## 22.3. Determining the location of the warehouse in the served territory

In the previous paragraph, solving the problem of determining the optimal number of warehouses in the distribution system, transport costs for delivering goods to consumers of material flow from warehouses of the distribution system were considered as one of the main dependent variables. The change in this value was studied depending on changes in the number of warehouses in the distribution system. However, the amount of transportation costs can vary significantly not only depending on the number of warehouses, but also depending on the location of these warehouses on the serviced territory (in the previous paragraph, it was assumed that the warehouses in the territory are located optimally).

The task of allocating the distribution center becomes relevant with a well-developed transport network, since otherwise the solution will most likely be obvious. For example, if there are only two intersecting highways on the territory of the district along which all consumers are located, then it is clear that the distribution center should be located at the intersection of highways.

The task of allocating distribution centers can be formulated as the search for an optimal solution or as a search for a sub optimal (close to optimal) solution. Science and practice developed a variety of methods for solving problems of both kinds. Briefly describe some of them.

** Full search method **. The task of choosing the optimal location is solved by a full search and evaluation of all possible variants of allocation of distribution centers and is performed on computers by mathematical programming methods. However, in practice, in conditions of branched transport networks, the method may not be applicable, since the number of possible options as the network scale increases, and with them the complexity of the solution grow exponentially.

** Heuristic methods **. Much less time-consuming suboptimal, or so-called heuristic methods for determining the location of distribution centers. These methods are effective for solving large practical problems; they give good, close to optimal results with low computational complexity, but do not provide an optimal solution. Name & he; heuristic means that the methods are based on human experience and intuition (in contrast to the formal procedure that underlies the method of full search). The method is based on a preliminary rejection of a large number of apparently unacceptable options. Experienced expert-expert analyzes the transport network of the region and, in his opinion, unsuitable options excludes from calculations. Thus, the problem is reduced to manageable sizes in terms of the number of alternatives that need to be evaluated. There are only controversial options, according to which the expert does not have an unequivocal opinion. For these options, calculations are performed in full.

** Method for determining the center of gravity of the physical distribution system model ** (used to determine the location of a single distribution center). The method is similar to determining the center of gravity of a physical body. The essence of it is as follows. From a light sheet material, a plate is cut out, the contours of which repeat the boundaries of the service area. On this plate, at the locations of consumers of the material flow, weights are strengthened, the weight of which is proportional to the amount of flow consumed at a given point. Then the model is balanced (Fig. 107). If the distribution center is located at the point of the district that corresponds to the point of the center of gravity of the model, the transportation costs for the distribution of material flow in the district will be minimal.

When using the method, one must take into account the inevitable error that will be introduced by the weight of the plate chosen for the basis of the model. This error is expressed by the presence on the model of the imaginary consumer, located at the center of gravity of the plate itself and with the cargo turnover proportional to its weight. The error will be less, the smaller the weight of the plate.

Fig. 107. Determining the location of the warehouse by building a physical model of material flows

The application of the described method has one limitation. On the model, the distance from the point of consumption of the material flow to the location of the distribution center is taken into account in a straight line. In this regard, the simulated area should have a developed network of roads, because otherwise the main principle of modeling will be violated - the principle of similarity of the model and the modeled object.

By using the method of determining the center of gravity, you can optimize, for example, the location of a warehouse of a wholesale trade enterprise that supplies grocery stores with grocery stores. In this case, it is necessary to balance the turnover of serviced stores. If the service area of a wholesale warehouse includes several settlements, supplied with a certain group of goods only from this warehouse, then on the model of the distribution system the goods can be proportional to the population of the corresponding settlements.

The problem of determining the point of the territory corresponding to the center of gravity of the physical model of the distribution system can be solved using known mathematical formulas. As an example, we will find a place for placing a warehouse in a distribution system serving five consumers (Figure 108). We plot coordinate axes on the service area map and find the coordinates of the points where consumers of the material flow are located, for example, shops (in Figure 108 the store numbers are indicated, in parentheses - their monthly turnover).

Fig. 108. Determining the location of the warehouse by the method of finding the center of gravity of the physical model of the distribution system

Coordinates of the center of gravity of cargo flows (x warehouse , y warehouse ), i.e. the point at which a distribution warehouse can be placed is determined by the formulas

where G i is the freight turnover of the i-th consumer;

X i , Y i - coordinates of the i-th consumer,

n - the number of consumers.

