired
utilizing the corporate approach.
Source: Paksoy & Deveci (2023)
1
Operations Management vs. Operations Strategy
Source: Paksoy & Deveci (2023)
2
Core Operational Strategy Areas
• Core strategies can be categorized in the following ways:
1.
2.
3.
4.
5.
Company’s overall strategy: Direction of the company’s mission and interrelated
departments’ customer orientation.
Customer-driven: Operational strategies to meet the needs of a targeted customer segment.
Core competencies: Strategies to develop the company’s key strengths and resources.
Competitive priorities: Strategies that differentiate the company in the market to better
provide a desired product or service.
Product or service development: Product design, value, and innovation strategies.
Source: Paksoy & Deveci (2023)
3
Source: Paksoy & Deveci (2023)
4
A sustainable operations and supply chain strategy
• Shareholders are those individuals or companies that legally own one or more shares of
stock in the company.
• Stakeholders are those individuals or organizations that are influenced, either directly or
indirectly, by the actions of the firm.
Source: Jacobs & Chase (2018)
5
Triple bottom line
Source: Jacobs & Chase (2018)
6
A sustainable operations and supply chain strategy
• Social responsibility pertains to fair and beneficial business practices toward labor, the
community, and the region in which a firm conducts its business.
• Economic prosperity means the firm is obligated to compensate shareholders who provide
capital through stock purchases and other financial instruments via a competitive return
on investment.
• Environmental stewardship refers to the firm’s impact on the environment. The company
should protect the environment as much as possible—or at least cause no harm.
Source: Jacobs & Chase (2018)
7
What is operations and supply chain strategy?
• Operations and supply chain strategy is concerned with setting broad policies and plans for
using the resources of a firm and must be integrated with corporate strategy.
• Operations effectiveness relates to the core business processes needed to run the
business.
• Operational effectiveness is reflected directly in the costs associated with doing business.
Strategies associated with operational effectiveness, such as quality assurance and control
initiatives, process redesign, planning and control systems, and technology investments,
can show quick near-term (12 to 24 months) results.
• A firm’s operations and supply chain capabilities can be viewed as a portfolio best suited
to adapting to the changing product and/or service needs of the firm’s customers.
• A successful strategy will anticipate change and formulate new initiatives in response.
Source: Jacobs & Chase (2018)
8
Source: Jacobs & Chase (2018)
9
Competitive Dimensions
• Cost or Price: “Make the Product or Deliver the Service Cheap”: higher quality
• Quality: “Make a Great Product or Deliver a Great Service”
• Delivery Speed: “Make the Product or Deliver the Service Quickly”
• Coping with Changes in Demand: “Change Its Volume”: agility
• Flexibility and New-Product Introduction Speed: “Change It”
• Other Product-Specific Criteria: “Support It”
• Technical liaison and support
• Ability to meet a launch date
• Supplier after-sales support
• Environmental impact
• Other dimensions
Source: Jacobs & Chase (2018)
10
The Notion of Trade-Offs
• Central to the concept of operations and supply chain strategy is the notion of operations
focus and trade-offs.
• The underlying logic is that an operation cannot excel simultaneously on all competitive
dimensions. Consequently, management has to decide which parameters of performance
are critical to the firm’s success and then concentrate the resources of the firm on these
particular characteristics.
• Straddling occurs when a company seeks to match the benefits of a successful position
while maintaining its existing position. It adds new features, services, or technologies onto
the activities it already performs.
Source: Jacobs & Chase (2018)
11
Order Winners and Order Qualifiers: The Marketing - Operations Link
• An order winner is a criterion that differentiates the products or services of one firm from
those of another. Depending on the situation, the order-winning criterion may be the cost
of the product (price), product quality and reliability, or any of the other dimensions
developed earlier.
• An order qualifier is a screening criterion that permits a firm’s products to even be
considered as possible candidates for purchase.
