CONSIDERATIONS ON THE LOCATION STUDY OF FACILITIES

Defining the location of facilities in a logistics network, be they factories, warehouses or transport terminals, is a common and one of the most important problems for logistics professionals. Its importance stems from the high investments involved and the profound impacts that location decisions have on logistical costs. Characterized by a high level of complexity and the intensive use of data, location studies currently make use of new information technologies that make it possible to treat logistical systems in an effectively integrated manner.

Below are some of the many examples of Brazilian companies that have recently carried out facility location studies. Motivated by the search for greater competitiveness, either by increasing the efficiency of their operation or by increasing the level of service offered, these companies have in common the fact that they have used computational models of their logistics network to help with studies of the location of their facilities.

• A beverage industry was preparing its expansion plan for the coming years. Forecasts indicated demand growth and a clear change in the consumption profile: in some regions of the country certain products should have their demand heated up while other regions showed a stabilization trend. This behavior, however, was quite different in different regions of the country. The company had a logistics network with factories in several states, each one capable of producing a certain mix of products. The company's management needed to decide how to expand the capacity of its factories: whether to install new production lines in the current factories or whether to open new factories to install the new lines. It still needed to decide in which of the existing factories the expansions should be carried out or in which municipalities to open the new production units.• The recent deregulation of the fuel distribution sector gave freedom for companies in the sector to define their supply chains – previously it was the government itself, through regulatory agencies, who defined. In one of these companies, the first reaction was to review the number and location of its distribution bases, the choice of which modes to use in transport between bases and the review of the allocation of demand points – the stations – to the bases.• A company which works with catalog sales and home deliveries, faced with growing competition, decided to increase the level of service offered, reducing the delivery time of its products to end consumers. In addition to a review of its information systems, the company began a study on the restructuring of its distribution network to assess what changes would be necessary in order to meet the desired level of service: would it be necessary to open new distribution centers closer to the areas of market? If so, where should they be located? And what would be the impact on inventory and transportation costs? How much would the reduction in delivery time be? Would it be worth it?

STRUCTURE OF LOCATION PROBLEMS

In general, location studies deal with the problem of minimizing the costs of a logistics network, which is subject to capacity constraints of facilities, having to meet a certain demand and having to satisfy certain service level limits. The input data for analysis are demand forecasts for each product, capacity limitations and production rates, probable installation locations, possible connections between them and the respective transportation costs of each mode.

Figure 1 below schematically shows a generic logistics network, where its various links are represented: suppliers, factories, primary distribution centers, secondary distribution centers (or terminals) and demand zones. The lines represent the possible connections between these links, that is, the possible physical flows between each network element. What we commonly want to determine is:

• Where should factories be located?
• Which suppliers should be used?
• How many distribution centers should the company operate?
• Where should they be located?
• Which customers or market zones should each distribution center supply?
• What product lines should be produced or stocked at each plant or distribution center?
• What modes of transport should be used for procurement and for distribution?

These issues are highly interdependent and therefore should not be analyzed sequentially or segmented. In its analysis, it is necessary to consider the existing trade-offs between decisions related to transport, the positioning of stock in the network and the number and location of installations. What is intended is to obtain an optimal solution, which meets the desired service level at the lowest total cost of operation (figure 2).

COMPLEXITY AND DIMENSION OF THE PROBLEMS

Localization problems typically have a very high complexity and involve a very large volume of data. The complexity is due to the fact that the analysis has to deal with an extensive set of decision variables that influence each other. Furthermore, the number of possible alternatives to be analyzed and compared is very high, even for small problems. It's not uncommon to have to work with hundreds of products, hundreds of potential terminal sites, distribution centers or factories, dozens of suppliers, multiple modes of transport and thousands of customers.

These numbers give an idea of ​​the volume of data to be handled, since the analysis requires detailed information about demand, transport costs, production costs and rates, location of customers, location of current and likely points of storage and supply, etc. And here begins one of the main difficulties in carrying out these studies: in most companies, data exists but is not structured, as there are normally no information systems aimed at generating it. As a consequence, about 2/3 of the time in facility location studies is spent on data acquisition and preparation!

