Problem 1: Little’s law application In Children’s Hospital in Seattle there) are
ID: 415681 • Letter: P
Question
Problem 1: Little’s law application
In Children’s Hospital in Seattle there) are on average 119 births per week (assuming 7 days per week). Mothers and babies stay, on average, two days before they leave the hospital. In Swedish hospital (also in Seattle), the average number of births per week is 35. Mothers and children stay in the hospital two days on average.
a. How many new mothers are staying in Children’s Hospital (at any time point)?
b. How many new mothers are staying in Swedish Hospital (at any time point)?
c. The directors of the two hospitals are negotiating unifying the children wards of the two hospitals. They believe that by doing so they will be able to reduce the number of new mothers staying in the hospital. Are they correct? How many new mothers will stay, on average, in the unified ward? You may assume that the average number of births and the lengths of stay of the new mothers will not change.
Note: please show your process of getting the results! Only providing the final answers is NOT acceptable and will get me a 0%.
Explanation / Answer
Solution:
According to Little’s law,
Work in Process, WIP = Throughput Rate x Throughput Time
WIP = TR x TT
(A) Number of births per week in Children’s hospital, Throughput Rate (TR) = 119
Number of days mothers and babies stay in hospital = 2 days (out of 7 days per week)
Throughput Time (TT) = 2/7 weeks
Therefore, Work in process is calculated as;
WIP = TR x TT
WIP = 119 x (2/7) = 34
WIP = 34
On average there are 34 new mothers staying in the Children’s hospital at any time point
(B) Number of births per week in Swedish hospital, Throughput Rate (TR) = 35
Number of days mothers and babies stay in hospital = 2 days (out of 7 days per week)
Throughput Time (TT) = 2/7 weeks
Therefore, Work in process is calculated as;
WIP = TR x TT
WIP = 35 x (2/7) = 10
WIP = 10
On average there are 10 new mothers staying in the Swedish hospital at any time point
(C) Number of births per week in Children’s and Swedish hospital combined or in the Unified ward,
Throughput Rate (TR) = 119 + 35 = 154
Number of days mothers and babies stay in hospital = 2 days (out of 7 days per week)
Throughput Time (TT) = 2/7 weeks
Therefore, Work in process is calculated as;
WIP = TR x TT
WIP = 154 x (2/7) = 34
WIP = 44
In the Unified ward, there will be on an average 44 new mothers staying at any time point. This means the number of mothers staying in the hospital will not get reduced even after unifying the children wards. Hence, the directors of the two hospitals are wrong in their approach of unifying the children wards of the two hospitals.