Operations Management Midterm Workshop

Start here: no background needed

Operations management = how a business makes its product or service, cheaply and on time. Every example below uses a bakery.

Words you need

Word	Plain meaning	Bakery example
Demand	How much customers want	Customers want 300 loaves on Friday
Forecast	Your guess of future demand	"Next Friday we expect 310"
Actual	What really happened	We really sold 320
Error	Actual − forecast	320 − 310 = 10 loaves off
Capacity	The most you can make	The oven can bake 100 loaves a day
Utilisation	How much of the full capacity you used	Baked 64 of 100 = 64%
Efficiency	How much of the realistic capacity you used	Baked 64 of a realistic 80 = 80%
Fixed cost	Cost that stays the same however much you make	Shop rent
Variable cost	Cost for each unit you make	Flour for one loaf
Break-even	Units to sell before you stop losing money	Sell 10,000 loaves to cover rent
Inventory	Stock kept for later	Frozen dough in the freezer
Holding cost	Cost of keeping stock	Freezer electricity
Aggregate plan	Month-by-month plan for workers and output (3 to 18 months)	How many bakers for each month of the year
Level plan	Make the same amount every month	Bake 250 a day all year, freeze the extra
Chase plan	Make exactly what is demanded; hire or lay off	Hire extra bakers for Ramadan
Scheduling	Deciding which job goes first	Wedding cake before birthday cake?
Flow time	When a job is finished, counted from now	Cake ready 7 hours from now
Tardiness	How late a job is (0 if on time)	Due at 5 h, ready at 7 h = 2 h late
Bottleneck	The slowest step, which limits everything	One slow oven holds up four fast mixers

Maths symbols you will see

Symbol	Read it as
Σ	"add them all up". Σy = add every demand number
n	how many periods (days, months) there are
x	the period number: day 1, 2, 3…
y	the demand in that period
x̄, ȳ	the average of x, the average of y
A, F	A = actual, F = forecast
α	"alpha": a number between 0 and 1 that sets how much the newest month counts
\|e\|	the error with its minus sign removed (\|−5\| = 5)
⌈ ⌉	round up to the next whole number (64.3 → 65)

Question bank → topic → CLO → tab

Bank question	What it asks	Module	CLO	Learn it in
MCQ 1 to 6	OM objective, functions, evolution, strategy, productivity, transformation	I	CLO1	Foundations
Blanks 1 to 3	Forecasting: demand · judgement · cyclical / random	II	CLO2	Forecasting
Blanks 4 to 6	Aggregate planning: capacity · subcontracting · cost	III	CLO3	Aggregate planning
True/false 1 to 3	Scheduling traps: F · T · T	III	CLO3	Scheduling
Descriptive Q1 to Q3	5-mark cases: factory, hospital, defects	I	CLO1	Written answers
Numerical Q2	Least squares line (newspaper / water)	II	CLO2	Forecasting
Numerical Q3	Chase hiring and layoff cost (Al Saleem / NPI)	III	CLO3	Aggregate planning
Numerical Q4	Blank in the bank. Likely forecast errors or capacity	II	CLO2	Forecasting, Capacity
Numerical Q5 (a)	Johnson's rule, two machines	III	CLO3	Scheduling
Numerical Q5 (b)	EDD / SPT mean flow time and tardiness	III	CLO3	Scheduling

CLO1 · Module IUnderstand why operations matter to a firm.

CLO2 · Module IIMake decisions on forecasting and capacity.

CLO3 · Module IIIBuild short-run plans: aggregate planning and scheduling.

Not on the midtermCLO4 supply chain and CLO5 quality/lean come after the midterm.

Mapped from Question Bank 1 MT and the HUM 4404 teaching plan (midterm = Modules 1 to 3, CLO1 to CLO3).

