The intent of this study is to develop an understand the component interaction with a organizational environment which provides on call solutions to an installed base of clients. The approach will be to develop a foundational model and then elaborate the model providing additional component detail.
We begin with an initial set of assumptions as depicted in the following influences diagram.
The assumptions depicted here are that the number of Installed Systems directly influences the Call Volume with the actual Call Volume being some fraction of the number of Installed Systems. This fraction is represented by System Call Fraction. As the number of Installed Systems increases it should influence the Call Volume to increase. The System Call Fraction is assumed to directly influence the Call Volume also. The Call Volume interacts with the number of Resources available to respond to calls and the number of calls which can be responded to by a Resource in a day. This is depicted as the Resource Call Rate.
This initial set of interactions can be represented as an ithink model [scst01.zip - 3k] as follows:
With an initial set of variable definitions and equations as follows:
- backlog(t) = backlog(t - dt) + (call_volume - res_rate) * dt
- INIT backlog = 100
- call_volume = inst_sys * sys_call_fract
- res_rate = resources * res_res_fact
- inst_sys = 1000
- resources = 10
- res_res_fact = 10
- sys_call_fract = .1
The initial values of the constants were chosen for this system to produce a steady state which when run produces the following results.
We know that we are not dealing with a steady state operation as the Sales organization is continually endeavoring to sell and additional systems which will increase the number of Installed Systems as depicted in the following diagram.
This will result in a modified ithink model [scst02.zip - 19k] as follows:
If we then run this model we begin to get a sense of the interactions depicted in the following graph.
What this indicates is that with a Sales Activity which results in an additional 5 systems installed a month the backlog does not grow in a linear fashion but more an exponential manner. The addition of another resource results in a rapid decline in the backlog. It is quite evident that the Call Volume is insufficient to support 11 Resources on a continual basis, yet reducing Resources back to the base value of 10 caused the Backlog to grow rapidly again. And, you know only too well it isn't possible to increase and decrease Resources rapidly as the Backlog would warrant.
Also, the one question that has probably come to mind already should have something to do with money. How could one even begin to consider this situation without considering where money comes into play in the model. Well here is the beginning of it.
This diagram adds the assumptions that there is a Service Revenue produced from the interaction of Installed Systems and Revenue Per System. The other side of this has to do with the Service Expense associated with the interaction of Resources and Resource Rate. Service Revenue and Service Expense then interact to produce Cash Flow.
These Cash Flow components then added to the ithink model [scst03.zip - 28k] then becomes:
And some initial interactions with this model produces the following trends:
The perceived implications of these interactions are as follows: