FUNDAMENTAL ASPECTS OF THE LOCATION PROBLEM OF FACILITIES IN LOGISTICS NETWORKS

Locating facilities along a supply chain is an important decision that shapes, structures and conforms the logistics system. Location problems typically fall into a limited number of categories covering: the nature of the overriding factors, the number of installations, the level of aggregation of the data and the time horizon. The location of facilities is usually determined by one factor more critical than the others. For example, in the location of a factory, economic aspects are predominant, while in retail, the location is determined by the revenue potential of a given location. Locating just one installation is also a considerably different problem than locating multiple installations at once. In the first, the need to consider competitive forces, disaggregation of demand between different installations, effects on the consolidation of inventories and fixed operating costs is avoided. In reality, transportation costs are the primary factor to be considered. Finally, the nature of location methods can be static or dynamic, that is, determining location based on data for a single period or for several periods. Depending on each case, installations may represent a high investment in fixed assets, difficult to reverse in the short and medium term, implying high costs to relocate the installation to another location.

Of all the location decisions faced by logistics managers, those referring to warehouses are the most frequent, involving the following strategic dimensions:

• adequate number of warehouses
• location of each warehouse
• size of each warehouse
• space allocation for each product in each warehouse
• allocation of customer products by each warehouse.

The objective must be the design or configuration of the logistics network in order to minimize the total costs, for a year of operation, production, purchases, maintenance of products in stock, installations (storage, handling and other fixed costs) and transport; subject to a certain level of service (delivery time) to the final customer. A very common belief in many businesses is that a business must have multiple local warehouses close to customers to be successful. It is often believed that customers expect the supplier to maintain inventory in each local market in order to provide adequate service levels.

This perception, known as the local presence paradigm, resulted in logistical placements in which inventories were spread across the supply chain to compensate for deficiencies in transportation and order processing activities. Two major transformations are motivating companies to reassess the paradigm of local presence. Firstly, transport services experienced a huge qualitative leap, with arrival and departure times being more predictable and reliable. Second, the advent of information technology reduced the time associated with the transmission and processing of information, allowing, moreover, continuous monitoring of vehicles and their loads. Advances in transportation and information technology, in addition to managerial motivations to reduce inventory levels, have contributed to the dimensioning of a smaller number of warehouses to serve customers in a given market area.

The trade-offs between costs and between cost and service level relative to an increase in the number of warehouses generally refer to:

• improvement in service levels due to reductions in delivery time to the final customer;
• increased costs of holding inventory due to increases in the levels of safety stock needed to protect each warehouse against uncertainty in demand;
• increase in administrative expenses;
• reduction in expenses with distribution transportation;
• increase in supply transportation expenses.

A basic principle involved in opening a new warehouse is consolidation of transport. If orders tend to be small or fractional in a given market, the potential for consolidation may justify opening a new warehouse in that region. The general relationship between the total cost of transportation (procurement and distribution) and opening a new warehouse for consolidation is illustrated in the following figure. The total transportation cost drops as warehouses are added to the logistics network. The reduction results from consolidated shipments to the warehouse, in supply, in parallel with small shipments sent over short distances in distribution to the final customer. If the number of warehouses increases a lot, the total cost of transport increases again because the volume capable of being consolidated in the supply of each installation tends to decrease due to the effect of dispersion of shipments.

Storage costs typically include three main components:

• handling costs: include labor and equipment in an amount proportional (variable) to the annual flow of products through the warehouse.
• Fixed costs: capture all cost components that are not proportional to the flow of products through the warehouse. Fixed costs vary in the form of a step with the size of the warehouses or with the opening of them.

• Inventory holding costs: include the opportunity costs of holding inventory, being proportional to the inventory levels in each warehouse.

Turnover and inventory levels are directly related to the number of warehouses in a logistics network. Allocation of inventories across multiple warehouses can offer the potential to provide high levels of service. For customers, this can also mean more frequent resupply of smaller quantities, resulting in lower inventory levels. On the other hand, a greater number of warehouses in the logistics system has a substantial impact on stock in transit and on safety stock, even if the impact on basic or cycle stock is negligible. The larger the number of warehouses, the lower the levels of inventory in transit, because the total time of products in transit to serve the customer is reduced. The same does not apply to safety stocks, as the uncertainty in the operation increases due to the disaggregation of demand by different geographic areas. That is, the introduction of a new warehouse to serve a given market implies disaggregating the demand database used to determine safety stock levels. As a consequence, the market served by the new warehouse has a lower average demand, but not necessarily a lower level of uncertainty, since it is not possible to aggregate it over a larger area.