What's on the midterm

Modules 1 to 3Intro, forecasting and capacity, planning and scheduling

30 marksLearning outcomes CLO1 to CLO3

1 hourTue 10 Nov, 2 PM

Topics by likelihood

Topic	Likelihood	Tab
Least squares · chase cost · Johnson · EDD/SPT	Certain	Forecasting, Aggregate, Scheduling
MCQ, blanks, true/false, case essay	Certain	Foundations, Written answers
Forecast errors (MAD, MSE, MAPE) · moving average · smoothing	Very likely	Forecasting
Utilisation, efficiency, break-even, make or buy	Very likely	Capacity
Level vs mixed vs chase cost	Very likely	Aggregate
PPC, capacity factors, planning options	Likely (theory)	Foundations, Capacity
Trend smoothing, seasonal index, tracking signal	Possible	Forecasting
TOC, supply chain, TQM, lean	Not on midterm	Skip

Topic

Likelihood

Tab

Least squares · chase cost · Johnson · EDD/SPT

Certain

Forecasting, Aggregate, Scheduling

MCQ, blanks, true/false, case essay

Certain

Foundations, Written answers

Forecast errors (MAD, MSE, MAPE) · moving average · smoothing

Very likely

Forecasting

Utilisation, efficiency, break-even, make or buy

Very likely

Capacity

Level vs mixed vs chase cost

Very likely

Aggregate

PPC, capacity factors, planning options

Likely (theory)

Foundations, Capacity

Trend smoothing, seasonal index, tracking signal

Possible

Forecasting

TOC, supply chain, TQM, lean

Not on midterm

Skip

Rough split of the 30 marks

Theory ~7

Case 5

Numericals ~18

An estimate from the bank layout and the teaching plan; it isn't published anywhere.

Bank Q4 is blankLikely one of: forecast-error comparison, capacity/break-even, or level vs chase. The mock has all three.

Study plan: Monday afternoon to Tuesday noon

Exam Tuesday 2 PM. Study stops at 12 noon Tuesday. Short breaks between blocks.

When	Do	Done when
Mon 1:30 to 4	What's coming → Foundations → Forecasting (least squares, moving average, smoothing)	Formulas for b, a, F(t) from memory
Mon 4:30 to 7	Forecast errors (port table) → Capacity	MAD 10.31 · break-even 10,000
Mon 8 to 10:30	Aggregate planning → Scheduling	Al Saleem $27,400 · Johnson 180 min
Mon 10:30 to 11:30	Written answers + one pass of recall drills, then sleep	Most cards without flipping
Tue 7 to 8	Mock under 60 min	Paper finished
Tue 8 to 10:30	Mark the mock, redo wrong numericals, ask Claude to quiz weak spots, recall drills again	Weak topics fixed
Tue 10:30 to 12	Cheat sheet · one of each numerical · stop at noon	Every recipe clean
Tue 12 to 2	Eat, rest, reach the hall early. No new topics	Seated by 1:50

In the exam hour

10 min · MCQ, blanks, T/F

35 min · numericals: table first, formula before numbers

15 min · case

Stuck?Ask Claude: "quiz me on capacity", "new Johnson problem, mark my answer", "find my mistake" (paste your table).

Foundations

Operations management = turning inputs into goods and services efficiently.

Inputslabour · materials · machines · energy · money · information

→

Transformationmachining · assembling · treating · storing · transporting

→

Outputsproducts · services

↺ feedback and control: compare output with plan, correct inputs

OM jobs (right answers)

Production planning & controlCapacityLayoutQualityInventorySchedulingMaintenanceSupply chain

Not OM (MCQ traps)

AdvertisingTax collectionPublic relationsRecruitment only

How OM evolved

Craft
Industrial revolution
Taylor: time study
Ford: assembly line
Toyota: TQM, JIT, lean
Now: automation, data, Industry 4.0

PPC: the planning ladder (links the whole midterm)

YearsCapacity planningfacility size, equipment

6 to 18 monthsAggregate planningworkforce, inventory, subcontract

WeeksMaster schedulewhich model, how many

Hours to daysSchedulingjob order on machines

PPC stages: plan → operate → control (feedback against plan).

