1. Dr. Ron Lembke Operations Management
5. Capacity and Waiting
Dr. Ron Lembke
Operations Management

2. How much do we have? Design capacity: max output designed for
Everything goes right, enough support staff
Effective Capacity
Routine maintenance
Affected by resources allocated
We can only sustain so much effort.
Output level process designed for
Lowest cost per unit

3. Loss of capacity

4. Utilization and Efficiency
Capacity utilization = actual output
design capacity
Efficiency = actual output
effective capacity
Efficiency can be > 1.0 but not for long

5. Scenario 1 Design Capacity 140 tons Effective Capacity 124 tons –
landing gear could fail in bad weather landing
With 120 ton load
Utilization: 120/140 = 0.857
Efficiency: 120/124 = 0.968

6. Economies of Scale Cost per unit cheaper, the more you make
Fixed costs spread over more units

7. Dis-economies of scale
Congestion, confusion, supervision
Running at 100 mph means more maintenance needed
Overtime, burnout, mistakes

8. Marginal Output of Time
Value of working n hrs is Onda
As you work more hours, your productivity per hour goes down
Eventually, it goes negative.
Better to work b instead of e hrs
S.J. Chapman, 1909, “Hours of Labour,” The Economic Journal 19(75)

9. Learning Curves time/unit goes down consistently
First 1 takes 15 min, 2nd takes 5, 3rd takes 3
Down 10% (for example) as output doubles
We can use Logarithms to approximate this
cost per unit after 10,000 units?
If you ever need this, me, and we can talk as much as you want

10. Break-Even Points FC = Fixed Cost VC = variable cost per unit
QBE = Break-even quantity
R = revenue per unit
R*Q
FC+VC*Q
Break-Even
Point
Volume, Q

11. Cost Volume Analysis Solve for Break-Even Point For profit of P,
QBE = FC
R – VC
FC = $50,000 VC=$2, R=$10
QBE = 50,000 / (10-2) = 6,250 units

12. 747 vs 777

13. vs 777
Monthly Debt Operating 747 $1,367,000 $50, $1,517,000 $50,000
$/ton-mile
$1.45
$1.38
QBE = FC
R – VC
Revenue = $2/ton-mile
Break-even:
747 ($1,367,000+$50,000)/(2-1.45)=
2,576,364 ton-miles per month
777 ($1,517,000+$50,000)/(2-1.38)=
2,527,419 ton-miles per month

14. Adjust for aircraft size
777 – 124 tons per flight 2,576,364/124 = 20,777 full miles/month 747 – 104 tons per flight 2,527,419/104 = 24,302 full miles/month

15. # Flights / month Tokyo-Singapore = 2,869 miles 747:
= 7.24 fully loaded flights
= 8 full flights
777:
24,302 miles/2,869
= 8.47 fully loaded flights
= 9 full flights

16. Service Differences Arrival Rate very variable
Can’t store the products - yesterday’s flight?
Service times variable
Serve me “Right Now!”
Rates change quickly
Schedule capacity in 10 minute intervals, not months
How much capacity do we need?

17. Everyone is Just Waiting

18. We are the problem Customers arrive randomly.
Time between arrivals is called the “interarrival time”
Interarrival times often have the “memoryless property”:
On average, interarrival time is 60 sec.
the last person came in 30 sec. ago, expected time until next person: 60 sec.
5 minutes since last person: still 60 sec.
Variability in flow means excess capacity is needed

19. Queueing Theory Equations
Memoryless Assumptions:
Exponential arrival rate =  = 10
Avg. interarrival time = 1/ 
= 1/10 hr or 60* 1/10 = 6 min
Exponential service rate =  = 12
Avg service time = 1/ = 1/12
Utilization = = /
10/12 = 5/6 = 0.833

20. Avg. # of customes
Lq = avg # in queue =
Ls = avg # in system =

21. Probability of # in System
Probability of no customers in system
Probability of n customers in system

22. Average Time
Wq = avg time in the queue
Ws = avg time in system

23. Example
Customers arrive at your service desk at a rate of 20 per hour, you can help 35 per hr.
What % of the time are you busy?
How many people are in the line, on average?
How many people are there in total, on avg?

