7. Quantitative Process Analysis Flashcards
What’s the cycle time?
Average time it takes between the moment the process (task) starts and the moment it completes
What are the equations for the 4 types of blocks?
Sequential: CT = T1+T2+..+Tn
XOR: CT = p1T1+p2T2+…+pn*Tn
AND = max(T1,T2,…,Tn)
Rework = CT = T/(1-r)
What are the components of the Cycle Time? Explain them
Waiting time: No work is being
done to advance the process
+
Processing time = Theoretical cycle time (TCC) Average time a case would take if there was no waiting time at all (i.e., if there was only processing time)
What’s CT efficiency? What’s the formula?
CT efficiency: Ratio of overall processing time, referred to as theoretical cycle time (TCT), relative to the overall CT
Formula = TCT/CT
What’s the critical path method? What are the main characteristics?
Sequence of process tasks that determines the (overall) theoretical cycle time (TCT) of the process
- cannot be applied to process models that contain (X)OR gateways
- Based on the notions of
Early start(ES)
Early Finish (EF)
Late start(LS)
Late Finish (LF)
What’s the little’s law? Describe formula, characteristics and an example
The (total) cycle time (CT) of a process is related to the arrival rate (lambda) and the work-in-process (WIP).*
Formula: WIP = lambda* CT
- Arrival rate (lambda): Average number of new process instances per time unit
- Work-in-process (WIP): Average number of active process instances at a given point in time
Alternative way of calculating the total CT, provided we know the arrival rate and WIP
e.g., CT = WIP / lambda = 200 loan applications / 10 applications per day = 20 business days
What’s the capacity and bottlenecks in flow analysis? Describe formula, characteristics
Theoretical capacity: Maximum number of instances that can be completed per time unit by a resource pool
Formula: µp = ucp / ulp
- Unit capacity (ucp): Total amount of time a resource pool (p) can deliver per time unit;
- Example: 3 clerks (pool size) x 8 hours per workday (unit capacity per clerk) = 24 hours per workday (ucp)
- Unit load (ulp): Amount of time a resource pool (p) needs to spend on one process instance;
Characteristics:
- The theoretical capacity of a resource pool implies that this pool is working at full capacity (no idle time);
- The resource pool with the minimum theoretical capacity is called the bottleneck of a process, as it determines the theoretical capacity of the entire process;
What’s the resource utilization formula and to which concept is related to?
pp = lambda (arrival rate) / µp (theoretical capacity of the resource pool p)
Related to capacity and bottlenecks
What are 3 limitations of flow analysis?
- Presented equations for calculating cycle time (CT) work only for block-structured process models
- Need to estimate the average CT of each task in the process model; two approaches: interviews vs IT logs
- Critical assumption that level of resource contention remains relatively stable over the long run
What’s the phenomenon called resource contention?
it occurs when there is more work to be done than resources available to perform the work (e.g., more insurance claims than claim handlers), leading to an, at least temporary, increase in waiting times (à queuing theory).
What are the key characteristics of queueing theory?
- Collection of mathematical techniques to analyze systems with resource contention, which inevitably leads to (waiting) queues (e.g., supermarket checkout, post office, government agency)
Generally, a queuing system consists of 1 or + queues (e.g., Mount Everest vs. supermarket), a service (e.g., checkout) that is provided by one or multiple servers (e.g., cashiers). The elements inside a queue are called jobs or customers
What are the two basic system types in queueing theory?
- Single-line queuing systems -> M/M/1 model (or queue);
- Multi-line queuing systems -> M/M/c model (or queue), where c is the number of servers (e.g., M/M/5).
How does the M/M/c models work? Name input and output elements (with formulas)
Input parameters:
- Arrival rate (λ) and inter-arrival time (1/λ): Average time that elapses between two consecutives process instances (e.g., if there are 5 arrivals per hour, then the mean inter-arrival time is 1/5 hours, or 12 minutes);
- Theoretical capacity per server (µ): Number of process instances that a server can execute per time unit
(e.g., µ = 6 instances per hour means that, on average, one instance is served in 10 minutes).
- Number of servers (c)
Output parameters:
- Resource utilization (p)
- Lq: Average number of instances in the queue2 Lq = p2 / (1-p)
- Wq: Average time one instance spends in the queue Wq = Lq / λ
- W: Average time one instance spends in the system W = Wq + 1/µ
- L: Average number of instances in the entire system L = λW
What are the 2 limitations of queueing analysis?
Assumption that inter-arrival (and processing) times follow a negative exponential distribution
Presented queuing analysis techniques can only deal with one process task at a time
- In other words, these basic techniques (i.e., M/M/1 and M/M/c models) are not suitable for analyzing an end-to-end process (with multiple tasks performed by multiple resources)
What’s process simulation? Name the key characteristics
- most popular and widely supported technique for quantitative analysis of process models
The essential idea is to use the process simulator for:
- Generating a large number of hypothetical instances
of a process,
- Executing these instances step-by-step, and
- Recording each step in this execution
The output of a simulator then includes the…
- Logs of the simulation, as well as
- Statistics of cycle times, average waiting times, and
average resource utilization