Productivity

Productivity = Output / Input Labour: 1,200 units / 300 h = 4 per hour Multifactor: (1,200 × $25) / $12,000 = 2.5

Operations strategy

Align operations with business goals. Compete on:

CostQualityDeliveryFlexibility

	Goods	Services
Tangible?	Yes	No
Can store?	Yes, inventory	No, made and used at once
Customer involved?	Rarely	Often

Easy version: productivity

How much you get out for what you put in. A baker makes 1,200 loaves in 300 hours.

Productivity = Output ÷ Input

Output = what was made: 1,200 loaves
Input = what was used: 300 hours
Divide: 1,200 ÷ 300 = 4 loaves per hour

TrapProductivity is output ÷ input, never the reverse.

Forecasting

Estimate future demand so staff, material and machines are ready in time.

Which method?

Past data available?

Qualitative: Delphi, expert opinion, sales force, market survey

Yes, flat

Moving average · weighted MA · exponential smoothing

Yes, trend

Least squares · trend-adjusted smoothing

A cause drives it

Associative regression (x = payroll, price…)

Four patterns inside demand data

Least squares: fit a straight line

b = (nΣxy − ΣxΣy) / (nΣx² − (Σx)²) a = ȳ − b·x̄ y = a + bx x = 1…7 → Σx = 28, Σx² = 140, x̄ = 4

Easy version: least squares (bank Q2)

Draw the best straight line through past demand, then extend it to guess the future. Line: y = a + bx, where b = growth per day and a = starting level.

b = (n×Σxy − Σx×Σy) ÷ (n×Σx² − (Σx)²) a = ȳ − b×x̄

Make a table: x (day 1 to 7), y (demand), x×y, x². Add each column.
For 7 days these never change: n = 7, Σx = 28, Σx² = 140, x̄ = 4, so the bottom line is always 7×140 − 28² = 196
Newspaper: Σy = 1,648, Σxy = 7,798 → b = (7×7,798 − 28×1,648) ÷ 196 = 43.07
ȳ = 1,648 ÷ 7 = 235.43 → a = 235.43 − 43.07×4 = 63.14
Answer: y = 63.14 + 43.07x. Day 8 forecast: put x = 8 → 407.7

Worked: both bank questions

Moving averages lag behind a trend

Method	Formula	Use when
Naive	next = last actual	quick baseline
Moving average	Σ last n ÷ n	no trend
Weighted MA	Σ (w × A) ÷ Σ w	recent data matters more

Easy version: moving average

Forecast = average of the last few actual values. A 3-month average uses the last 3.

Next forecast = (sum of last n actuals) ÷ n

Pick the last n actuals, e.g. 120, 132, 128
Add them: 380
Divide by n: 380 ÷ 3 = 126.67
Weighted: multiply each by its weight, add, divide by the total of the weights

Worked: shed sales

Exponential smoothing: α sets the reaction speed

F(t) = F(t−1) + α × (A(t−1) − F(t−1)) 142 + 0.2 × (153 − 142) = 144.2 high α = reacts fast · low α = stable demand

Easy version: exponential smoothing

New forecast = old forecast, nudged towards what really happened. α decides the size of the nudge.

New forecast = Old forecast + α × (Actual − Old forecast)

Old forecast 142, actual 153, α = 0.2
Miss = 153 − 142 = 11
Nudge = 0.2 × 11 = 2.2
New forecast = 142 + 2.2 = 144.2

Forecast errors: smaller wins

Measure	Formula	Tells you
MAD	Σ\|A − F\| ÷ n	average miss, in units
MSE	Σ(A − F)² ÷ n	punishes big misses
RMSE	√MSE	MSE back in units
MAPE	Σ(100\|A − F\| ÷ A) ÷ n	average miss as %

Worked: Port of Baltimore error tables

Easy version: MAD, MSE, MAPE

They all measure how wrong a forecast was. The method with the smaller number is better.

