(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.

Consider the following information.

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.

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.

Each customer zone can be a potential depot location.

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.)

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:

1. 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.

 

2. The annual number of trips to each city: Here it is known that an average trip includes 40 customers.

 

3. 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)

 

4. 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.)

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.