The point of the territory that provides a minimum of transportation work for delivery, in general, does not coincide with the found center of gravity, but, as a rule, is located somewhere close. Find an acceptable location for the warehouse will allow subsequent analysis of possible locations in the vicinity of the center of gravity.

** Determine the location of the distribution center by the trial point method. **

The proposed method allows to determine the optimal location of the distribution warehouse in the case of a rectangular configuration of the road network on the serviced site.

First, let's analyze the essence of the method using the example of a separate linear part of the transport network. Let there be 8 users of the material flow on the road segment of an arbitrary length (section AH, Figure 109): A, B, C, D, E, F, G and N. The monthly volume of delivery of goods to each of them is indicated in parentheses. The optimal location for the distribution warehouse can be easily determined by a method that can be called a "test point method".

The essence of the method consists in the sequential verification of each segment of the served site.

We introduce the concept of a test point of a segment, as well as the concepts of the left and right with respect to this point of the volume of imports of goods.

Fig. 109. Determination of the optimal location of the warehouse at the service site by the trial point method (the numbers indicate the freight turnover of consumers, tons per month)

** The** ** Trigger point ** of a segment is any point on that segment that does not belong to its ends (i.e., the ** test point does not match ** strong> with points A, B, C, D, E, F, G and H).

** The amount of goods delivered from the trial point to the point ** is the flow of goods to consumers located on the entire service area to the left of this point.

** The amount of goods delivered from the trial point to the point ** is the flow of goods to the consumers located to the right of it.

The maintenance area is checked starting at the far left end of the site. First, the first segment of the segment is analyzed (in our case, the segment AB). On this segment a test point is put and the sum of the volumes of delivery of goods to consumers located to the left and to the right of the set point is counted. If the volume of delivery to the consumers on the right is greater, then the next segment is checked. If less, then the decision is made to place the warehouse at the beginning of the analyzed segment.

The transfer of test points continues until a point appears for which the sum of the volumes of delivery to consumers on the left side does not exceed the sum of the volumes of delivery to the consumers on the right side. The decision is made about placing the warehouse at the beginning of this segment, i.e. to the left of the trial point. In our example, this is the F point.

Consider the variant shown in Fig. 110, when the sum of the volumes of delivery to the left and right of the test point of the next segment becomes the same. Note the beginning of this segment - point O as the first possible location of the distribution warehouse in the service area and continue the analysis until the segment appears, for the trial point of which the value of the left volume of delivery will be higher than the right. The beginning of this segment (point P) will determine the last possible location of the distribution center in the service area. The distribution center can be located at any of the points of the PR segment of the service area.

Fig. 110. Determination of the optimal location of the warehouse with the equality left and right freight turnover of the pilot point (the figures indicate the freight turnover of consumers, tons per month)

To determine the optimum node of a transport network of a rectangular configuration using the test point method to place a distribution warehouse in it, you should plot the coordinate axes aligned with the roads on the area map. Having determined the coordinates of consumers, it is necessary to find on each coordinate axis the optimum location of the coordinate X and the coordinate Y of the desired node by the trial point method.

As an example, consider a serviced system consisting of four consumers (Figure 111, to the right of consumers the monthly volume of delivery is indicated). The network of roads is rectangular. Assigning the ordinates and abscissas of consumers the appropriate values of the volume of delivery, we find the ordinate and abscissa of the optimal node of the transport network by the trial point method. Placement of the distribution warehouse in the found node will ensure the minimum value of freight turnover of the transport for the delivery of goods to stores.

Fig. 111. Determining the location of the warehouse in a rectangular configuration of the road network

At the conclusion of the paragraph, we list and characterize the factors that must be taken into account when choosing a site for the distribution center after the decision on the geographical location of the center is taken.

** 1. The size and configuration of the site. ** A large number of vehicles serving input and output material flows require a sufficient area for parking, maneuvering and passage. Lack of such areas will lead to congestion, loss of client time (perhaps, the customers themselves). It is necessary to take into account the requirements set by the fire protection services: to warehouses, in case of fire there must be free passage of fire equipment.

Any distribution center, being an element of some logistical system, in turn, turns into a complex system. The warehouses of the distribution center are only one of the elements of this system. For the effective functioning of the distribution center in the allotted area, it is necessary to organize the functioning of all other elements, since underestimation of any of them may adversely affect the work of the entire center. In particular, it is necessary to place the following in the allocated territory:

o administrative premises, including the central office, dining room, sanitary facilities for workers;

o guard post;

o devices for collecting and processing waste.