Error = Actual − Forecast · MAD = average of |error| · MSE = average of error² · MAPE = average of (|error| ÷ actual × 100)

For every period: error = actual − forecast
MAD: drop minus signs, add, divide by number of periods
MSE: square each error, add, divide
MAPE: |error| ÷ actual × 100 for each, add, divide
Port example (α = 0.1): MAD 10.31, MSE 190.82, MAPE 5.59%

TrapsError = actual − forecast · MAPE divides by actual · count only periods that have a forecast.

Possible extras: trend smoothing, seasonal index, regression, tracking signal

Trend smoothing: F = αA + (1−α)(F + T) T = β(F − Fold) + (1−β)T FIT = F + T Seasonal index = season average ÷ overall average Associative = least squares with a cause as x; r from −1 to +1; r² = share explained Tracking signal = Σ errors ÷ MAD (outside limits = biased forecast)

Capacity

Capacity = the most a unit can produce. Match it to forecast demand.

Three capacities, two ratios

Design

100

Effective

Actual

Utilisation = actual ÷ design = 64 ÷ 100 = 64%

Efficiency = actual ÷ effective = 64 ÷ 80 = 80%

Easy version: the three capacities

Design = the most possible in a perfect world. Effective = the most possible after normal breaks, cleaning and maintenance. Actual = what really came out.

Utilisation = Actual ÷ Design × 100 Efficiency = Actual ÷ Effective × 100

Find the three numbers: design 100, effective 80, actual 64
Utilisation = 64 ÷ 100 = 64%
Efficiency = 64 ÷ 80 = 80%
Check: efficiency is always the bigger one

Worked: cars and pumps (slides)

Break-even: where revenue meets cost

Break-even units = Fixed cost ÷ (Price − Variable cost) BEP = F ÷ (P − V) = 20,000 ÷ (3 − 1) = 10,000 units

Easy version: break-even

Each unit sold leaves (price − variable cost) to pay the fixed cost. Break-even = how many units it takes to pay it all.

Fixed cost F = 20,000 (rent), price P = 3, variable cost V = 1
Each unit leaves 3 − 1 = 2 towards rent
Units needed = 20,000 ÷ 2 = 10,000 units

Make or buy

	Make	Buy
Cost at 1,000 units	20,000 + 10 × 1,000 = AED 30,000	27 × 1,000 = AED 27,000 ✓
Switch point	20,000 ÷ (27 − 10) = 1,177 units; above it, make

Easy version: make or buy

Make = pay fixed cost + your cost per unit. Buy = pay the supplier price per unit. Pick the cheaper total.

Make cost = F + V × N Buy cost = Price × N

Make: 20,000 + 10 × 1,000 = AED 30,000
Buy: 27 × 1,000 = AED 27,000
Buy is cheaper at 1,000 units

Bottleneck: the slowest step sets the pace

10/h

30/h

10/h

→ output 10/h

Machines needed

hours needed ÷ hours per machine 5,800 ÷ (250 × 8) = 2.9 → 3

What lowers effective capacity

LayoutSkillsQualityShifts policySchedulingSupplyRegulations

Easy version: machines needed

Total hours of work ÷ hours one machine can give in a year. Always round up, you cannot buy part of a machine.

Machines = Hours needed ÷ Hours per machine, round up

Hours needed = 5,800
One machine: 250 days × 8 h = 2,000 h
5,800 ÷ 2,000 = 2.9 → 3 machines

TrapUtilisation ÷ design, efficiency ÷ effective. Efficiency is always the bigger %.

Aggregate planning

Medium-term plan (3 to 18 months): meet forecast demand at the lowest total cost.

Strategy	How	Main cost
Level	Same output every month; stock absorbs swings	Holding inventory
Chase	Output = demand; hire and fire every month	Hiring + layoff
Mixed	Mix: steady core + subcontract or overtime	Subcontract / overtime

Easy version: level vs chase

Level: make the same amount each month; extra goes into stock, so you pay holding cost. Chase: make exactly what is demanded each month; you pay to hire and lay off.

