FacilityNetworkML - Business Process Example
The Sales Department of a Large Multinational with a Network of Processes
|
Read the introduction to FacilityNetworkML first if you have not done it yet!
In the sales department of a large multinational three types of orders arrive. Each type of order goes through specific steps or with other words through specific processes. Let us designate the five processes in the sales department with letters A, B, C, D, E. Each type of order takes a different path through these processes depending on some conditions. From historical data the average arrival rate of the three types of orders is known. The routes of the orders and the arrival rates can be seen in Table 1. It is assumed that the arrival rates of the orders are Poisson distributed (the inter-arrival times are exponentially distributed). One working day is eight hours.
Table 1 Process paths and arrival rates
The total order rate (arriving to the sales department) is 11 arrivals/day = 11/8 arrivals/h = 1.375 arrivals/h (because there are eight hours in a working day). 
The layout of the
routes can be seen on Figure 1. The average service
time (S), the μ
service rate (1/S) and the number of office workers (‘c’ servers) of the
different processes can be seen in Table 2.
It is assumed that the service times at each process are exponentially
distributed. Table 2 Service rate and initial number of
servers
From the arrival rates
of the three types of orders and from the process paths (routes) we can
calculate the probabilities that an order is moving from one process to
another. We call this the transfer probability. For example the total orders
per day is 11 orders/day, and from process A there are three routes, one to
B, one to C and one to E. The route from A to B is order ‘type 1’, which
arrives with three orders/day. The probability that an order goes in this
direction is thus 3 divided by 11 = 0.273 = 27.3%. There is thus 27.3% chance
that an order is going from A to B. If there is only one route, the
probability that an order is going in that direction is 100% (1). All of the transfer
probability calculations can be seen in Table 3. Table 3 Transfer probabilities matrix
Modeling in FacilityNetworkMLAfter we have prepared all necessary input data in the former section, we can start FacilityNetworkML and design the facility network of the business process. Each process step (A, B, C, D and E) will be modeled as a separate facility.
 Figure 2 Sales department modeled in FacilityNetworkML Calculation Results – Standard Wait Time Weight (1.0)Machine learning model parameters can be seen in
Table 4 and the results in Table 5. Table
4 Calculation 1 - ML model parameters
Table
5 Calculation 1 - Facility network
results
Calculation Results 2 – Increased Wait Time Weight (4.0) |
By increasing the weight of the wait time we can
force the machine learning (ML) model to use more servers in order to reduce
the total wait time in the system.
Machine learning model parameters can be seen in Table 6 and the results in Table 7.
Table
6 Calculation 2 - ML model parameters
|
Wait
time weight |
4.0 |
|
Maximum
number of servers |
not limited |
|
Population
size |
100 |
|
Generation
size |
100 |
|
Selection
method |
Transform ranking |
|
Crossover
method |
One-point random |
|
Mutation
method |
Single point |
Table
7 Calculation 2 - Facility network
results
|
Name |
Servers |
W
[h] |
T
[h] |
N |
Q |
|
Facility:
E |
4 |
0.022 |
1.022 |
1.405 |
0.030 |
|
Facility:
B |
2 |
0.328 |
2.328 |
0.874 |
0.123 |
|
Facility:
C |
2 |
0.271 |
2.771 |
0.693 |
0.068 |
|
Facility:
D |
2 |
0.159 |
1.759 |
0.660 |
0.060 |
|
Facility:
A |
3 |
0.048 |
0.848 |
1.166 |
0.066 |
|
Total
wait time in facility network: |
0.8278 hours |
|
Total
time spent in facility network: |
8.7278 hours |
NOTE:
Since the machine learning algorithm also uses random decisions (exploration
strategy) it is possible that you get slightly different results if you train
the model twice (this depends also on the input parameters population size
and generations size). You should train the model several times and choose
the best result!
Conclusions
- This kind of analysis of a whole network of processes can be very useful in order to determine the properties of such systems which would be otherwise very difficult or not possible to obtain.
- The average total throughput time (total time in the system or waiting time) can be calculated by adding all corresponding values of each facility. E.g. the average total waiting time (W) of orders in the whole system is 0.8278 hours (calculation 2) in this example, or the total time (T) an order spends in the system on average is 8.7278 h (service time + waiting time; calculation 2). It may be very useful to estimate these parameters.
- By increasing the weight of the wait time in the ML model we could decrease the total wait time in the system, of course with the extra cost of having one more server (employee) assigned to the first and last steps.
- The totals of N and Q may also be interesting because they tell you the estimate of how many orders are in the whole system on average (Q – in waiting, N – all orders in processing and waiting).
- And there are many more conclusions possible even in the case of this simple example.
Abbreviations
|
Abbreviation |
Definition |
|
c |
Number of servers in the
service facility. |
|
λ |
(lambda) - Mean arrival
rate of customers into the system [arrival/time unit]. It is the inverse of
the mean inter-arrival time: |
|
μ |
(mu) - Mean service rate
per server, that is, the mean rate of service completions while the server
is busy [jobs/time unit]. It is the inverse of the mean service time: |
|
N |
Steady state number of
customers in the system. |
|
Q |
Steady state number of
customers in the queue (queue length). |
|
|
Service time [time
unit]. |
|
T = W + S |
The total time a
customer spends in the queuing system (waiting + service). [time unit] |
|
W |
Steady state time a
customer spends in the queue before service begins. [time unit] |
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