Although the difficulties seem great, a large number of computational tools are currently available that make easier the modeling and optimization tasks of the problem and the treatment of the large mass of data typically present in location studies. That's what we'll cover next.

TOOLS FOR ANALYSIS

Since the 70s, the foundations for computational applications of facility location studies had already been developed. But problems of practical, large-scale dimensions were basically restricted to the academic community or government agencies, through the use of mainframe computers. It was very recently, after the widespread use of personal computers equipped with high-speed processors, that the commercial use of computational tools applied to the location problem expanded.

In Brazil, the offer is still limited, but representatives of some of the main suppliers of software in this area are already present. However, as geographic barriers are not such serious limiting factors in this case, access to the same products available on the international market is possible.

The options are many and the differences start with the price. They range from US$ 10.000 to US$ 150.000 apparently depending on whether or not consultancy is included to carry out the localization study itself, training for system operation or after-sales support.

Most software have predetermined models of logistics networks. They are generic models that represent most of the real systems. The difference between them lies in the ability to represent the operational costs and constraints involved. Virtually all consider transportation costs (supply, distribution, and transfer), storage costs, and purchase or production costs. The same does not happen with inventory costs that are more related to the temporal dimension, still not well handled by location software, more focused on the spatial or geographic dimension.

The basic constraints are capacity constraints, which limit product flows through facilities, demand constraints and, less basic due to greater modeling difficulty, service level constraints. The latter are generally of two types:

• those that limit the maximum service time by limiting the maximum distance between a demand zone and the nearest facility
• those that limit the maximum number of installations that can serve a certain demand zone, thus guaranteeing exclusivity of supply.

Most localization software uses graphical interfaces to control and vary parameters through menus, rotate the model, inspect the results and generate reports. Another very common characteristic is the possibility of visualizing the results through maps, thus allowing a more qualitative analysis of the results, as shown in figure 3. They also offer the ability to communicate with commonly used database systems, such as database managers databases, electronic spreadsheets, which facilitate the handling, preparation and checking of large masses of data.

The most used solution methods are heuristic methods, simulation and optimization, more specifically mixed integer programming (MIP), the latter being the predominant technique in the vast majority of software. One of its main advantages is the ability to properly model the fixed and variable costs of a logistics network. Furthermore, as it is an optimizing technique, it guarantees that the solutions found are the best possible within the set of assumptions adopted. Its main disadvantage is that, depending on the size of the problem, long processing times are required, which may even make its resolution unfeasible. Heuristic methods, on the contrary, require less computational resources, but are also less rigorous in identifying the best alternatives.

ORGANIZATION OF LOCATION STUDIES

The possible applications for location studies are very wide. If we look at them according to the level of decisions, in terms of being more strategic or more operational, we have some examples:

• Strategic Level – determination of the number, size and location of factories and warehouses.
• Tactical Level – defining the allocation of customers to distribution centers and distribution centers to factories.
• Operational Level – elaboration of contingency plans, where it is intended to optimally reallocate customers in the event, for example, of a production line stoppage in a factory.

On the other hand, location studies can be used for more exploratory purposes, when one wants to assess the impact of changes in the company's business environment on its supply and distribution structure. This is what we call scenario analysis. An example:

• Privatization of railways and ports: if changes in the practiced price and availability of services are expected, these assumptions can be adapted to the models through changes in cost parameters, the addition of new connections between facilities or new possibilities for modal choices carriage. You can then run the modified model and observe the results against the current situation.

Parametric analyzes are also interesting applications, where the impact of the systematic variation of a single factor on the variables of interest is studied: for example, one may be interested in the effect of varying the number of distribution centers on the total cost. Or the effect of increased production capacity on transportation costs. The objective of parametric analyzes is to quantify relevant relationships for decision making, through the construction of parametric curves, obtained through several runs with the model.

The tools for carrying out location studies have been available for some years and are increasingly accessible. Used with creativity and intelligence, they can reveal great opportunities for reducing costs and improving the level of service.