1.Industrial Purchasing Process................................................................................................
1
2.FMEA:........................................................................................................................................ 3
3. Crashing Cost:......................................................................................................................... 5
4. Life Cycle Cost:......................................................................................................................10
5 CPI_SPI.................................................................................................................................... 11
6.7 periods..................................................................................................................................15
7. Cost Estimate.........................................................................................................................19
1.Industrial Purchasing Process
Question 1:Industrial purchasing process, giải thích từng dòng. (soạn dư example,
có hỏi thì ghi)
1. Forecast and Plan Requirements
Explanation:
This step involves anticipating future needs for raw materials, components, or services
based on production schedules, maintenance plans, or upcoming projects.
Example:
A car manufacturing company forecasts that it will need 10,000 sets of brake systems in
Q3 to support the assembly of a new vehicle model.
2. Needs Clarification (Technical Profile, Quantity, Date Required, Estimated Cost,
etc.)
Explanation:
Define the exact specifications of what is needed, including technical details, required
quantity, delivery date, and budget. This ensures that procurement matches operational
requirements.
Example:
The engineering team specifies that they need 200 stainless steel pipes, 5 meters in
length, to be delivered within 3 weeks, with an estimated budget of $5,000.
3. Supplier Selection (Financial Health, Expertise, Operational Performance,
Business Practices, Cultural & Risk Factors)
Explanation:
Evaluate and choose suppliers based on their financial stability, technical capabilities,
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past performance, ethical business practices, cultural alignment, and associated risks
(e.g., geopolitical, delivery delays, etc.).
Example:
A company shortlists three suppliers of industrial lubricants and selects one with ISO
certification, strong financials, and a local warehouse for faster delivery.
4. Place the Purchase Order (PO or Blanket Purchase Order)
Explanation:
Issue a formal document (Purchase Order) to the selected supplier detailing the items,
quantity, delivery terms, and payment conditions. A Blanket PO is used for recurring
purchases over a period.
Example:
The procurement team issues a PO for 1,000 units of bearings at $8/unit with delivery
scheduled in two lots over two months.
5. Receipt and Inspection
Explanation:
Receive the goods/services and inspect them for quality, quantity, and compliance with
the specifications. This is critical to avoid production delays or safety issues.
Example:
Upon delivery of hydraulic pumps, the quality team checks each unit for defects,
ensuring they meet pressure capacity requirements before signing the receipt.
6. Invoice Settlement and Payment
Explanation:
Match the supplier’s invoice with the PO and goods received (3-way match), then process
the payment as per agreed terms.
Example:
The supplier sends an invoice of $10,000. After confirming the goods were received and
the amounts match, the finance department processes payment within 30 days.
7. Records Maintenance
Explanation:
Keep detailed records of procurement activities, contracts, communications, and payment
history for audits, future reference, or dispute resolution.
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Example:
All related documents for a supplier contract—including RFQs, POs, inspection reports,
and invoices—are stored in the company’s ERP system.
8. Continuously Measure and Manage Supplier Performance
Explanation:
Monitor supplier performance over time based on quality, delivery reliability,
responsiveness, and cost. Use this data to manage relationships or make changes.
Example:
The company tracks on-time delivery rates and product defect rates of suppliers quarterly,
and may replace underperforming suppliers or work with them to improve.
2.FMEA:
Definition, Explain the RPN function, Example of our Project FMEA? (nên in thêm
slide nếu có hỏi ý ngoài rìa)
Definition:
Failure Modes and Effects Analysis (FMEA) is a systematic, proactive method used to:
● Identifying the ways in which a product or process can fail
● Estimating risk associated with specific causes
● Prioritizing the actions that should be taken to reduce risk
● Evaluating design validation plan (design FMEA) or current control plan (process
FMEA)
Risk Priority Number (RPN) = Severity × Occurrence × Detection
For a given potential failure mode, how bad the outcome is multiplied by how likely it
would actually happen multiplied by what things are in place today to prevent or notice it
before it happens.
● Severity (S): How serious the impact would be if the failure occurs
● Occurrence (O): How likely the failure is to happen
● Detection (D): How likely it is that the failure will be detected before reaching the
customer
➡️ A higher RPN means higher risk, and that issue should be prioritized for
corrective action.
Project Group FMEA:
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Process step Potential Possible Effects SEV OCC DEC Risk Mitigation
failure mode causes priority strategies
number
(RPN)
Food Contaminated Poor supplier Food 9 4 6 216 Source
preparation or spoiled quality, poisoning, reputable
ingredients improper health suppliers,
storage violations enforce
strict
storage
checks
Customer Long waiting Understaffing Customer 7 6 5 210 Optimize
service times , inefficient dissatisfaction staff
workflow , lost sales scheduling,
train for
efficiency
Payment POS system Technical Transaction 6 5 4 120 Implement
system failure issues, power delays, lost backup
outages sales payment
methods
(cash,
mobile
payments)
4
Inventory Stockouts or Poor demand Wastage or 5 7 5 175 Use
management overstocking forecasting inability to inventory
serve popular tracking
items software,
analyze
sales trends
Regulatory Failure to Lack of Fines, business 8 3 7 168 Consult
compliance obtain permits awareness of shutdown legal
local laws experts,
apply for
licenses
early
3. Crashing Cost:
Giảm project duration xuống tới ngưỡng target, tìm activity nào giảm mà tốn ít tiền
nhất.
Step 1: Compute the crash cost per time period. If crash costs are linear over time.
𝐶𝑟𝑎𝑠ℎ 𝑐𝑜𝑠𝑡 − 𝑁𝑜𝑟𝑚𝑎𝑙 𝑐𝑜𝑠𝑡
𝐶𝑟𝑎𝑠ℎ 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 = 𝑁𝑜𝑟𝑚𝑎𝑙 𝑡𝑖𝑚𝑒 −𝐶𝑟𝑎𝑠ℎ 𝑡𝑖𝑚𝑒
Step 2 : Using current activities times (Normal time) to find the critical path and
identify the critical activities. => Làm lại bảng gồm ES, EF, LS, LF, Slack để tìm
critical path
Critical Path: A-C-E-G-H (longest)
Total completion time = 15 weeks
Step 3 : Select the activity to crash:
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● If there is only one critical path: Select the activity on this critical path that:
○ Can still be crashed
○ Has the smallest crash cost per period
● If there is more than one critical path: Select one activity from each critical path
such that
○ Each selected activity can still be crashed
○ The total crash cost of all selected activities is the smallest
Note - the same activity may be common to more than one critical path
Example:
Hướng dẫn thì ghi tiếng việt, còn tiếng anh là câu kết luận nên phải ghi vô
Activity Immediate Normal time Crash Normal Crash Crash
predecessor (weeks) time cost ($) cost ($) cost per
(weeks) week
A - 4 3 2000 2600 600
B - 2 1 2200 2800 600
C A 3 3 500 500 0
D B 8 4 2300 2600 75
E B 6 3 900 1200 100
F C, D 3 2 3000 4200 1200
G E, F 4 2 1400 2000 300
Tự tính Crash cost per week bằng công thức ở step 1
Solution: Create table to find critical path
Activity ES EF LS LF SLACK
A 0 4 3 7 3
B 0 2 0 2 0
C 4 7 7 10 3
D 2 10 2 10 0
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E 2 8 7 13 5
F 10 13 10 13 0
G 13 17 13 17 0
Critical path: B – D – F – G.
Total completion time of the project = 2 + 8 + 3 + 4 = 17 weeks.
(Yêu cầu đề) Crashing the project within 10 weeks
Nhìn vào critical path, tìm activity nào có cost thấp nhất thì lấy ra để giảm, giảm hết
mức có thể để đạt được target.