Source: Jacobs & Chase (2018)
12
Strategies are implemented using operations and supply chain
activities—IKEA’S strategy
Source: Jacobs & Chase (2018)
13
Assessing the risk associated with operations and supply chain
strategies
• Covid-19 pandamic, adaptability and crisis management, cost efficiency
• Supply chain risk is defined as the likelihood of a disruption that would impact the ability
of the company to continuously supply products or services.
• Supply chain disruptions are unplanned and unanticipated events that disrupt the normal
flow of goods and materials within a supply chain and expose firms within the supply
chain to operational and financial risks.
• We can categorize risk by viewing the inherent uncertainties related to operations and
supply chain management along two dimensions:
(1) supply chain coordination risks that are associated with the day-to-day management of the
supply chain, which are normally dealt with using safety stock, safety lead time, overtime,
and so on; and
(2) disruption risks, which are caused by natural or human-made disasters, such as earthquakes,
hurricanes, terrorism, and even pandemics.
Source: Jacobs & Chase (2018)
14
Risk Management Framework
• Risk mapping involves assessment of the probability or relative frequency of an event
against the aggregate severity of the loss. Depending on the evaluation, some risks might
be deemed acceptable and the related costs considered a normal cost of doing business.
In some cases, the firm may find it is possible to insure against the loss. There may be
other cases where the potential loss is so great that the risk would need to be avoided
altogether.
1. Identify the sources of potential disruptions.
2. Assess the potential impact of the risk.
3. Develop plans to mitigate the risk.
Source: Jacobs & Chase (2018)
15
Source: Jacobs & Chase (2018)
16
Productivity measurement
• Since operations and supply chain management focuses on making the best use of the
resources available to a firm, productivity measurement is fundamental to understanding
operations-related performance.
𝑂𝑢𝑡𝑝𝑢𝑡𝑠
𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 =
𝐼𝑛𝑝𝑢𝑡𝑠
• Productivity is what we call a relative measure.
Source: Jacobs & Chase (2018)
17
Productivity measurement
• Productivity may be expressed as:
• partial measures,
• multifactor measures, or
• total measures.
Source: Jacobs & Chase (2018)
18
Productivity measurement
Source: Jacobs & Chase (2018)
19
Productivity measurement
Source: Jacobs & Chase (2018)
20
Question 1
A furniture manufacturing company has provided the following data (units are $1,000).
Compare the labor, raw materials and supplies, and total productivity for the past two years.
Last year This year
Output: Sales value of production
Input:
$22,000
$35,000
Labor
8,000
12,500
Raw materials and supplies
10,000
15,000
700
1,200
2,200
4,800
Capital equipment depreciation
Other
21
Question 2
As operations manager, you are concerned about being able to meet sales requirements in
the coming months. You have just been given the following production report:
Jan
Units produced
Feb
Mar
Apr
2,300 1,800 2,800 3,000
Hours per machine
325
200
400
320
Number of machines
3
5
4
4
Find the average of the monthly productivity figures (units per machine hour).
22
Question 3
Sailmaster makes high-performance sails for competitive windsurfers. Below is information
about the inputs and outputs for one model, the Windy 2000. Calculate the productivity in
sales revenue/labor expense.
Units sold
1,217
Sale price each
$1,700
Total labor hours
46,672
Wage rate
$12/hour
Total materials
$60,000
Total energy
$4,000
23
Question 4
Live Trap Corporation received the data below for its rodent cage production unit. Find the
total productivity.
Output
50,000 cages
Input
Production time
Sale price: $3.50 per unit Wages
Raw materials (total cost)
620 labor hours
$7.50/hour
$30,000
Component parts (total cost) $15,350
24
Question 5
Two types of cars (Deluxe and Limited) were produced by a car manufacturer last year.
Quantities sold, price per unit, and labor hours are given below. What is the labor
productivity for each car? Explain the problem(s) associated with the labor productivity.
