ISyE 4803 – Homework 5
Due: November 12, 2009 (15 Points)
NOTE: In answering these questions, do not copypaste text from the articles. Use your own words.
1.
(6 points) A clinic has
S
doctors. A schedule needs to be created for the
doctors to satisfy the patients’ needs during the working hours of the hospital.
The clinic is open for T hours per day. There is a forecast of patients arriving
at each hour, and it is denoted by f
j
, j=1, …, T. The time (in hours) needed to
attend each patient is 1. Let b
ij
=1 if doctor i works during hour j, and b
ij
=0
otherwise.
a.
(2 points) Write a set of constraints to ensure that there are enough doctors
working at each hour to attend all the patients forecasted to arrive during that
hour.
j
S
i
ij
f
b
≥
∑
=
1
j=1,…,T
b.
(2 point) Write the objective function to minimize the total number of doctor
hours needed during the day.
minimize
∑∑
=
=
S
i
T
j
ij
b
1
1
c.
(2 points) Formulate a set of constraints to ensure that the work hours of
doctor i are consecutive, for all i=1,…,S. (For example, if the doctor is
working during the hours of 3,4,5, and 6, and is not working on the 7
th
hour,
then he should be off duty for the remaining hours of that day.)
1
1
)
1
(
+
+
=
+

≤
∑
ij
ij
T
j
k
ik
Mb
b
M
b
for i=1,…,S,
j=1,…,T1 where M is a large
number (e.g., M=T is a sufficiently large number to make this constraint
work)
2.
(2 points) Please refer to the Big Depot Game case:
a.
(1 points) Uncertainty in the size and the location of a disaster were identified
as important factors leading to logistics challenges when planning for a
disaster. Among other challenges faced during disaster preparedness and
response are (i) the uncertainty in the timing of the disaster (and the resulting
demand) and (ii) the uncertainty in supply availability. How are these
challenges similar or different from the ones faced during daytoday
operations of a company such as BigDepot?