Xenon
Question 1.
We calculated the average customer downtime (W) and the total number of tech reps required by utilising the given formulas and assumptions to work out the relationship between the number of machined allocated to each sales rep with the downtime and tech reps required.
The result was a plot showing:
1. the inverse relationship between the number of tech reps required and the number of machines allocated to each rep;
2. The increasing number of hours required for waiting as each rep is assigned additional machines
It is difficult to quantify an “optimal” number of tech reps. To do so, one would need to quantify the cost of each tech rep as well as the cost of each hour of downtime for the consumer. If one could make sensible assumptions for these, then we would be able to add these costs into the model and work out an “optimal” number of reps for each level of downtime.
Question 2.
We re-calculated the numbers for this question using the formulas given for multi-server queues and the fact that s=2.
We did not plot as many points on this chart as for Question 1 as this time we limited it to the 29 data variables we were given for Lq values for the multi-server queue. We used the ρ values given in Appendix 1 to work backwards and work out λp, then Np and N and the rest using the formulas given.
The result was a plot showing a similar relationship to that observed in Question 1 except now average customer downtime was significantly reduced. This is intuitive and follows the logic presented in the case as it explains that when you are able to pool tech reps into teams, it means they cover the same number of machines per person but are able to “help” each other when one may have more work than they can handle but the other one is free.
We calculated the average customer downtime (W) and the total number of tech reps required by utilising the given formulas and assumptions to work out the relationship between the number of machined allocated to each sales rep with the downtime and tech reps required.
The result was a plot showing:
1. the inverse relationship between the number of tech reps required and the number of machines allocated to each rep;
2. The increasing number of hours required for waiting as each rep is assigned additional machines
It is difficult to quantify an “optimal” number of tech reps. To do so, one would need to quantify the cost of each tech rep as well as the cost of each hour of downtime for the consumer. If one could make sensible assumptions for these, then we would be able to add these costs into the model and work out an “optimal” number of reps for each level of downtime.
Question 2.
We re-calculated the numbers for this question using the formulas given for multi-server queues and the fact that s=2.
We did not plot as many points on this chart as for Question 1 as this time we limited it to the 29 data variables we were given for Lq values for the multi-server queue. We used the ρ values given in Appendix 1 to work backwards and work out λp, then Np and N and the rest using the formulas given.
The result was a plot showing a similar relationship to that observed in Question 1 except now average customer downtime was significantly reduced. This is intuitive and follows the logic presented in the case as it explains that when you are able to pool tech reps into teams, it means they cover the same number of machines per person but are able to “help” each other when one may have more work than they can handle but the other one is free.