Quantity
$/Unit
Deluxe car
4,000 units sold $8,000/car
Limited car
6,000 units sold $9,5000/car
Labor, Deluxe
20,000 hours
$12/hour
Labor, Limited 30,000 hours
$14/hour
25
Question 6
A U.S. manufacturing company operating a subsidiary in an LDC (less-developed country)
shows the following results:
U.S.
LDC
Sales (units)
100,000
20,000
Labor (hours)
20,000
15,000
Raw materials (currency)
$20,000 (US)
20,000 (LDC)
Capital equipment (hours)
60,000
5,000
a. Calculate partial labor and capital productivity figures for the parent and subsidiary. Do
the results seem confusing?
b. Compute the multifactor productivity figures for labor and capital together. Do the
results make more sense?
c. Calculate raw material productivity figures [units/$ where $1 = 10 (FC)]. Explain why
these figures might be greater in the subsidiary.
26
Question 7
Various financial data for the past two years follow. Calculate the total productivity measure
and the partial measures for labor, capital, and raw materials for this company for both
years. What do these measures tell you about this company?
Last year
Output: Sales
This year
$200,000 $220,000
Input: Labor
30,000
40,000
Raw materials
35,000
45,000
Energy
5,000
6,000
Capital
50,000
50,000
Other
2,000
3,000
27
Question 8
An electronics company makes communications devices for military contracts. The company
just completed two contracts. The navy contract was for 2,300 devices and took 25 workers
two weeks (40 hours per week) to complete. The army contract was for 5,500 devices that
were produced by 35 workers in three weeks. On which contract were the workers more
productive?
28
Question 9
A retail store had sales of $45,000 in April and $56,000 in May. The store employs eight fulltime workers who work a 40-hour week. In April, the store also had seven part-time workers
at 10 hours per week, and in May the store had nine part-timers at 15 hours per week
(assume four weeks in each month). Using sales dollars as the measure of output, what is
the percentage change in productivity from April to May?
29
Question 10
A parcel delivery company delivered 103,000 packages last year, when its average
employment was 84 drivers. This year, the firm handled 112,000 deliveries with 96 drivers.
What was the percentage change in productivity over the past year?
30
Question 11
A fast-food restaurant serves hamburgers, cheeseburgers, and chicken sandwiches. The
restaurant counts a cheeseburger as equivalent to 1.25 hamburgers and chicken sandwiches
as 0.8 hamburger. Current employment is five full-time employees who each work a 40-hour
week. If the restaurant sold 700 hamburgers, 900 cheeseburgers, and 500 chicken
sandwiches in one week, what is its productivity? What would its productivity have been if it
had sold the same number of sandwiches (2,100), but the mix was 700 of each type?
31
1. The Transportation Model
• The transportation model is formulated for a class of problems with the following unique
characteristics: (1) A product is transported from a number of sources to a number of
destinations at the minimum possible cost, and (2) each source is able to supply a fixed
number of units of the product, and each destination has a fixed demand for the product.
Source: Taylor III (2018)
32
Example
Wheat is harvested in the Midwest and stored in grain elevators in three different cities—
Kansas City, Omaha, and Des Moines. These grain elevators supply three flour mills, located
in Chicago, St. Louis, and Cincinnati. Grain is shipped to the mills in railroad cars, each car
capable of holding 1 ton of wheat. Each grain elevator is able to supply the following
number of tons (i.e., railroad cars) of wheat to the mills on a monthly basis:
Each mill demands the following
number of tons of wheat per month:
Source: Taylor III (2018)
33
Example
The cost of transporting 1 ton of wheat from each grain elevator (source) to each mill
(destination) differs, according to the distance and rail system. (For example, the cost of
shipping 1 ton of wheat from the grain elevator at Omaha to the mill at Chicago is $7.)
These costs are shown in the following table:
The problem is to determine how many tons of wheat to transport from each grain elevator
to each mill on a monthly basis to minimize the total cost of transportation.