In the critical path, activity D has the smallest Crash cost per week
==> we will decrease the length of activity D from 8 weeks to 4 weeks.
Cập nhật Table Activity. Lúc này normal time của D đã giảm đi 4.Tính lại critical
path đã thỏa mãn TARGET chưa.
Activity ES EF LS LF SLACK
A 0 4 0 4 0
B 0 2 1 3 1
C 4 7 4 7 0
D 2 6 3 7 1
E 2 8 4 10 2
F 7 10 7 10 0
G 10 14 10 14 0
Lúc này critical path đã bị thay đổi sang thành A – C – F – G
Total completion time of the project = 4 + 3 + 3 + 4 = 14 weeks (chưa)
In the critical path, activity G has the smallest crash cost per week.
Therefore, we will decrease the length of activity G from 4 weeks to 2 weeks.
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Cập nhật table Activity. Lúc này normal time của G đã giảm đi 2. Tính lại critical
path đã thỏa mãn TARGET chưa.
Activity ES EF LS LF SLACK
A 0 4 0 4 0
B 0 2 1 3 1
C 4 7 4 7 0
D 2 6 3 7 1
E 2 8 4 10 2
F 7 10 7 10 0
G 10 12 10 12 0
Critical path: A - C - F - G
Total completion time of the project = 4 + 3 + 3 + 2 = 12 weeks (chưa)
In the critical path, activity A has the smallest crash cost per week.
Therefore, we will decrease the length of activity A from 4 weeks to 2 weeks.
Cập nhật lại Table Activity khi normal time của A đã giảm đi 2. Tính lại critical
path đã thỏa mãn TARGET chưa.
Activity ES EF LS LF SLACK
A 0 3 0 3 0
B 0 2 0 2 0
C 3 6 3 6 0
D 2 6 2 6 0
E 2 8 3 9 1
8
F 6 9 6 9 0
G 9 11 9 11 0
Critical path: A - C - F - G or B - D - F - G
Total completion time of the project = 11 weeks
Lúc này chúng ta vô 2 trường hợp có 2 critical path( đọc lại step 3):
In the critical path, activity F has the smallest crash cost per week (in common).
Therefore, we will decrease the length of activity F from 3 weeks to 2 weeks. ( chỉ còn 1
week nữa là đủ thì giảm 1 thôi).
Cập nhật lại Table Activity khi normal time của F đã giảm đi 1. Tính lại critical
path đã thỏa mãn TARGET chưa.
Activity ES EF LS LF SLACK
A 0 3 0 3 0
B 0 2 0 2 0
C 3 6 3 6 0
D 2 6 2 6 0
E 2 8 2 8 0
F 6 8 6 8 0
G 8 10 8 10 0
Critical path: A - C - F - G or B - D - F - G
Total completion time of the project = 10 weeks (thỏa mãn)
In total, We decreased the length of 5 activities: A, D, F, and G
Decreased activity Number of Week Crash cost per week Additional cost
D 4 75 300
G 2 300 600
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A 2 600 1200
F 1 1200 1200
Sum 3300
Conclusion :Therefore, the extra cost will be $3,300 in total.
4. Life Cycle Cost:
Bài này tính cost nên cộng tất cả cost, riêng salvage value là trừ và không cộng giá mua
(Purchase price) nếu đề cho
Consider the total cost of ownership, or development plus support costs, for a project.
