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Fall 1999

IE 425 Project on Facility Location

Due: Jan. 25st, 2000 (Monday, 5:00 p.m.)

(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