Christine,
This is indeed a complex question. One, you want to formulate the business process for an order-to-cash process (the industry name for it); and Two, you want to simulate how long it takes to do (execute) the process.
- Lets start with 1) It now depends on the order, is it a single or multiple item order? Is it for an item we have in stock? ( I assume we selling items rather than services). Is the order for a known customer or do I have to create the customer first? etc.
- This bring us to 2) how long does it take? For this task you need to simulate the process and ensure that you cover all the branches (out of stock, new customer etc).
Having said the above and without belabouring you with concepts of queuing theory, managing constraints (people, resources and time), simulation and linear programming, I still think your approach of using a matrix is sound. It might not have all the features of the special tools out there but it gives you some data at the “aggregate” level. For example, if you have all you tasks in Column A. The next column (say C) has the times for a “New Order”; Column D has the times for a “Repeat order” etc. Column E has the time for the “Out of Stock” etc.
When you summarise your columns you’ll get the “aggregated” time for New Orders, Repeat Order and Out of Stock.
When you summarise your rows, you’ll get the “aggregated” time for your task, such as Receive Order, Validate Order, Establish New Client, Confirm Stock availability etc.
For each of these tasks create an activity called Wait_Receive_Order, Wait_Validate_Order, Wait_Establish_New_Client, Wait_Confirm_Stock to determine how long an activity WAITs to be processed. One of your objectives is to have this wait “variable” is small as possible.
When you want to add resources and manage constraints you’ll need a tool. There are tools available for you to simulate these activities/processes. Most of the latter tools rely on BPMN to define the activities, delays and events in a process. BPMN resources and Tools see http://bpmsoftware.wordpress.com/2008/03/11/free-bpmn-and-not-only-tools/
Have a look at BIZAGI at www.bizagi.com and watch their demos.
Also cast your eye over the first part of this presentation the latter part goes crazy with technologies and stuff http://www.ibm.com/developerworks/kr/event/seminar/dwlive_soa/download/SOA_new_business.pdf.
All the best
K.