Question

In many services, the acquisition and allocation of capacity plays a significant role in determining the level of operational responsiveness. Our purpose in studying this case is to develop an understanding of the relationship between capacity allocations and responsiveness. We will also try to gain an appreciation for the role that queuing models play in providing insight for operational decisions. The primary focus of your executive summary should be the following: • Assuming that you have 18 patrol cars, how should you allocate them among the 6 precincts? (Each car can be assigned to only one precinct.) What is the objective that you are trying to achieve when you make your allocation decision? Are there alternative objectives that should be considered? • Why might the actual delays experienced by callers to 911 be different from those predicted by the model that you have used?

Answer 1

Solution and Explanation:

Findings and Conclusions

Under the assumption, we have 18 cars. So now we have 3 extra cars to allocate. For each precinct, we have two options: k and k+1.

1. There are apparent decrease of waiting time in B,D and F after we assigned an extra car to each of them. So we recommend to put the 3 extra cars to B,D and F.

2. If we follow 1. , the longest waiting time in the system is 0.9587 hour, which means we can limit the waiting time in the system into 0.96 hour.

Recommendation

If we were not constrained to only 18 cars,

1. We would recommend to cover the precincts in the order of F, A, D, B, C and E if we consider the percentage of high priority calls as the key factor.

2. We would recommend to cover the precincts in the order of D, B, A, F, C and E, if we consider the number of felonies per Sq. Miles (the travel time would also matter) as the key factor.