Lecture 3: Process analysis: Flow Diagrams and Deterministic Performance Estimation

Question 1

What is capacity and what are the capacity planning time durations? Why capacity planning is important? What are the costs associated with capacity?

Answer 1

Capacity is in the static, physical sense means
the scale of an operation

› Long range: greater than one year
- Productive resources including buildings, equipment and facilities
› Intermediate range: monthly or quarterly plans for the next six to 18 months
- Capacity variation by hiring, layoffs, new tools, and minor equipment purchases, and subcontracting
› Short range: less than one month
- Alternatives include overtime, personnel transfers, and changes in production routings

Question 2

Why capacity planning is important? What are the costs associated with capacity?

Answer 2

Important because:
- Cost implications (idle capacity, excess inventory,
higher operating costs)
- Revenue implications (unfulfilled customer demand)
- Uncertainty associated with future demand (forecasting -> uncertainties)
- Customer dissatisfaction (unfulfilled customer demand)

› Cost of upgrading too frequently:
-removing and replacing old equipment
-training employees on new equipment
-purchase of new equipment will be much expensive
than selling old equipment.

› Cost of upgrading too infrequently
-infrequent expansion means that capacity is
purchased in larger chunks. The possibility of excess
capacity is higher.

Question 3

Define inter-arrival time and arrival rate

Answer 3

• Inter-arrival time: Time between two subsequent arrivals of products/customers at their entrance in the process
• Arrival rate: number of products that arrive per unit of time (e.g. number of products that arrive per hour)

Question 4

Define throughput time and deterministic throughput time

Answer 4

Time that passes between the moment at which the customer/product enters the system and the moment at which the customer/product is ready

Note: Throughput is not throughput time;
Throughput refers to the amount of items passing through a system or process,

› Deterministic throughput times can be estimated
by adding up the expected processing times of the
different processes
- Deterministic means that you ignore any
probability distributions and just use the average
value (or mean or expected value), ignore waitingline effects in the system

Question 5

Define design and effective capacity

Answer 5

› Design capacity: Theoretical maximum output of a system or process in a given period.

› Effective capacity: actual capacity that
can be expected given the product mix,
methods of scheduling, maintenance, and
standards of quality.

Question 6

What is a bottleneck?

Answer 6

• Bottleneck: an operation that limits output in the system.
• If none of the processes (e.g., machines, workers) in the system is a bottleneck, then the arrival process is to be the bottleneck.

Question 7

Define utilisation rate and productive utilisation rate

Answer 7

› Utilisation rate: fraction of the total time in which a machine is used for production.
› Utilisation rate = total operating time / total time = actual output/design capacity

› The utilisation rate “p” for a workstation consisting of
n identical, parallel servers can be computed from p= (lambda)/(n*(mean)), (lambda): arrival rate and (mean): production rate per station

Only if the arrival process is the bottleneck!

Productive utilisation rate is calculated similar to normal utilisation, only now set-up times are excluded.

Question 8

What does WIP mean and how to calculate it?

Answer 8

› WIP - Work-in-Progress: The number of products that have been taken into production, but have not yet been finished

1) Little’s law: L=lambdaW (lambda: arrival rate, W: deterministic throughput time)
2) sum(p(i)X(i)), p:utilisation rate of processs i, X:batch size of process i

Note: Only if the arrival process is the bottleneck, we can apply the Little’s equation to accurately estimate WIP