Level cost = total stock carried × holding cost Chase cost = hires × hire cost + layoffs × layoff cost

Level: output per month = total demand ÷ number of months
Chase: workers each month = demand ÷ output per worker (round up)
Compare the two totals. The smaller one is the better plan

Same demand, three plans (roofing supplier, units per month)

Worked: roofing plans and Example 5

Chase recipe (bank Q3)

Step	Do
1	Output per worker per month (Al Saleem: 2 × working days)
2	Month 1 need = demand − opening stock; later months = demand
3	Workers = need ÷ output per worker, round up
4	Up from last month → hire · down → lay off
5	Hires × hire cost + layoffs × layoff cost

Easy version: Al Saleem, April only

Do this for every month, then add up.

Workers needed = (Demand − Opening stock) ÷ (Output per worker per day × Working days), round up

Output per worker in April = 2 sets × 21 days = 42
April need = 3,400 − 700 opening stock = 2,700
Workers = 2,700 ÷ 42 = 64.29 → 65
We have 60, so hire 5 → 5 × $300 = $1,500
Repeat each month (no opening stock after April). Total = $27,400

Worked: Al Saleem ($27,400) and NPI ($22,400)

Capacity options (react)

InventoryHire / lay offOvertimePart-timeSubcontract

Demand options (influence)

Price / promotionBackordersCounter-seasonal products

TrapsOpening stock only in month 1 · output per worker changes with working days · say whether you rounded workers.

Scheduling

Choose the order of jobs to cut waiting, lateness and total time.

Term	Formula
Flow time	running total of processing times
Mean flow time	Σ flow ÷ n
Tardiness	max(0, finish − due)
Makespan	time to finish all jobs

One machine: pick a rule

Rule	Order by	Best for
FCFS	arrival	fairness
SPT	shortest job first	lowest mean flow time
EDD	earliest due date	lateness
LPT	longest job first	rarely best

Easy version: EDD / SPT (bank Q5)

Put jobs in order by a rule, then see when each finishes and how late it is. EDD = earliest due date first. SPT = shortest job first.

Flow time = running total of job times · Tardiness = Flow time − Due (0 if negative) · Mean = Total ÷ Number of jobs

Sort jobs by the rule (EDD: by due time; SPT: by job time)
Flow time: keep adding job times. TV2 10 h → 10, then TV1 7 h → 17…
Tardiness: flow − due. TV1: 17 − 15 = 2 h late. If negative, write 0
Mean flow time = sum of flow times ÷ jobs. Average tardiness = sum of tardiness ÷ jobs

Worked: TV shop (EDD) and garage (SPT)

Two machines: Johnson's rule

Find the smallest time left

→

on Machine 1 → put job first

on Machine 2 → put job last

→

Cross out, repeat

Easy version: Johnson's rule (bank Q5)

Two machines in a row (lathe, then grinder). Find the job order that finishes everything soonest.

Smallest time on Machine 1 → goes as early as possible · smallest on Machine 2 → as late as possible

List all times. Find the single smallest number in the table
If it is on Machine 1, put that job in the first free slot. If on Machine 2, the last free slot
Cross that job out. Repeat until all are placed
Bank set 1: smallest is C = 9 on M2 → C goes last; then D = 12 on M1 → D goes first…
Draw the timeline: Machine 2 starts a job only when Machine 1 has finished it. Last finish = minimum total time

Worked: both bank sets step by step

Tricky true/false

Statement		Why
Least idle time always gives least total time	F	"always": bad order can still waste time
Job order affects waiting and completion time	T	see the chart above
Machine fully busy but jobs late	T	TV shop: busy all along, 7 of 8 late

5-mark case answers

One frame for every case: define → 3 or 4 levers → result.