Source: Taylor III (2018)
34
Example
Source: Taylor III (2018)
35
Example
Minimize Z = $6X1A + 8X1B + 10X1C + 7X2A + 11X2B + 11X2C + 4X3A + 5X3B + 12X3C
subject to
X1A + X1B + X1C = 150
X2A + X2B + X2C = 175
X3A + X3B + X3C = 275
X1A + X2A + X3A = 200
x1B + X2B + X3B = 100
X1C + X2C + X3C = 300
Xij ≥ 0
36
1. The Transportation Model
• In a balanced transportation model in which supply equals demand, all constraints are
equalities.
• In an unbalanced transportation model, supply is greater than demand or demand is
greater than supply.
Source: Taylor III (2018)
37
Solving balanced transportation problems
1. North West corner rule
2. Minimum cost method
3. Vogel's approximation method (Reinfeld & Vogel, 1958)
Source: Srinivasan (2017)
38
1.1. North West corner rule
1. In a balanced transportation problem, identify the north west corner or top left hand
corner where allocation can be made. Find the available supply and the required
demand. Allocate the maximum possible to this position, which is the minimum of the
two values.
2. If the supply in the row is exhausted, mark the row. If the column requirement is
entirely met, mark the column update supply/demand.
3. Repeat Steps 1 and 2 till all the supplies are used (all requirements are met).
Source: Srinivasan (2017)
39
1.2. Minimum Cost Method
1. From the available positions, find the one with the minimum cost coefficient. Break ties
arbitrarily.
2. Find the available supply and the required demand Allocate the maximum possible to
this position, which is the minimum of the two values.
3. If the supply in the row is exhausted, mark the row. If the column requirement is
entirely met, mark the column update supply/demand.
4. Repeat Steps 1 to 3 till all the supplies are used (all requirements are met).
Source: Srinivasan (2017)
40
1.3. Vogel's Approximation Method (Penalty Cost Method)
1. Calculate penalties for every row and column.
This is equal to the difference between the
second lowest cost and the least cost. Identify
the maximum penalty and the corresponding
row or column. Break ties arbitrarily.
2. Find the least cost position in the identified
row/column. Find the available supply and the
required demand. Allocate the maximum
possible to this position, which is the
minimum of the two values.
3. If the supply in the row is exhausted, mark the
row. If the column requirement is entirely
met,
mark
the
column
update
supply/demand.
4. Repeat Steps 1 to 3 till all the supplies are
used (all requirements are met).
Source: Srinivasan (2017)
41
Basic feasible solution to a Transportation problem
A basic feasible solution to a transportation problem satisfies the following conditions:
1. The row column (supply-demand) constraints are satisfied.
2. The non-negativity constraints are satisfied.
3. The allocations are independent and do not form a loop.
4. There are exactly m + n - 1 allocations.
Source: Srinivasan (2017)
42
Example
43
1.4. Finding the optimal solution to the transportation problem
1. Stepping stone method (Charnes & Cooper, 1954)
2. Modified distribution (MODI) method (also called u-v method)
Source: Srinivasan (2017)
44
Stepping stone method (Charnes & Cooper, 1954)
45
Stepping stone method (Charnes & Cooper, 1954)
46
Modified distribution (MODI) method (also called u-v method)
47
Getting started - which method?
All of them have the advantage that the solutions are basic feasible and do not contain a
loop. Among the three the Vogel's approximation method is often used as the method for
the starting solution because the quality of the feasible solution is superior (on the average)
compared to the other two methods. However, the Vogel's approximation method takes
more time as compared to the other two.
