University of Engineering and Technology Peshawar Jalozai
Campus
Department of Industrial Engineering
Subject: Industrial Facilities Design
(LAB)
Lab No # 08
Submitted to: Engr. Muhammad Zubair
Submitted by: Zaka Ullah
Registration No: 18JZIND0106
Date: 25th Feb, 2022
Lab No 08:
To Allocate Multiple Facilities of different types using Half-Sum method
Objectives:
 To learn about the concept of Half-Sum Method.
 To learn about the allocation of multiple facilities of different types.
 To learn about the allocation of multiple facilities of different types using Half-Sum
Method in MS Excel.
Introduction:
Half-sum method is used to find the location of a new facility. According to this method, the X
coordinate of the new facility will be such as the X coordinate of some existing facility; and the
optimum X coordinate will be such that no more than half the total weight is to the left of X and
no more than the half of the total weight is to the right of X. Hence the location of new facility will
be on the median or half the sum of the coordinates of the existing facilities. That is reason due to
which this method is known as half-sum method.
Both these properties also apply in determining the optimum value of Y. Half-sum method is used
single-facility location problems considering only the cost of transportation.
Problem Statement:
Procedure:
Open the MS Excel and create a new sheet, insert the data in the sheet.
Figure 8.1
Now after inserting the data, calculate Abscissa for F1. Arrange the abscissa of existing facilities
in ascending order and take distance travelled here no. of trips of facility F1. Now calculate
cumulative no. of trips using Sum command as shown below;
Figure 8.2
Now in the next step, applying optimality rule, we have to take 50% of the cumulative value i.e.
𝟓𝟎% ∗ 𝑭𝟏𝟕 = 𝟏𝟖. So we can clearly see that both the x coordinate 1 and 3 can satisfy the value 18
so to select the exact coordinate we need to take average of the weight of both the x coordinate i.e.
1 and 3 so it will be 8+11=19 which is divide by 2 which become 9.5. Thus its Abscissa will be 3
as shown below in the figure.
Figure 8.3
Now in next step, we cannot assign it here because if we assign it after 8 i.e. at coordinate 1 then
it’s below value is higher than 9.5 that is 11. Thus we have to assign that at coordinate 3 i.e. after
11. Now for Abscissa or X-coordinate of F2, arrange the abscissa of existing facilities in
ascending order and take distance travelled here no. of trips of facility F2. Now calculate
cumulative no. of trips using Sum command taking F1 as one coordinate as shown below in the
figure.
Figure 8.4
Now in next step, as median is 22 which lie at facility 2 cumulative trips so Abscissa of F2 will be
that of facility 2 i.e. Abscissa of F2 = 3 as shown as shown below in the figure.
Figure 8.5
Now as the calculation of Abscissa of F1 was without the consideration of F2 so again calculate
the Abscissa for F1 taking facility F2 into consideration. So arrange Abscissa of existing facilities
along with F2 in ascending order and taking no. of trips of facility F1, calculate cumulative no. of
trips as shown below in the figure.
Figure 8.6
Now as the Median = 21 which lie at facility F2 cumulative trips hence Abscissa for F1=3 as
shown below in the figure.
Figure 8.7
Now the Abscissa of new facility = 3. Repeat the procedure from step 2 to calculate the Ordinate.
Now to calculate coordinate for F1, arrange the coordinates of existing facilities in ascending
order and take distance travelled here no. of trips of facility F1. Now calculate cumulative no. of
trips using Sum command.
Now as the median is 18 which lie at facility 2 cumulative trips so ordinate of F1 will be that of
facility 2 i.e. Ordinate of F1 = 1 as shown below in the figure.
Figure 8.8
Now for ordinate of F2, arrange the ordinates of existing facilities in ascending order and take
distance travelled here no. of trips of facility F2. Now calculate cumulative no. of trips using Sum
command.
Now as median is 22 which lie at facility 2 cumulative trips so ordinate of F2 will be that of facility
2 i.e. ordinate of F2 = 1 as shown below in the figure.
Figure 8.9
Now as the calculation of ordinate of F1 was without the consideration of F2 so again calculate
the ordinate for F1 taking facility F2 into consideration. So arrange ordinates of existing facilities
along with F2 in ascending order and taking no. of trips of facility F1, calculate cumulative no.
of trips.
Here the Median = 21 which lie at facility F2 cumulative trips hence Ordinate for F1=1 as shown
as shown below in the figure.
Figure 8.10
So from the above calculation we got our both X and Y coordinate for F1 and F2 that is (3,3) and
(1,1) respectively. So the resulted table will be as shown below in the figure.
Figure 8.11
Conclusion:
In this lab we have learned about the concept of Half-Sum method. We also have practice
different formulas and methodology of half sum method. Also we have find the optimum
locations for multiple facilities using half sum method in MS Excel.