1. DefineOM in this case, one line

→

2 to 4. Leversaction → effect, one line each

→

5. Resulttie to the KPI the case cares about

Case	Levers (action → effect)	Result
Factory costs, breakdowns, late	Preventive maintenance → less downtime Planning + sequencing → on-time delivery Lean → less scrap and waiting Inventory control → lower holding cost	Lower cost per unit, higher productivity
Hospital waits, shortages	Capacity matched to arrivals Rosters built on demand Reorder points for medicine Online booking, e-records	Shorter waits, happier patients
Defects competition, complaints	Process mapping, root cause Automation (CNC, robots) SPC charts, TQM Operator training	Fewer defects, more competitive

Interactive solvers

Type any numbers from a past paper or the mock and the page shows each step. Use them to check your own working, not to replace it; the exam wants the table on paper.

Least squares

Demand values, comma separated (x = 1, 2, 3, ...)

Chase strategy

Demand per month

Working days per month (blank if output per worker is fixed)

Units per worker per day, or per month if no days

Starting workers

Opening inventory

Hire cost per worker

Layoff cost per worker

Johnson's rule

Job names

Machine 1 times

Machine 2 times

Priority rules (FCFS, SPT, EDD, LPT)

Job names

Processing times

Due dates

Forecast methods and errors (MA, weighted MA, exponential smoothing)

Actual demand, oldest first

Moving average periods n

Weights, newest first (blank to skip)

Smoothing constant α

First forecast for exponential smoothing

Capacity and break-even

Design capacity

Effective capacity

Actual output

Fixed cost

Price per unit

Variable cost per unit

Level against chase (workers per period)

Demand per period

Output per worker per period

Starting workers

Hire cost per worker

Fire cost per worker

Holding cost per unit per period

Recall drills

Tap a card to see the answer. Say the answer out loud before you tap. Go through the deck three times; on the third pass you should not need to tap.

Mock exam: 60 minutes, 30 marks

Built from the bank's layout and the topics the teaching plan and slides add. The real paper will be shorter. Part E has one question for every topic that could fill the blank Q4, so treat E2 to E4 as a choice of two if you are short of time.

Part A: multiple choice (1 mark each)

Which of these is an input to a transformation process? (a) Customer satisfaction (b) Raw material (c) Finished car (d) Profit
A firm makes 900 units with 150 labour hours. Labour productivity is (a) 0.17 (b) 6 (c) 750 (d) 1,050 units per hour
Aggregate planning normally covers (a) 1 to 7 days (b) 3 to 18 months (c) 5 to 10 years (d) one shift
Utilisation is actual output divided by (a) effective capacity (b) design capacity (c) demand (d) inventory
Which error measure is expressed as a percentage? (a) MAD (b) MSE (c) RMSE (d) MAPE
Which rule gives the lowest mean flow time on a single machine? (a) FCFS (b) EDD (c) SPT (d) LPT

Part B: fill in the blanks (1 mark each)

The Delphi method is a __________ forecasting technique.
In exponential smoothing, α is called the __________ constant.
The operation with the lowest capacity in a sequence is the __________.
Under a chase strategy the main costs are hiring and __________.
Tardiness is never __________.

Part C: true or false (1 mark each)

On a single machine, changing the job order changes the makespan.
Efficiency can never be lower than utilisation for the same output.
A larger n in a moving average makes the forecast react faster to change.
Opening inventory reduces the production needed in the first month of a chase plan.

Part D: short case (5 marks)

A restaurant chain has long queues at lunch, food waste at night, and staff who are idle in the afternoon. Explain how capacity, workforce scheduling, inventory and technology decisions can fix this.

Part E: numericals

E1. Daily demand for a coffee kiosk over seven days was 98, 110, 131, 140, 162, 175, 190. Derive the least-squares linear forecast equation and forecast day 8.

E2. Monthly demand was 120, 132, 128, 141, 150, 146. For months 4 to 6, compare a 3-month moving average with exponential smoothing (α = 0.3, forecast for month 1 = 118) using MAD and MSE. Which method is better?

