Operations Management Midterm Workshop

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

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

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

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

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

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%

Worked: cars and pumps (slides)

Break-even: where revenue meets cost

BEP = F ÷ (P − V) = 20,000 ÷ (3 − 1) = 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

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

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

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

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

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

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.

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.

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

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