Completion of Projects by Orion Controls

Mr. Armstrong estimates from the previous data that about 30 projects come in per year from the permanent contract clients, 10 per year from the occasional clients, and if he implements the new measures, another 10 per year from new clients. This makes an estimated average of 50 incoming projects per year. A single team can handle 12 projects at a time, and as previously estimated from the permanent contract clients, these last an average of 3 months each. He believes that this implies that each team can finish an average of 36 projects per year. He currently has two teams working for him and is considering how many project teams he should be running in order to minimize his costs. Projects have always been randomly assigned to the available teams. He knows that the cost for running each team is approximately $300,000 per year and has estimated the opportunity cost for making a company wait to start a project at $800 per day.

Mr. Armstrong is also considering assigning each team to a specific type of client. His focus would be keeping a type of team only on projects from permanent contract clients and another type of team on projects from new and occasional clients. From more recent data it appears that the new and occasional client projects may take longer since they are less familiar with Orion Controls and there is more initial paperwork to be completed. This creates only a small difference but would mean teams focusing on new and occasional client projects could only complete an average of 34 projects per year rather than 36. He would like to know how this new model and information changes his estimated costs. He would also like to know how many of each type of team he should use to minimize his total costs. He expects that projects would still be assigned randomly between multiple teams of the same type.

Questions and Concepts to Consider:

M/M/1 Queues, assume exponentially distributed data

1. What kind of results should Mr. Armstrong expect if he uses a single queue system with all project and client types together, considering projects randomly assigned to the teams?

2. How many teams should Mr. Armstrong run to minimize his total costs?

3. What is the difference when considering two separate teams which only process specific client types?

4. How many teams of each type should he have to minimize his total costs?