Target Cost (TC)
LCC = I + F + E + OMR + D + R
Where:
LCC = Life-cycle costs
I = Initial costs
F = Financing costs
E = Energy costs
OMR = Operating, maintenance, and repair costs
D = Disposal cost or value
R = Replacement costs
Đề sẽ cho kiểu % chứ không cho thẳng số để tính, cho dạng có 2 option rồi tính ra
để lựa
Tiêu chí Disposal Cost 🗑️ Salvage Value 💰
Là gì? Chi phí để xử lý, tháo dỡ, tiêu hủy tài Giá trị thu hồi được nếu bán lại tài sản
sản cũ
Bản chất Là chi phí phát sinh thêm Là khoản tiền thu lại (income)
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𝐿𝐶𝐶 = 𝐼 + 𝑟𝑒 + 𝐷 + 𝐸 + 𝑊 + 𝑀 + 𝑂 − 𝑅𝑠
Building A:
LCCA=
49,409,990.87+20,500,000+5,000,000+2,450,000+60,000+2,200,000+100,000−20,000,0
00 = 79,719,990.87−20,000,000= $59,720,010.87
Building B:
LCCB=63,527,131.12+20,500,000+0+400,000+32,000+750,000+100,000−40,000,000
=85,309,131.12−40,000,000= $ 45,309,151.12
Question 4:
Calculating Total Lifecycle Costs for Manufacturing Project based on the following
information
Project Details:
● Initial Costs: $3,500,000
● Financing Costs: $100,000
● Fuel Costs: $0.10 per production unit, with an estimated annual production of
1,000,000 units for the first 5 years and 1,200,000 units for the next 5 years.
● Operating, Maintenance, and Repair Costs: $40,000 per year for the first 8 years,
$55,000 per year for the next 2 years.
● Disposal Cost: $150,000 after 10 years
● Replacement Costs: $500,000 after 10 years.
Solution:
Áp dụng công thức LCC = I + F + E + OMR + D + R, ta có:
I = $3,500,000
F = $100,000
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E = 11,000,000 × $0.10 = $1,100,000 (với 5 năm đầu sản xuất 1,000,000 đơn vị/năm và
5 năm sau là 1,200,000 đơn vị/năm)
OMR = (8 × $40,000) + (2 × $55,000) = $320,000 + $110,000 = $430,000
D = $150,000
R = $500,000
Vậy tổng chi phí vòng đời:
LCC = $3,500,000 + $100,000 + $1,100,000 + $430,000 + $150,000 + $500,000 =
$5,780,000.
5 CPI_SPI
Nếu EV = PV → đúng tiến độ
Nếu EV < PV → trễ tiến độ
Nếu EV > PV → vượt tiến độ
Definition real trong slide Project cost management (Slide 70)
Acronym Term Interpretation
PV Planned value Giá trị mà lên kế hoạch từ trước
EV Earned value Giá trị công việc thực sự đạt được( quy tiền ra theo kế
hoạch)
AC Actual cost (total Số tiền, chi phí thực tế đã tiêu
cost)
BAC Budget at
completion Tổng ngân sách ban đầu bạn dự tính cho toàn bộ dự án.
EAC Estimate at Là dự báo tổng chi phí thực tế bạn nghĩ sẽ cần để hoàn
completion thành toàn bộ dự án, dựa trên tình hình hiện tại.
ETC Estimate to Số tiền bạn nghĩ sẽ còn cần để hoàn tất phần việc còn lại
complete của dự án.
VAC Variance at Là mức bạn sẽ tiết kiệm hoặc vượt chi khi dự án kết thúc,
completion so với ngân sách ban đầu.
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Name Formula Interpretation
Cost variance EV – AC Negative is over budget; positive is under budget.
(CV)
Schedule EV – PV Negative is behind schedule; positive is ahead of schedule.
variance (SV)
Cost 𝐸𝑉 We are getting $___ worth of work out of every $1 spent.
performance 𝐴𝐶 Funds are or are not being used efficiently. Greater than
index (CPI) one is good; less than one is bad.
Schedule 𝐸𝑉 We are (only) progressing at ___ percent of the rate
performance 𝑃𝑉 originally planned. Greater than one is good; less than one
index (SPI) is bad.
Estimate at AC + As of now, how much do we expect the total project to
completion Bottom-up cost? $___ This formula calculates actual costs to date
(EAC) ETC plus a revised estimate for all the remaining work. It is
used when the original estimate was fundamentally
flawed.
