MS 3053
Northwest
General
Hospital
Logistic Distribution
Jamal Keeba Jefferson
4-2-2015
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Table of Contents
Executive Summary ................................................................................................ 2
The Logistic Problem .......................................................................................... 2
Available business function ................................................................................ 2
Recommendations ............................................................................................... 2
Network diagram .................................................................................................... 3
Logistic Integer Program (IP) ................................................................................. 3
Excel Spreadsheets.............................................................................................. 5
Narrative Interpretation ........................................................................................... 5
Decision and Recommendations ......................................................................... 6
References ............................................................................................................... 8
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Executive Summary
The Logistic Problem
Northwest general hospital has initiated a new procedure to ensure that
patients receive their meals while the food is still hot as possible. The hospital
should continue to prepare their food in its kitchen but will now deliver it in bulk
to one of the three new serving stations in the building. From where the food will
be reheated, the food is then placed individual trays, loaded onto a cart and
distributed to the floors and wings of the hospital. Therefore the shortest time that
it can take to serve the patient before the food gets cold.
Available business function
For this new procedure to work with the intended goal of getting the food
to clients when it is still hot; the minimum time sets which imply optimum routes
for service must be evaluated to obtain this goal.
The objective function will define all factors and constraints given the
situation- these include the kitchen, serving stations and the hospital wings.
1. Kitchen- Defines where Northwest hospital prepares the food.
2. Serving stations- Defines where Northwest hospital does the service of the
prepared food.
3. Time- long it takes to get to a given hospital wing.
4. Decision Variables- Defines the route of optimal efficiency from kitchen to
service station to hospital wing.
5. The Objective Function- Accounts for the total movement time.
6. Constraints- Defines all outbound and inbound constraints from kitchen,
service stations, and hospital wings.
Recommendations
This IP formulation will help in the determination the most optimum ways
to follow when doing the serving to the patient and ensuring that the food get to
the patient when still hot. This can be achieved by minimizing resources as much
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as possible. The solution to the Northwest hospital Case Study shows that in order
to serve all the hospital wings and get the food when it is still hot; there is a
minimum total time of 4825 minutes that will satisfy all the requirements.
Network diagram
Figure 1
Logistic Integer Program (IP)
Let Xij = transportation time from origin i to destination j.
Objective Function: Minimize total transportation time within the distribution
network.
Minimize total time =
12X14+11X15+8X16+9X17+6X18+6X19
6X24+12X25+7X26+7X27+5X28+8X29
8X34+9X35+6X36+6X37+7X38+9X39
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Constrains
Capacity constrains at origins
X14+X15+ X16+X17+ X18+X19≤ 200
X24+X25+ X26+X27+ X28+X29≤ 225
X34+X35+ X36+X37+ X38+X39≤ 275
Balance Constrains at serving stations
X01–X14- X15- X16- X17- X18- X19= 0
X02–X24- X25- X26- X27- X28- X29 = 0
X03–X34- X35- X36- X37- X38- X39 = 0
Demand constrains at outbound
X14+X24+X34= 80
X15+X25+X35= 120
X16+X26+X36= 150
X17+X27+X37=210
X18+X28+X38=60
X19+X29+X39= 80
Non-negative constraint
All Xij ≥ 0
Integer Constraint
All Xij = int
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Excel Spreadsheets
Figure 2
Narrative Interpretation
Our Northwest service procedure will contain one kitchen (which will be
the origin for the food), three service stations; station 5A, 3G and 1S with food
capacity of 200, 225 and 275 respectively. The n the hospital wings where the
food should be served will include wings; 1, 2, 3, 4, 5 and 6 with patient
capacities of 80, 120, 150, 210, 60 and 80 respectively. This logistic model should
therefore choose the optimum ways of service and food delivery to ensure that the
shortest time possible is spent to deliver food to the patient. The Northwest
hospital starts all their operation from the kitchen.
The meal capacities of the various serving station are as shown in the table
below
Figure 3
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The number of patients in the various wings of the hospital is shown in the
table below:
Figure 4
The time taken to serve patients from each service station to the various
hospital wings is as shown below.
Figure 5
Decision and Recommendations
The solution to the North West General hospital Case Study shows the
hospital will need a total of 4825 minutes so as to ensure that the patients get their
food when it is still hot and also avoid time wastage. The minutes are computed as
shown below:
FROM
TO
TIME IN
PATIENTS
TOTAL
MINUTES
SERVED
TIME
Station 5A
Wing 1
12
0
0
Station 5A
Wing 2
11
0
0
Station 5A
Wing 3
8
120
960
Station 5A
Wing 4
9
0
0
Station 5A
Wing 5
6
0
0
Station 5A
Wing 6
6
80
480
Station 3G
Wing 1
6
80
480
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Station 3G
Wing 2
12
0
0
Station 3G
Wing 3
7
0
0
Station 3G
Wing 4
7
85
595
Station 3G
Wing 5
5
60
300
Station 3G
Wing 6
8
0
0
Station 1S
Wing 1
8
0
0
Station 1S
Wing 2
9
120
960
Station 1S
Wing 3
6
30
180
Station 1S
Wing 4
6
125
750
Station 1S
Wing 5
7
0
0
Station 1S
Wing 6
9
0
0
Total time
Table 1
4875
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References
Defining integrality constraint in excel solver. (n.d.). Retrieved April 2, 2015,
from https://www.or-exchange.org/questions/4403/defining-integralityconstraint-in-excel-solver
Garfinkel, R. S., & Nemhauser, G. L. (1972).Integer programming (Vol. 4). New
York: Wiley.
Integer Programming 9 - MIT. (n.d.). Retrieved April 2, 2015, from
http://web.mit.edu/15.053/www/AMP-Chapter-09.pdf
Wolsey, L. A. (1998). Integer programming (Vol. 42). New York: Wiley.