24. Queueing Example λ=20, μ=35 so Utilization ρ=20/35 = 0.571
Lq = avg # in line =
Ls = avg # in system = Lq + /
= = 1.332

25. How Long is the Wait? Time waiting for service =
Lq = 0.762, λ=20
Wq = / 20 = hours
Wq = * 60 = 2.29 min
Total time in system =
μ=35, service time = 1/35 hrs = min
Ws = = 4.0 min

26. Memoryless Property Interarrival time = time between arrivals
Memoryless property means it doesn’t matter how long you’ve been waiting.
If average wait is 5 min, and you’ve been there 10 min, expected time until bus comes = 5 min
Exponential Distribution
Probability time is t =

27. Poisson Distribution Assumes interarrival times are exponential
Tells the probability of a given number of arrivals during some time period T.
Binomial when # trials large and Pr(x) tends to zero
Simeon Denis Poisson

28. Larger average, more normal

29. What did we learn?
Memoryless property means exponential distribution, Poisson arrivals
Results hold for simple systems: one line, one server
Average length of time in line, and system
Average number of people in line and in system
Probability of n people in the system

30. Cost-Effectiveness
How much money do we lose from people waiting in line for the copy machine?
Would that justify a new machine?
How much money do we lose from bailing out (balking)?

31. Queues In England, they don’t ‘wait in line,’ they ‘wait on queue.’
So the study of lines is called queueing theory.

32. Retail Lines Things you don’t need in easy reach
Candy
Seasonal, promotional items
People hate waiting in line, get bored easily, reach for magazine or book to look at while in line
Deposit slips
Postal Forms

33. In-Line Entertainment
Set up the story
Get more buy-in to ride
Plus, keep from boredom

34. Disney FastPass Wait without standing around
Come back to ride at assigned time
Only hold one pass at a time
Ride other rides
Buy souvenirs
Do more rides per day

35. Benefits of Interactivity
Slow me down before going again
Create buzz, harvest addresses

36. False Hope
Dumbo
Peter Pan

37. Time Horizons
Long-Range: over a year – acquiring, disposing of production resources
Intermediate Range: Monthly or quarterly plans, hiring, firing, layoffs
Short Range – less than a month, daily or weekly scheduling process, overtime, worker scheduling, etc.

38. Adding Capacity Expensive to add capacity
A few large expansions are cheaper (per unit) than many small additions
Large expansions allow of “clean sheet of paper” thinking, re-design of processes
Carry unused overhead for a long time
May never be needed

39. Capacity Planning How much capacity should we add?
Conservative Optimistic
Forecast possible demand scenarios (Chapter 4)
Determine capacity needed for likely levels
Determine “capacity cushion” desired

40. Capacity Sources In addition to expanding facilities:
Two or three shifts
Outsourcing non-core activities
Training or acquisition of faster equipment

41. What Would Henry Say? Ford introduced the $5 (per day) wage in 1914
He introduced the 40 hour work week
“so people would have more time to buy”
It also meant more output: 3*8 > 2*10
“Now we know from our experience in changing from six to five days and back again that we can get at least as great production in five days as we can in six, and we shall probably get a greater, for the pressure will bring better methods.
Crowther, World’s Work, 1926

42. Henry Ford 1919 bought paper Buys newspaper Jan, 1919
May, 1920, anti-Jewish articles start
Mein Kampf, p. 929
Grand Cross of the German Eagle, 1938
1920, German version 1922
1925
1919 bought paper

43. Denial
“Shocked!” Closes paper, 12/27 Apologized 4/5 of letters to Ford in July, 1927 were supportive, from Jews. Jan, 1937 disavows “any connection whatsoever with the publication in Germany of a book known as The International Jew.”
With son Edsel, 1927

44. Toyota Capacity 1997: Cars and vans? That’s crazy talk
First time in North America
292,000 Camrys
89,000 Siennas
89,000 Avalons

45. Decision Trees
Consider different possible decisions, and different possible outcomes
Compute expected profits of each decision
Choose decision with highest expected profits, work your way back up the tree.

46. Draw the decision tree