** 2. Transport accessibility of the area. ** Transportation costs are a significant component of the cost of operation of any distribution center. Therefore, when choosing a site, it is necessary to evaluate the roads leading to it, to get acquainted with the plans of the local administration to expand the road network. Preference should be given to sites located on the main (main) routes. In addition, it requires studying the equipment of the territory with other modes of transport, including public ones, on which the availability of the distribution center for both its own personnel and customers essentially depends.

** 3. Plans of local authorities. ** When choosing a site, it is necessary to familiarize yourself with the plans of the local administration for the use of adjacent territories and to verify that there are no factors that could subsequently have a deterrent effect on the development of the distribution center.

In addition to the above factors, when choosing a particular area under the distribution center, it is necessary to familiarize yourself with the peculiarities of local legislation, analyze the costs of upgrading the territory, assess the existing buildings on the site (if any), take into account the possibility of attracting local investments, labor market.

As an example of accounting for various factors solving the problem of determining the location of the distribution center in the served territory, consider the problem of placing a wholesale food market in the territory of the served settlement. The placement of wholesale markets requires consideration of a large number of factors. The main ones are:

o the size of the service area, within which there are a sufficient number of potential users of wholesale market services;

o the presence of a developed transport infrastructure: roads, railways, airports, waterways;

o the possibility of expanding the land in connection with the growth of the market's trading activity.

For example, when placing the Togliatti wholesale market, several possible options were evaluated. One of them assumed the placement of the wholesale market on a site free from buildings, the location of which would allow a potential buyer to reach the market at an acceptable time. However, economic calculations have shown that the costs of posting the main communications and laying the road connecting the market with the urban transport system do not pay off with the expected revenues from the rent. Preference was given to the option of placing a wholesale food market on the site with existing communications and buildings. The market was located in the central part of the city on the territory of the former vegetable base, with the simultaneous employment of part of its staff. The choice of the option was due to its economic advantages, convenient location for the visitors of the market, as well as the ability of the staff to work with the food group of goods

** 4. Local legislation **. It is necessary to take into account the local rules of construction, safety, height of buildings, restrictions on types of buildings and, possibly, other factors.

** 5. Building factors **. It is necessary to take into account generally accepted standards for similar structures, i.e. distance between buildings, access to them, etc.

## 22.4. Deciding on the use of hired warehouse services

The logistics chain can be organized using own or leased warehouses, or using public warehouses. Strategic orientation for a long-term presence in the region is the basis for organizing your own warehouse. Short-term economic ties for supplies - the basis for renting warehouse space or purchasing services of a public warehouse.

The choice between the organization of your own warehouse and the use of a public warehousing warehouse for placement of stocks belongs to the class of decisions "to make or buy" (Make-or-Buy Problem). The decision-making technique is shown in Fig. 112.

Fig. 112. Deciding on the use of hired warehouse services

Line Z on the graph shows the dependence of the costs of storing the stock in a warehouse from the projected size of cargo turnover. Dependence of the costs of storing stocks in your own warehouse on the size of the warehouse turnover is represented by the line F 3 .

The function F 3 is determined by summing the conditionally fixed and conditionally variable costs of your own warehouse (functions F 2 and F 1 respectively).

The function F 1 is assumed to be linear and is determined based on the price for performing the logistics operations.

The graph of the function F 2 is parallel to the OX axis, since the fixed costs (C post ) are independent of the turnover. This includes the costs of renting a warehouse (C leases ), amortization of equipment (C amort ), electricity (C el ), staff and specialists (C salary ):

The graph of the function Z is built on the basis of market tariff rates for storage and processing of goods in a warehouse.

Dependence of Z (dependence of costs for storage of goods in a warehouse warehouse on the volume of turnover) is determined by the following formula:

where a - the tariff for the services of a warehouse - the daily cost of using 1 m of cargo area of a warehouse

365 - number of days of storage in a warehouse for a year;

S n - the required warehouse area (m), calculated using the formula

where Z - the size of the stock in days of turnover, days;

D - annual turnover, t/year;

D - number of working days per year;

q - load per 1 m of area when stored in a warehouse, t/m .

The graph of the function Z is constructed from the assumption that it is linear.

The question of using hired warehousing services arises if the volumes of cargo turnover are higher than the turnover of indifference G b , for example equal to Г 1 . The decision is made on the basis of comparison of the difference in costs (ΔC) for the use of own and hired warehouses with capital investments (K), necessary for the organization of their own warehouse. The period of their payback must satisfy the investor.

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