(This
project will be prepared in-groups of two)
In 1996, two leading beer breweries in Turkey have merged. Each of these breweries had its own depots
and they continued to operate after the merger. The management will renew the
rent contracts for those depots found useful.
At this point, the management believes that there are too many depots
and is convinced that a study should be carried out to determine
·
How many depots are really needed
·
Where to locate them
·
How to allocate the customers to the depots
In the problem formulation, it can be assumed that the depots are uncapacitated. Actually the depots are not uncapacitated, however, their capacity is sufficiently flexible, and throughput can easily be increased or decreased. Figure 1 represents the overall distribution system. Management assigns highest priority to the depot distribution problem and expects considerable savings from solving this problem. So consideration of the lower part of the center branch only is required.
2 breweries
Distributors depots supermarkets
Households hotels/bars retail shops distributors dealers
Figure 1. The distribution system
Consider the following
information.
Products:
The company distributes about 15 different products. Since the distribution cost per unit is
virtually the same, the products can be aggregated into one single product.
Customers:
There are about 46,000 possible depot customers belonging to 5
different types as seen from Figure 1.
The customers can be aggregated into a much smaller size because of the
constraints on the problem size. A
preliminary study has been carried out to determine how the customers can be aggregated. First the customers were aggregated by
‘city’. The second step was to
aggregate the five customer types in a single type to be served weekly by a
truck (assuming 52 weeks annually).
This reduced the customer types to 52.
In Table 1, the number of customers in each city is summarized.
Potential Depot Locations:
Each customer zone can be a potential depot location.
Depot Fixed Costs:
The fixed costs for the depots include:
¨
Rent for the warehouse. The
expected annual rent for a depot in each of the cities is given in Table 1.
¨
Wages for the administrative staff and warehouse operators.
¨
Cost of the utilities
In Marmara, Aegean, and Mediterranean regions 15 workers and a chief
will be employed for each depot, whereas in other regions 10 workers and a
chief will be employed. Workers will be
paid around the minimum acceptable wage while the chiefs get 1.5 times as much
as the drivers can get. The annual cost
of electricity, water, insurance, etc. will incur around 30% of the annual rent
paid by the company for each depot.
(minimum acceptable wage can be taken as 150,000,000 TL) - note that
this is the amount to be paid by the employee, not the amount a worker gets.)
Transportation Cost:
Lack of detailed information (distances travelled, driving time, time
to load and unload the trucks, etc.) makes it difficult to estimate
transportation costs. However, the
transportation costs can be expressed as a function of the following:
(i)
Distances: The distance between any two points in the map via highways can
be found by using the well-known from-to matrices on the lower right-most
corner of the highway maps. Another
method can be to use the formula:
where K is
a correction factor that is used for the anomalies of the road system and is
usually a value between 1 and 2.
To account for the
round-trip within a city, an additional 10 km can be added to the distance
found.
(ii)
The annual number of trips to each city: Here it is known that an
average trip includes 40 customers.
(iii)
Wages of the drivers. A driver
can work 8 hours a day. Their annual
wage will be at least twice the annual salary of an engineer working for as a
civil servant in the government. (An
engineer, working as a civil servant, costs about, on the average, 400,000,000
TL per month)
(iv)
Operating costs of the trucks, including the fuel costs, maintenance
and repair costs. It can be assumed
that maintenance and repair is no more than 25% of the total fuel expenditure
since the fleet consists of new trucks. (An average truck makes 6 kilometres
with a litre of gasoline. Take the
current gasoline price as 500,000 TL/lt.)
Expected Methodology
You are expected to solve the location-allocation problem. The following aspects should be included in
your study:
¨
The description of your approach (your solution plan, how you have
overcome computational difficulties, assumptions you needed to have and why you
needed, other simplifications you have applied, etc.)
¨
Determine the location of the depots using both continuous and discrete
models and compare the results.
¨
Plot total cost as a function of the number of depots opened.
¨
Conduct sensitivity analysis for different parameters, like changes in
the price of fuel, unexpected changes in the number of customers in regions,
etc.
¨
Your favorite solution alternative and the reason behind it.
Additional comments on report writing will be given after the grading
of the first projects is finished.
Table 1. # of customers and annual rents by zone (rents in million TL)
Zone |
# of customers |
annual rent |
Zone |
# of customers |
annual rent |
İstanbul-A |
2900 |
60 000 |
K.Maraş |
1000 |
18 000 |
Ankara |
2200 |
45 000 |
G.Antep |
900 |
24 000 |
Çankırı |
300 |
24 000 |
Malatya |
1100 |
18 000 |
Bolu |
350 |
24 000 |
Samsun |
1000 |
24 000 |
Zonguldak |
300 |
24 000 |
Amasya |
300 |
18 000 |
Eskişehir |
550 |
24 000 |
Çorum |
800 |
18 000 |
Sakarya |
250 |
30 000 |
Adana |
1800 |
35 000 |
Kocaeli |
950 |
30 000 |
Hatay |
500 |
24 000 |
Bilecik |
200 |
24 000 |
İçel |
750 |
24 000 |
Bursa |
1800 |
35 000 |
Antalya |
2000 |
35 000 |
Tekirdağ |
700 |
24 000 |
Alanya |
1000 |
35 000 |
Kırklareli |
500 |
24 000 |
Side |
500 |
24 000 |
Edirne |
700 |
30 000 |
Burdur |
350 |
18 000 |
Çanakkale |
600 |
30 000 |
Isparta |
400 |
18 000 |
Balıkesir |
400 |
30 000 |
Fethiye |
600 |
24 000 |
Manisa |
500 |
30 000 |
Marmaris |
1000 |
35 000 |
İzmir |
2500 |
40 000 |
Bodrum |
1200 |
35 000 |
Aydın |
800 |
30 000 |
Tokat |
300 |
18 000 |
Uşak |
300 |
24 000 |
Sinop |
350 |
18 000 |
Kütahya |
250 |
24 000 |
İstanbul-E |
2900 |
60 000 |
Afyon |
300 |
24 000 |
Ordu |
550 |
18 000 |
Konya |
1500 |
30 000 |
Giresun |
400 |
18 000 |
Kırşehir |
300 |
24 000 |
Trabzon |
700 |
18 000 |
Nevşehir |
1500 |
24 000 |
Rize |
400 |
18 000 |
Kayseri |
950 |
30 000 |
Erzurum |
800 |
18 000 |
Niğde |
600 |
24 000 |
Diyarbakır |
1200 |
18 000 |