Source: Srinivasan (2017)
48
1.5. Solving unbalanced transportation problems
Added dummy row
Source: Srinivasan (2017)
49
1.5. Solving unbalanced transportation problems
Added dummy column
Source: Srinivasan (2017)
50
Important points
Unless stated otherwise, the transportation problem is a minimization problem. If the
objective is to maximize, it is customary to change the sign of the objective function
coefficients (make them negative) and solve the resultant problem as a minimization
problem (as we did in simplex algorithm). Otherwise we have to modify the rules of North
west corner, Minimum cost, VAM and MODI method, which is not desirable.
Source: Srinivasan (2017)
51
Example 1
A department store wishes to purchase the following quantities of ladies dresses per month:
Dress type
A
B
C
D
Quantity
100
300
200
100
Tenders are submitted by 3 different manufacturers who undertake to supply not more than the
quantities below (all types of dress combined).
Manufacturer
W
X
Y
Quantity
500
600
400
The store estimates that its profit per dress will vary with the manufacturer as shown in table below.
How should orders be placed?
A
B
C
D
W
2
3
4
2
X
1
3
3
2
Y
3
4
5
4
52
Example 2
A manufacturer must produce a certain product in sufficient quantity to meet contracted
sales in the next three months. The product may be produced in one month and then held
for sale in a later month, but at a storage cost of $1 per unit per month. No storage cost is
incurred for goods sold in the same month in which they are produced. There is presently
no inventory of this product and none is desired at the end of the four months. The
production can be in regular time or using overtime. Regular time cost to produce a unit is
$10 while overtime cost is $15. You cannot meet the demand of a month by producing in a
subsequent month. Regular time capacity is 300 units/month and overtime capacity is 100
units/month. The demand for the three months are 200, 400 and 300 units, respectively.
Formulate a transportation problem for the above situation to minimize the total cost.
53
Question 1
A chemical company has plants at three locations (A to C). The company has been
prohibited from disposing of its effluents in these places. Instead the company has to
transport the effluents in tankers to their disposal sites at four different places, where they
are eventually destroyed. The effluents generated from the three plants are 9000, 8000 and
7000 litres per day, respectively. Sometimes the Plant A generates more than 9000 but
never exceeds 12,000 and whatever be the quantity, has to be destroyed. The sites have
destruction capacities of 7000, 7500, 8000 and 4000, respectively. The last site, can handle
an additional 1500 if required. The costs of transportation per 1000 litres of effluent are
given in table below. Formulate a transportation problem in standard form to minimize total
cost.
Site 1
Site 2
Site 3
Site 4
A
130
110
80
75
B
110
100
95
105
C
90
120
105
115
54
Question 2
A private taxi company in the Vietnam has recently procured 300 taxicabs to meet the rising demands in three
districts - Binh Tan, Tan Binh, and Go Vap. Of these taxicabs, 100 are 4-seaters, 100 are 7-seaters, and 100 are
14-seater minivans.
District
Taxicabs needed
Binh Tan
120
Tan Binh
150
Go Vap
170
The company has identified the maximum number of taxicabs needed in each city as follows:
Taxi type
Binh Tan
Tan Binh
Go Vap
Taxicabs available
4-seaters
1600
1800
1900
100
7-seaters
2000
1400
1800
100
14-seaters
3200
2800
3600
100
Taxicabs needed
120
150
170
Besides, each city needs at least 20 4-seater taxicabs. Determine how many taxicabs of each type need to be
55
operational in each city to maximize profit.
2. The Transshipment Model
• The transshipment model is an extension of the transportation model in which
intermediate transshipment points are added between the sources and destinations.
56
2. The Transshipment Model
Minimize Z = $16X13 + 10X14 + 12X15 + 15X23 + 14X24 + 17X25 + 6X36 + 8X37 + 10X38 + 7X46 +
11X47 + 11X48 + 4X56 + 5X57 + 12X58
subject to
X13 + X14 + X15 = 300
X23 + X24 + X25 = 300
X36 + X46 + X56 = 200
X37 + X47 + X57 = 100
X38 + X48 + X58 = 300
X13 + X23 - X36 - X37 - X38 = 0
X14 + X24 - X46 - X47 - X48 = 0
X15 + X25 - X56 - X57 - X58 = 0
Xij ≥ 0
57
Question 1
World Foods, Inc., imports food products such as
meats, cheese, and pastries to the United States from
warehouses at ports in Hamburg, Marseilles, and
Liverpool. Ships from these ports deliver the products
to Norfolk, New York, and Savannah, where they are
stored in company warehouses before being shipped to
distribution centers in Dallas, St. Louis, and Chicago.