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Percent Complex Indexes: Indicated how much of the work accomplished represents of
the total budgeted (BAC) and actual (AC) dollars to date
● Cost Performance Index CPI = EV / AC
● Schedule Performance Index SPI = EV / PV
● Earned value EV = PV to date * RP
● Estimate time to complete ETC = Original time estimate / SPI
Interpretation of Indexes
Index Cost (CPI) Schedule (SPI)
>1 Under budget Ahead of schedule
=1 On budget On schedule
<1 Over budget Behind schedule
Earned value management (EVM) :A project performance measurement technique that
integrates scope, time and cost data
Rate of performance (RP): Ratio of actual work completed to the percentage of work
planned to have been completed at any given time during the life of the project or activity
𝐾ℎố𝑖 𝑙ượ𝑛𝑔 𝑐ô𝑛𝑔 𝑣𝑖ệ𝑐 đã ℎ𝑜à𝑛 𝑡ℎà𝑛ℎ
𝑅𝑃 = 𝐾ℎố𝑖 𝑙ượ𝑛𝑔 𝑐ô𝑛𝑔 𝑣𝑖ệ𝑐 𝑑ự 𝑘𝑖ế𝑛 𝑝ℎả𝑖 ℎ𝑜à𝑛 𝑡ℎà𝑛ℎ
To illustrate the concept of EVM and all the formulas, assume a project that
has exactly one task. The task was baselined at 8 hours, but 11 hours have been
spent and the estimate to complete is 1 additional hour. The task was to have
been completed already. Assume an Hourly Rate of $100 per hour.
● Hourly Rate = $100
● PV = $800 ($100 × 8 hours)
● AC = $1100 ($100 × 11 hours)
● EV = $734 (baseline of $800 × 91.7% complete)
● BAC = $800 (8 hours × $100)
● SV = –$66 ($734 EV – $800 PV)
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● SPI = 0.91 ($734 EV / $800 PV)
● CV = –$366 ($734 EV – $1100 AC) → indicating a cost overrun
CPI = 0.66 ($734 EV / $1100 AC) → indicating over budget
=> The project is behind schedule (SPI <1) and over budget (CPI <1)
Example : A project has a budget of £10M and is scheduled for 10 months. It is
assumed that the total budget will be spent equally each month until the 10th month
is reached. After 2 months, the project manager finds that only 5% of the work is
finished and a total of £1M spent.
● PV = £2M
● EV = £10M × 0.05 = £0.5M
● AC = £1M
● CV = EV – AC = 0.5 – 1 = –0.5M
● CV% = 100 × (CV / EV) = 100 × (–0.5 / 0.5) = –100% overrun
● SV = EV – PV = 0.5 – 2 = –1.5 months
● SV% = 100 × (SV / PV) = 100 × (–1.5 / 2) = –75% behind
● CPI = EV / AC = 0.5 / 1 = 0.5 → Indicating Over cost
● SPI = EV / PV = 0.5 / 2 = 0.25
Example :"7. Given an activity in an advertising project whose planned cost was $12,000
but the actual cost to date is $10,000 so far and the value completed is only 70 percent,
calculate the cost and schedule variances. Will the client be pleased or angry?"
