Supply Chain Network Planning for Humanitarian Operations During Seasonal Disasters Page: 39
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Note that the cost structures of products are different at different locations. This can
happen for example, when suppliers quote prices based on their location, transportation cost and
4.4 Model 4- Multiple Locations, Multiple Products of Any Quantity with Full Forecasting and
Quality of Information
Model 4 differs from Model 3 only in n and J. With full information n = J. Replacing n of
equation 14 by J, I get the pooled mean and variance as
(O1,2,...,J)~, N 0j,((1-p)(J-1)+ J[1+(J-1)p ](1-r) 2 (20)
Expression 21 yields the optimal order size to full forecasting scenario.
/ J I J I
S -k2ji p -Z Ik2ji c 2ji
y- = 8 +(I-' -1i--1 i- ... (1- p)(J-1) + J [1+ (J-1) p] (1- r) o (21)
=lk2jP j l - k2jiVji
j=1 i=1 j=1 i=1
The objective function for full forecasting can be obtained from equation 14 by replacing n by J.
The optimal second instance order size for the ith product of jth location (xhi) can be calculated
from equation 18. A numerical example is introduced to demonstrate analytical results.
Example 4: A relief agency plans to distribute relief packets to persons, who live in seven
counties in the West Virginia region, which is prone to an imminent flood. All the persons
seeking shelters in this region need relief packets. Using HAZUS software, the agency generates
an estimate of affected population for four potential scenarios. HAZUS data (Table 4-3)
(http://www.regionvii.com/images/18_AppxHAZUSDATA.pdf, accessed 10/10/12) include
the estimation of number of households expected to seek shelter in each county. I assume that the
number of persons affected follows a normally distribution with a mean of 200 and a standard
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Ponnaiyan, Subramaniam. Supply Chain Network Planning for Humanitarian Operations During Seasonal Disasters, dissertation, May 2013; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc271880/m1/47/: accessed June 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; .