The products are then distributed to specialty food
stores and sold through catalogs. The shipping costs
($/1,000 lb.) from the European ports to the U.S. cities
and the available supplies (1,000 lb.) at the European
ports are provided in the following table:
The transportation costs ($/1,000 lb.) from each U.S.
city of the three distribution centers and the demands
(1,000 lb.) at the distribution centers are as follows:
Determine the optimal shipments between the
European ports and the warehouses and the
distribution centers to minimize total transportation
costs.
58
Question 2
A computer manufacturer plans to enter new markets in three African countries—Senegal, Ghana, and Ethiopia. The
company has two manufacturing facilities in China and Vietnam that can be used to supply to the new markets.
Because of logistics issues and travel routes, computers will be shipped to two distribution centers in Egypt and the
UAE and then shipped to the three countries. The transportation cost per computer in dollars from the manufacturing
facilities to the distribution centers and from the distribution centers to the different countries, the supply of the
manufacturing facilities, and the demand of the different markets are summarized in the following tables:
Determine the optimal shipment patterns from the manufacturing facilities to the distribution centers, and from the
distribution centers to the three different countries that will minimize the transportation cost.
59
3. The Assignment Model
• The assignment problem is one of assigning resources (i = 1,...,n) to tasks (j = 1,...,n) to
minimize the total cost of performing the tasks. The cost associated is Cij when resource i
is assigned task j. Each task goes to exactly one resource and each resource gets only one
task. Typical examples of assignment problems are the assignment of jobs to machines or
assignment of people to tasks.
• The assignment problem problem when the 0-1 restriction on the variables is relaxed. is a
zero-one problem where variable Xij takes value '1' when resource i is assigned task j and
takes value '0' otherwise.
• The assignment problem becomes a linear programming
Source: Srinivasan (2017)
60
Properties of the optimal solution
• If the cost coefficients Cij ≥ 0, a feasible solution with Z = 0 is optimal.
• If all the elements of a row or a column is increased or decreased by the same constant,
the optimal solution to the assignment problem does not change. Only the value of the
objective function changes.
61
Example 1
A plant has four operators to be assigned to four machines. The time (minutes) required by
each worker to produce a product on each machine is shown in the following table:
Determine the optimal assignment and compute total minimum time.
62
Example 2
A shop has four machinists to be assigned to four machines. The hourly cost of having each machine
operated by each machinist is as follows:
However, because he does not have enough experience, machinist 3 cannot operate machine B.
a. Determine the optimal assignment, and compute total minimum cost.
b. Formulate this problem as a general linear programming model.
63
Solving the assignment problem - Hungarian algorithm - Procedure 1
• Row and column minimum subtraction
12
11
8
14
10
9
10
8
14
8
7
11
6
8
10
9
5
2
0
5
4
1
3
0
8
0
0
3
0
0
3
1
64
Solving the assignment problem - Hungarian algorithm - Procedure 1
• If a row or column has exactly one assignable zero, make the assignment. The other zeros
in the corresponding column (or row) is not assignable.
• If a row or column has more than one assignable zero, do not make any assignment. Move
to the next row or column and go to Step 1. Terminate when no assignment is possible.