PV = $12000
AC = $10000
EV = 0.7 x 12000= 8400
SV= EV -PV = 8400-12000= -3600
CP = EV/ AC= 8400/10000 = 0.84 < 1 SCI= EV/ PV = 8400/12000 = 0.7 <1
=> The project is behind schedule (SPI <1) and over budget (CPI <1)
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6.7 periods
Step1 : Điền PV tới thời điểm đang xét của mỗi Job
Step 2: Điền EV = Total PV ( mỗi job) x % complete
Step 3: Cái nào 100% xuất hiện lại thì điền y chang cái 100% lần đầu tính
Status report: ending P1
Task % complete EV AC (given) PV CV SV
(given)
A 50% 10 10 10 0 0
Cumulative 10 10 10 0 0
total
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Status report: ending P2
Task % complete EV AC (given) PV CV SV
(given)
A 100% 20 30 20 -10 0
Cumulative 20 30 20 -10 0
total
Status report: ending P3
Task % complete EV AC (given) PV CV SV
(given)
A 100% 20 30 20 -10 0
B 33% 5 10 5 -5 0
C 20% 20 30 20 -10 0
D 60% 21 20 15 1 6
Cumulative 66 90 60 -24 6
total
Status report: ending P4
Task % complete EV AC PV CV SV
(given) (given)
A 100% 20 30 20 -10 0
B 100% 15 20 15 -5 0
C 50% 50 70 50 -20 0
D 80% 28 30 25 -2 3
cumulative 113 150 110 -37 3
total
Status report: ending P5
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Task % complete EV AC (given) PV CV SV
(given)
A 100% 20 30 20 -10 0
B 100% 15 20 15 -5 0
C 60% 60 100 80 -40 -20
D 80% 28 50 35 -22 -7
Cumulative 123 200 150 -77 -27
total
Status report: ending P6
Task % complete EV AC (given) PV CV SV
(given)
A 100% 20 30 20 -10 0
B 100% 15 20 15 -5 0
C 80% 80 110 100 -30 -20
D 100% 35 60 35 -25 0
Cumulative 150 220 170 -70 -20
total
Status report: ending P7
Task % complete EV AC (given) PV CV SV
(given)
A 100% 20 30 20 -10 0
B 100% 15 20 15 -5 0
C 90% 90 120 100 -30 -10
D 100% 35 60 35 -25 0
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E 0% 0 0 30 0 -30
F 0% 0 0 0 0 0
Cumulative 160 230 200 -70 -10
total
Another exercise
Activity Immediate Normal Crash Crash Normal Percent Money
predecessor time time cost ($) cost ($) complete spent
(weeks) (week)
A - 4 2 900 300 100% 200
B - 3 1 600 200 100% 200
C A, B 2 1 100 50 100% 60
D A, B 3 2 300 100 80% 90
E A 4 1 750 150 70% 100
F C, D 4 1 550 250 _ _
G D, E 2 1 500 300 _ _
H F, G 3 2 300 200 _ _
Task Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Week 8
A X X X X
B X X X
C X X
D X X X
E X X X X
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Gantt chart with earliest starting plan
The PV is calculated based on the plan at week 7.
At the beginning of week 7, A,B,C are supposed to be completed. D is supposed to be 2/3 finished and E
2/4 finished
Activity Normal Percent Money PV AC EV
cost ($) complete spent
A $300.00 100% $200.00 $300.00 $200.00 $300.00
B $200.00 100% $200.00 $200.00 $200.00 $200.00
C $50.00 100% $60.00 $50.00 $60.00 $50.00
D $100.00 80% $90.00 $66.67 $90.00 $80.00
E $150.00 70% $100.00 $75.00 $100.00 $105.00
SUM $691.67 $650.00 $735.00
7. Cost Estimate
A simple example of cost estimating is to forecast the expense of getting a Bachelor of
Science (B.S.) from the university you are attending. In our solution, we outline the two
basic approaches just discussed for estimating these costs.
Solution
A top-down approach would take the published cost of a four-year degree at the same (or
a similar) university and adjust it for inflation and extraordinary items that an incoming
student might encounter, such as fraternity/sorority membership, scholarships, and
tutoring. For example, suppose that the published cost of attending your university is
$15,750 for the current year. This figure is anticipated to increase at the rate of 6% per
year and includes full-time tuition and fees, university housing, and a weekly meal plan.
Not included are the costs of books, supplies, and other personal expenses. For our initial
estimate, these “other” expenses are assumed to remain constant at $5,000 per year.
The total estimated cost for four years can now be computed. We simply need to adjust
the published cost for inflation each year and add in the cost of “other” expenses.