Production and order processing costs are also affected by these cost trade-offs. The primary objective in facility location is to identify the warehouse/factory configuration that results in the lowest total cost relevant to the supply chain, subject to service constraints or any other factor deemed important. The following figure illustrates the various cost trade-offs present in the facility location problem.

Usually, localization problems are characterized by being quite complex and intensive in the use of a database. The complexity derives from multiplying the number of different alternative locations by the storage strategies in each of these facilities and by the different modes of transport. The intensity in the use of information is generated by the need to analyze in detail data on demands and transportation, among others. In general, the information relevant to a location study, with no pretense of exhaustion, involves the following topics:

• location of customers, retailers, existing warehouses, distribution centers, factories and suppliers;
• all products handled, including the respective volumes/weights and special characteristics;
• annual demand for each product in each location;
• freight rates for each relevant mode of transport;
• warehousing costs, including labor, fixed expenses with facilities, space and taxes;
• size and frequency of shipments from one facility to another;
• order processing costs;
• service goals and requirements.

The location of multiple warehouses is a more realistic, yet more complex problem faced by many companies. The complexity stems from the fact that the various warehouses cannot be reasonably treated as economically independent, in addition to the possible combinations for location being enormous. It is important to identify potential locations for new warehouses. Typically these locations must satisfy a wide variety of conditions:

• infrastructure and geographic aspects;
• natural resources and labor;
• local industry and taxes;
• public interest.

Probably the most promising technique for locating multiple stores is mixed-integer programming, and it is definitely the most frequently encountered in commercial software. However, even though location models provide optimal results, it must be considered that the optimal solution for real problems is not necessarily better than a detailed description of the problem. Furthermore, optimization models are usually difficult to understand and require specific technical skills. Defenders of greater precision in the description and modeling are in favor of using simulation to determine the location of installations, even if the solution found is not optimal.

While algorithms look for the best number, location and capacity of warehouses, simulation techniques try to determine the best network configuration through repeated replications of a model with different storage and allocation patterns. The quality of the results obtained depends directly on the synthesis capacity of the decision maker in selecting the choices to be evaluated. An important feature of simulation models is their ability to relate temporal aspects of inventory policies with geographic aspects of location.

More broadly, the problem of logistical network design involves spatial and temporal aspects. Spatial or geographic aspects refer to the location, in a given market region, of factories, warehouses and retail outlets. The number, size and location of these facilities is determined, as we have seen, by balancing production/purchasing costs, inventory maintenance, facilities (variable cost of storage, handling and fixed cost of operations), transport (supply and distribution) with the level of service you want to provide.

The temporal aspects refer to maintaining a given product availability to meet service level objectives. Creating product availability can be achieved through quick response to placed production/purchase orders, or through allocating stock close to the customer. The time needed to make the product available to the consumer is the biggest concern in this regard. Balancing the costs of capital, order processing, and transportation will also determine how to trigger the processing of product flow through the facility network (pull or push decision, determination of lot sizes, reorder points, replenishment levels). and their allocation. These decisions affect the location of the facilities.

Most mathematical models, however, fail to include inventory costs as a component of their objective function, assuming the anticipated choice of certain modes of transport. Evaluating strategic changes to the logistics network design should involve estimating various costs and benefits, including their impact on total inventory levels. Among the trends that emerge from the advent of new information technologies, several companies are becoming convinced not to consider only a single mode of transport when evaluating alternative locations, or to consider inventory decisions related only to the number and location of warehouses, independently of transport decisions. Integrated inventory and shipping decisions can be quantified through the frequency of shipments and the average size of each shipment.

BIBLIOGRAPHY

BALLOU, RH, 1992, Business Logistics Management, 4th ed, Prentice Hall.

BOWERSOX, DJ, CLOSS, DJ 1996, Logistical Management – ​​The Integrated Supply Chain Process, 1st ed, McGraw-Hill.

JAYARAMAN, V., 1998, “Transportation, Facility Location and Inventory Issues in Distribution Network Design”, International Journal of Operations & Production Management, Vol.18, No.5, pp.-471-494.

SIMCHI-LEVI, D., KAMINSKY, P., 2000, Designing and Managing the Supply Chain – Concepts, Strategies and Case Studies, 1st ed, New York, McGraw-Hill.