Abdullah Bilgin
Selman Benlioğlu
INDR 460
Case Assignment - 1
Part - 2
In part 1, we discuss the current capacity of Efes by thinking years separately. In
this part, we find an optimal solution for next three years together and also we think
up the idea of opening new breweries and to expand them. These new breweries
can be build at Izmir, Sakarya and Adana. The report includes mixed linear
programming model and answers to the some related problems.
MIP Formulation
Objective: To minimize the total cost
Decision Variables:
( calculated seperately for every three years)
Xa- i - j : The amount of malt that send from malt plant i to brewery j in year a
(Million ltr)
Ya- j - k:The amount of beer that send from brewery j to distribution center k in
year a (Million ltr)
Oa - m : Binary variables that equals 1 if a new brewery opens to m in year a
equals 0 otherwise.
Ea - m : Binary variables that equals 1 if a new opened brewery m expanded in
year a , equals 0 otherwise.
i : AF, KO, IM ; j : IS, AN, IZ, SA, AD ; k : IS, IZ, ANT, BU, KA, EX ;
m: IZ, SA,AD ; a: 1,2,3.
Min
z=
a [ ji
c(i,j) * ( Xa - i – j ) +
kj
c(j,k) * ( Ya - j – k )
m (Oa - m)* (CO-m) + m (Ea - m)*(CE-m) ]
+
/ (( 1 + int )^(a-1)
)
+ b [
ji
b: 4,5,….20.
c(i,j) * ( X3 - i – j ) +
kj
] / (( 1 + int )^(b-1) )
c(j,k) *( Y3 - j – k )
y:1,2,3,4,5,…,20
CO-m : Cost of opening brewery to m
CE-m : Cost of expanding brewery in m
s.t
Malt plants cap.
j
Xy - AF - j <= 30
for all y
j
Xy - IM - j <= 20
for all y
Brewery cap.
k
Yy - IS - k <= 220
for all y
j
Xy - KO - j <= 68 for all y
k
Yy - AN - k <= 200
k
Yy - m - k <= 70*(
for all y
r=1y Or - m)
r=1y
+ 50*(
Er - m )
for all y , for all m
Balance
k
Yy - j - k = (Xy-AF-j + Xy-KO-j ) * 8,333 + Xy-IM-j * 9,091
for all y ,for all
j
Demand
j
Yy - j - k <= dk
for all k : IS, IZ, ANT, BU, KA, EX
for all y : 1,2,3,….,20
( dk : Demand for all distribution centers)
New breweries
r=1a Or - m
>=
r=1a Er - m
a Oa - m
<= 1
for all m
a Ea - m
<= 1
for all m
for all a:1,2,3. , for all m
Non-negativity and Binary
All of X and Y variables are positive; O and E variables are binary.
Question 1 : Opening a new brewery or capacity expansion are very costly
investments. If they put into the objective function, it will directly result as not to
open or expand because all of the production or transportation benefits that gained
from that new investment can not be comparable with the cost of that investment.
Because of that, the cost of the investment must be dividing into some parts like for
every year. By that way, the balance of costs and benefits can be made.
Otherwise, the optimal solution never results to invest. Also if the cost and benefits
are compared for only the first year that the investment made, the benefits for the
future years that the new brewery or expansion are made are ignored. This is also
caused some unreasonable. For these reasons, the cost of the new investments
and the benefits gained from that investment for the future years must be
combining together in a time horizon (20 years in the solution).
Question 2 : Because the current solution, in another word opening in Izmir in
year 2 and expanding it in year 3, is optimum, we can say that to open and/or
expand early would result a higher objective function.
For higher opportunity cost of capital value, opening and expanding years
do not change. As an example, we take opportunity cost as %12 instead of %10,
solution does not change. Even in %60 interest rate, solution does not change.
For lower opportunity cost of capital value, opening and expanding years do
not change for a while, then become earlier. For example, with opportunity cost of
% 8 and %6, solution does not change. For opportunity cost of % 4, in optimal
solution, opening year becomes 1 and expanding year becomes 2. For opportunity
cost of % 3, in optimal solution, opening and expanding years both become 1.
Question 3 : We use 20 year long time horizon to see the effects of opening or
expanding new breweries more accurately although we do not have demands of
left 17 years. Thus, we use the demand of third year as same with left 17 years. So
this part of the model can be thought most prone.
We look up which new breweries have smallest transshipment cost to any
distribution centers. For example, a new brewery in Izmir has smallest
transshipment cost of distribution center Izmir, Antalya, and Export. A new brewery
in Sakarya has smallest transshipment cost of distribution center Bursa. So we
make some changes of demands of these sensitive cities to new breweries to see
the effects of opening/expanding schedule. For example, if we increase the
demand of distribution centers Izmir, Bursa, Antalya, and Export, the difference in
the optimal solution is to open new brewery in Sakarya in year 3. If we decrease
them, difference becomes not expanding the new brewery in Izmir. Finally, we
should spend more effort on the accuracy of distribution centers that relatively
close to potential brewery places.