5
2
0
5
4
1
3
0
8
0
0
3
0
0
3
1
65
Solving the assignment problem - Hungarian algorithm - Procedure 1
11
6
9
18
11
13
20
6
12
14
5
4
6
6
7
18
9
12
17
15
12
7
15
20
11
4
0
3
10
2
6
14
0
4
5
0
0
2
0
0
8
0
3
6
3
4
0
8
11
1
66
Solving the assignment problem - Hungarian algorithm - Procedure 2
1. Tick all unassigned rows.
2. If a row is ticked and has a zero then tick the
corresponding column (if the column is not
yet ticked).
3. If a column is ticked and has an assignment
then tick the corresponding row (if the row
is not yet ticked).
4
0
3
10
2
6
14
0
4
5
0
0
2
0
0
8
0
3
6
3
4
0
8
11
1
4. Repeat Steps 2 and 3 till no more ticking is
possible.
5. Draw lines through unticked rows and ticked
columns The number of lines represent the
maximum number of assignments possible.
67
Solving the assignment problem - Hungarian algorithm - Procedure 3
1. Identify the minimum number (say ) that have no lines passing through them.
2. Update the Cij matrix using the following changes:
• Cij = Cij -  if the number has no lines passing through it
• Cij = Cij if the number has one line passing through it (No change)
• Cij = Cij +  if the number has two lines passing through it
4
0
3
10
2
3
0
2
9
1
6
14
0
4
5
6
15
0
4
5
0
0
2
0
0
0
1
2
0
0
8
0
3
6
3
7
0
2
5
2
4
0
8
11
1
3
0
7
10
0
68
Solving the assignment problem - Hungarian algorithm - Procedure 3
• Applying procedure 3:
3
0
2
9
1
2
0
1
8
0
6
15
0
4
5
6
16
0
4
5
0
1
2
0
0
0
2
2
0
0
7
0
2
5
2
6
0
1
4
1
3
0
7
10
0
3
1
7
10
0
69
Solving the assignment problem - Hungarian algorithm - Procedure 3
• Applying procedure 2
2
0
1
8
0
1
0
1
7
0
6
16
0
4
5
6
17
0
4
5
0
2
2
0
0
0
3
2
0
0
6
0
1
4
1
5
0
0
3
0
3
1
7
10
0
2
1
6
9
0
70
Solving the assignment problem - Hungarian algorithm - Procedure 3
• Applying procedure 2
1
0
1
7
0
0
0
0
6
0
6
17
0
4
5
5
17
0
3
5
0
3
2
0
0
0
3
2
0
0
5
0
0
3
0
4
0
0
2
0
2
1
6
9
0
1
1
6
8
0
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Example 3
Vinamilk makes three types of milk products. They own three plants, one of which is to be
selected for each product. Tables below give the estimated processing costs and distribution
costs per unit of each product processed at each plant. Formulate this problem as an
assignment problem to maximize total profit. Find the optimal solution and the profit
associated with it.
Unit processing cost
($/litre)
I
II
III
Unit distribution cost
($/litre)
I
II
III
Standard milk
5.5
5
6
Standard milk
1
2
1
Flavoured milk
6
7
6.5
Flavoured milk
0.5
1
1.3
Yogurt
6.5
6
7
Yogurt
0.6
0.5
0.8
Daily Production and Selling Price of Products
Planned production (litres) Planned price ($/litre)
Standard milk
8000
13
Flavoured milk
5000
18
Yogurt
2000
20
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Question 1
An electronics firm produces electronic components, which it supplies to various electrical
manufacturers. Quality control records indicate that different employees produce different
numbers of defective items. The average number of defects produced by each employee for
each of six components is given in the following table:
Determine the optimal assignment that will minimize the total average number of defects
produced by the firm per month.
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Question 2
A company wants to assign ten salesmen to
eight different sales zones. The expected
profit from each salesman differs from one
zone to another based on their experience
with the different customers in the respective
zone. The company needs at least one
salesman to be assigned to each zone. The
following table shows the expected revenue
per month in $1,000 of each salesman in the
different zones.
a. Determine the optimal assignment.
b. What is the effect on the expected
revenue?
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