Year Tuition, Fees, Room and Board “Other” Expenses Total Estimated Cost for Year
1 $15,750 × 1.06 = $16,695 $5,000 $21,695
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2 $16,695 × 1.06 = $17,697 $5,000 $22,697
3 $17,697 × 1.06 = $18,759 $5,000 $23,759
4 $18,759 × 1.06 = $19,885 $5,000 $24,885
Grand Total = $93,036
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In 2002 Acme Chemical purchased a large pump for $112,000. Acme keys their cost
estimating for these pumps to the industrial pump index, with a baseline of 100
established in 1992. The index in 2002 was 212. Acme is now (2010) considering
construction of a new addition and must estimate the cost of the same type and size of
pump. If the industrial pump index is currently 286, what is the estimated cost of the new
pump?
Năm 2002, Acme mua một máy bơm với giá $112,000
Chỉ số giá năm 2002 (I₀) = 212
Chỉ số giá năm 2010 (I ) = 286
Cần ước tính chi phí hiện tại (C ) của máy bơm tương tự trong năm 201
286
𝐶𝑡 = 112, 000 × ( 212 ) = 112, 000 × 1. 3491 ≈151, 100. 8
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Phần đầu ∑ 𝐶𝑑 cộng tất cả các thành phần được ước tính trực tiếp (như chi phí máy móc
𝑑
riêng biệt)
Phần sau∑ 𝑓𝑚𝑈𝑚 cộng tất cả chi phí ước lượng theo đơn vị (giống phương pháp đơn vị:
𝑚
đơn giá × số lượng)
Một nhà máy được ước tính gồm:
● Chi phí máy chính (ước lượng trực tiếp): $50,000
● Ống dẫn: $25/m, dài 200m
● Cửa sổ: $400/cái, cần 10 cái
Áp dụng công thức:
C=50,000+(25×200)+(400×10)=50,000+5,000+4,000=59,000
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Một nhà máy B có công suất 100 MW, chi phí $200 triệu.
Bạn cần ước tính chi phí cho nhà máy A có công suất 150 MW, biết hệ số X = 0.7.
150 0.7 0.7
𝐶𝐴 = 200 × ( 100 ) = 200 × (1. 5) ≈200×1. 38≈ 276 𝑡𝑟𝑖ệ𝑢 𝑈𝑆𝐷
👉 Nhà máy lớn hơn, nhưng do lợi thế quy mô, chi phí không tăng tuyến tính mà chỉ
tăng khoảng 38%.
𝑛
𝑍𝑢 = 𝐾 × (𝑢 )
Ký Ý nghĩa
hiệu
u Số thứ tự của sản phẩm đầu ra (ví dụ: đơn vị thứ 8)
𝑍𝑢 Số đơn vị đầu vào cần thiết (ví dụ: giờ công) để sản xuất
đơn vị uu
K Số đơn vị đầu vào cần để sản xuất đơn vị đầu tiên
s Hệ số tốc độ học hỏi (learning rate) – ví dụ: 0.75 tức là 75%
n Số mũ của đường cong học tập, tính theo công thức:
𝑙𝑜𝑔 𝑆
𝑛= 𝑙𝑜𝑔 2
Learning curve example: Assume the first unit of production required 3 hours time for
assembly. The learning rate is 75%. Find:
(a) the time to assemble the 8th unit, and
(b) the time needed to assemble the first 6 units.
(𝑙𝑜𝑔 0.75/ 𝑙𝑜𝑔 2
a) 𝑍8 = 3 × (8 ) = 1. 27 ℎ𝑜𝑢𝑟𝑠
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𝑥
𝑛
b) 𝑇𝑥 = 𝐾 × ∑ 𝑢
𝑢=1
6
(𝑙𝑜𝑔 0.75/𝑙𝑜𝑔 2)
𝑇6 = 3 × ∑ 𝑢 = 11. 8 ℎ𝑜𝑢𝑟𝑠
𝑢=1
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