E3. A bottling line has a design capacity of 1,200 bottles a shift and an effective capacity of 1,000. Last shift it filled 850. Find utilisation and efficiency. A new product has fixed cost AED 45,000, price AED 12 and variable cost AED 7 per unit: find the break-even volume.

E4. Quarterly demand is 60,000, 90,000, 150,000 and 100,000 units. One worker makes 1,000 units a quarter and the firm starts with 100 workers. Hiring costs $200, firing $400, and holding $0.40 per unit per quarter. Compare a level plan with a chase plan.

E5. Six jobs pass through machine 1 then machine 2 (hours). P: 8, 6. Q: 5, 10. R: 12, 3. S: 4, 11. T: 9, 8. U: 7, 9. Find the Johnson sequence and the minimum total time.

E6. Six jobs A to F have processing times 6, 2, 8, 3, 9, 4 days and due dates 10, 6, 18, 8, 25, 12. Compare FCFS, SPT and EDD on mean flow time and average tardiness.

Show answers

Answer key

A: 1 (b), 2 (b) 900/150 = 6, 3 (b), 4 (b), 5 (d), 6 (c).

B: 1 qualitative, 2 smoothing, 3 bottleneck, 4 layoff (firing), 5 negative.

C: 1 False, the machine runs all jobs back to back whatever the order. 2 True, effective capacity is never above design capacity, so dividing by it gives the larger percentage. 3 False, a larger n smooths more and reacts more slowly. 4 True.

D: Use the hospital frame: capacity (more counters and tables at lunch), workforce (split shifts, fewer staff mid-afternoon), inventory (forecast-based prep, smaller evening batches, first-in-first-out), technology (online pre-orders, kitchen display, sales data to forecast). Close on shorter queues, less waste, lower labour cost.

One-page cheat sheet

BasicsOM turns inputs into outputs efficiently. Inputs → transformation → outputs. Productivity = output ÷ input. Operations strategy lines up operations with business goals. Priorities: cost, quality, delivery, flexibility.

ForecastingQualitative: expert opinion, experience, judgment (Delphi). Time series parts: trend, seasonality, cyclical, random.

b = (nΣxy − ΣxΣy)/(nΣx² − (Σx)²) a = ȳ − b·x̄ y = a + bx

x = 1..7: Σx = 28, Σx² = 140, x̄ = 4. In words: b = growth per day, a = starting level, y = forecast.

Aggregate planningMedium term (3 to 18 months). Balance demand with capacity at minimum cost. Decisions: workforce, inventory, production rate, overtime, subcontracting. Chase: workers = ⌈net demand ÷ output per worker⌉. Month 1 net = demand − opening stock. Hire if up, lay off if down.

Johnson's ruleSmallest time left: on M1, place first; on M2, place last. Cross out, repeat. M2 start = max(M1 finish, M2 free). Makespan = last M2 finish.

Priority rulesSPT lowest mean flow time. EDD good for lateness. Flow = running total. Tardiness = max(0, C − due). Mean = total ÷ n. Single machine: makespan same for every rule.

Smoothing and errors

MA = Σ last n / n WMA = Σ w·A / Σ w F(t) = F(t−1) + α(A − F) MAD = Σ|e|/n MSE = Σe²/n RMSE = √MSE MAPE = Σ(100|e|/A)/n

e = actual − forecast. Low α for stable demand. Smaller error = better method.

CapacityUtilisation = actual ÷ design. Efficiency = actual ÷ effective. Machines = hours needed ÷ hours per machine, round up. BEP = F ÷ (P − V). Make or buy: compare F + V·N with price·N. Bottleneck = slowest step sets output.

Plan costingLevel: one rate = total ÷ periods; cost = Σ ending inventory × holding. Mixed: level at minimum need, subcontract the rest. Chase: hire/fire every period. PPC: capacity (years) → aggregate (6 to 18 months) → MPS (weeks) → scheduling (days).

Bank answers

Edits

Write any correction or change you want here and send it back.

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