Homework #1 Solution
1.
a. Applying to a Graduate School (somewhat simplified version – based on my experience)
b. Input: applicant, college degree, GRE score, 3 recommendation letters, essay, fee
Output: acceptance/rejection
Process management: school selection (for the applicant), acceptance decision (for the school), …
Resources: computer, on-line application service, school committee members (who makes the
decision), …
Activities: taking GRE test, requesting and collecting recommendation letters, writing an essay,
filing application on-line, …
c.
2.
a. McDonald’s (or 김밥천국)  price, time, convenience
Cornerstone  quality, experience, customization
b. McDonald’s  flow shop (McDonald’s deal with large volume of customers and their menu is
fairly limited; their process focus on making hamburgers quickly and efficiently with minimal
customization; although they delay the final assembly until the actual order comes in, their
process is very close to “make-to-stock.”)
Cornerstone  job shop (Corner provide variety of Italian entrees (various pastas, seafood, steak,
etc.) but the number of customers per day is fairly limited; also, high-end restaurants try to
accommodate each customer’s preference/ taste as much as possible, so often times, each dish
becomes quite customized.)
3.
Throughput = 3,500 kilograms per week (= 500 kilograms per day)
Average flow time = 2 days
Average inventory = Throughput x Average flow time (Little’s Law)
= 500 x 2 = 1,000 kilograms
Turnover rate = 1/T = 0.5/day
4.
a. First draw the flowchart with all the data given:
There are two flow units: potential admits (flow rate = 55*10% = 5.5/hr) and simple prescription
(flow rate = 55*90% = 49.5/hr). Using Little's Law at each activity, we find out the unknowns:
-
Buffer 1: R = 55/hr, I = 7, so that waiting time in buffer 1 = 7/55 hr = 0.127 hours = 7.6 minutes.
Registration: T = 2 min = 2/60 hr, R = 55 / hr, so the inventory is I = 55*2/60 = 1.83 patients.
Buffer 2: R = 55/hr, I = 34, so the waiting time is T = 34/55 hr = 0.62 hours = 37.1 minutes.
Doctor time: (i) potential admits T1 = 30 minutes; (ii) simple prescription: T2 = 5 minutes.
b. We now calculate the flow time of each flow unit:
(i) For a potential admit, average flow time (buffer 1 + registration + buffer 2 + doctor) = 7.6 + 2 +
37.1 + 30 = 76.7 minutes.
(ii) For a person ending up with a prescription, average flow time (buffer 1 + registration + buffer
2 + doctor) = 7.6 + 2 + 37.1 + 5 = 51.7 minutes.
Therefore, the average flow time is: 10% of total flow units spend 76.7 minutes while 90% spend
51.7 minutes. Thus, T = 10%*76.7 + 90%*51.7 = 54.2 minutes.
c. Calculate inventory of each type of flow unit:
(i) Potential admits: R = 5.5 patients/hr, T = 30 min = 0.5 hr, thus, I = 5.5/hr*0.5 hr = 2.75 patients
(ii) Simple prescription: R = 49.5 patients/hr, T = 5 min = (5/60) hr, thus I = 49.5*(5/60) = 4.125
patients
Thus, total inventory at the doctor is 2.75 + 4.125 = 6.875 patients.
d. The total inventory in ER = inventory in buffer 1 + inventory in registration + inventory in buffer
2 + inventory with doctors = 7 + 1.83 + 34 + 6.875 = 49.705 patients.
5.
a. Current process at Fast Service Hair Salon
Reception
3 minutes
Lulu
Shampooing
10 minutes
Stylists
Styling
15 minutes
Stylists
Billing
5 minutes
Stylists
b. The unit load from the three hair stylists is 10+ 15 +5 = 30 minutes per customer. Checking in
(Lulu) takes 3 minutes. Thus, the capacity of the stylists is 3 * 60 /30 = 6 customers per hour,
and of receptionist is 1* 60/3 = 20 customers per hour. The bottleneck are the stylists and
thus the capacity of the current process is 6 customers per hour.
Resource capacity
Process
Resource
capacity
utilization
Unit capa.
Unit #
total
Stylists
30min/cust. 2 cust./hr
3
6 cust./hr
100%
6 cust./hr
20
20
Receptionist 3min/cust.
1
30%
cust./hr
cust./hr
c. If Lulu does the billing, the unit load of the stylists is reduced to 25 minutes per customer, and
their capacity increases to 3* 60/ 25 = 7.2 customers per hour. On the other hand,
receptionist’s unit load increases to 3+5 = 8 minutes per hour, and her capacity decreases to
60/8=7.5 customers per hour. The bottlenecks are still stylists, but the capacity will increase
to 7.2 customers per hour.
Resource capacity
Process
Resource
resource
Unit load
capacity
utilization
Unit capa.
Unit #
total
2.4
7.2
Stylists
25min/cust.
3
100%
cust./hr
cust./hr
7.2
cust./hr
7.5
7.5
Receptionist 8min/cust.
1
96%
cust./hr
cust./hr
resource
6.
Unit load
a. Since Rizzo is utilized less than 100%, he cannot be the BN. Between Lester and Maddon, one
can find the BN through the table below.
resource
Unit load
Resource capacity
Unit capa.
Unit #
total
1.5/min
1
1.5
2/min
1
2
Process
capacity
Lester
40sec
1.5/min
Maddon
30sec
Rizzo
The bottleneck is Lester. Then, one can show that Rizzo’s unit load is 30 sec.
b. TFT will be 15+25+30 = 70sec.
Resource
utilization
100%
75%
75%