Some points of the warehouse theory Текст научной статьи по специальности «Математика»

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на отдельных участках, а следовательно, и справедливость сделанных выше предположений.

Таким образом, при планировании перевозки грузов по некоторому новому маршруту и определении минимального числа подвижного состава,

Библиографический список

1. Теория вероятностей / Е. С. Вентцель. -М. : Наука, 1969. - 576 с.

2. Определение времени отправки грузов из условия их гарантированной доставки по назначению / В. Н. Арсеньев, Б. Л. Сорокин, А. Н. Цирикидзе // Труды всеармейской научно-UDC 656.073.27

O. B. Malikov

Petersburg State Transport University

обеспечивающего перевозку заданного объема грузов за требуемое время, в качестве характеристик разброса времени движения по всему маршруту могут использоваться приближенные оценки дисперсии и СКО - (4) и (5).

практиче-ской конференции «Инновационная деятельность в Вооруженных Силах РФ». -СПб. : ВАС, 2008. - С. 81.

3. Моделирование сложных систем / Н. П. Бус-ленко. - М. : Наука, 1978. - 400 с.

SOME POINTS OF THE WAREHOUSE THEORY

Warehouses play significant role in all logistic chains of cargo delivery from manufacturers to consumers, preparing goods for transportation, handling and consuming. Modern mechanized and automatic warehouses are very complicated technical objects which feature with many parameters, a lot of technical decisions and operate under stochastic flows of arriving and dispatching cargoes. So they run in permanently changing and very different conditions of cargo volumes, handling equipment and employees used, trucks and railway cars processed etc. Special theory is needed for the due research and project of these complex technical objects. Some parts of the Theory of Warehouse Systems (TWS) are considered in the article.

warehouse, transport system, general system theory, material flow, logistics, supply chain.

Modern mechanized and automatic warehouses are very complicated technical objects: they are rigged with specific complex equipment (racking systems of various kinds of performance, industrial trucks and stacker cranes with automatic control, automatic conveyor systems and automatic guided vehicles (AGV), means of robotics, palletizers, computers and on-line electronic data exchange systems etc). They are characterized with hundreds of various parameters and display stochastic sort of activity. In every case of reconstruction or

building some new warehouse a lot of options with different parameters and economical characteristics are possible.

Therefore, the most efficient approach to creating modern warehouses is to represent them as complicated stochastic systems in accordance with the Theory of Warehouse Systems (TWS), which was worked out by the author of this article in the late 1980s. The General Cybernetic Theory of Systems (GCTS) was applied as the foundation of this theory. The principal statements of this theory are as follows.

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A warehouse should be considered as a system, i. e. as a complex of connected components of definite technological areas, having been created for reaching the unified objective. According to GCTS, various parts of the object under consideration could be taken as components of the Warehouse system. The most productive approach, however, (as research had displayed) was proved to select technological areas as components of the warehouse systems.

The basic aspect of TWS is the purpose of creating and functioning of a warehouse.

The common, or at any rate, very widely spread opinion is that warehouses are created

for storage or, perhaps, for storage and proceeding of merchandise. This opinion, however, does not explain what the merchandise should be stored or proceeded for. It is known certainly, that no products or merchandise are manufactured just for storage. They should move to the consumers.

In order to understand the real objective of a warehouse creation it is necessary to consider a Supply Chain that always consists of 2 sorts of elements: warehouses and transport links connecting these warehouses (Fig. 1).

a)

b)

F1F2

Т1ТТ2

c)

TiT0

AjBj

W2

{ >

Fig. 1. Logistic chain (a) with components - transport T and warehouses Wj, the simplest transport process (b) between any two facilities F1 and F2with warehouses W1, W2 and the scheme of warehouse W interaction (c)

with in-bound transport Tand out-bound transport T0

Analysis of logistic systems shows that any well organized logistic chain and every transportation process start and terminate at some warehouses (W1, W2 in Figure 1, b).

A warehouse always interacts with two types of transport - the first T that delivers cargoes to the warehouse and the second To that delivers cargoes from a warehouse to customers (they can be of the same or different modes of transport) - see Figure 1, c. Certainly, the whole amount of in-bound

materials flow per rather a long period Q (for example, per year) should be equal to the whole amount of out-bound materials flow Q0.

A material flow, however, is characterized not only with this single parameter but with the whole amount of cargoes delivered to or dispatched from a warehouse for a year, although this one is a very important one. Other main features of a material flow are as follows:

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- amount of transport batches (these may be very different), arriving and dispatched from a warehouse;

- number of different denominations of cargoes in transport batches;

- types and features of transport tare and packing of cargoes;

- types and features of freight transport units (pallets, Stock Keeping Units (SKU), containers), which cargoes arrive and dispatch in;

- time of arrival and dispatching of transport batches, regularity and conformity of these processes to somerules;

- time intervals between arrival and dispatch of transport batches and their regularity.

For example, the amount of transport batches can be changed from big to the small ones if goods come to warehouses in big batches in long distance heavy-duty trucks and are delivered to customers in small batches in small local trucks. At the same time the number of goods denominations in transport batches can lessen dramatically. Moreover, if the warehouse under consideration is of a Logistic Center type, goods can be unpacked in it and stored in some other or even special tare, pallets or containers. In that case, characteristics of packing and freight transport units can be transformed as well, when goods are retrieved from the storage area and transport batches are prepared for delivering them to customers.

Time characteristics of transport batches dispatched from a warehouse are also different from those of transport batches that had arrived to the warehouse. This time, parameters difference creates the term of cargo storage in the warehouse t, which is needed to receive requirement for this specific good, pick it from the stock, pack and include it in some transport batch for delivering to customers. Therefore, the storage of cargo is not some self-purpose, but only one of many technological operations

Comparison of these characteristics of in-bound and out-bound goods flows displays that they may be different from each other. So, although the whole amount of arrived goods to a warehouse for some long period Q;would be equal to the whole amount of dispatched goods from a warehouse Q0 for the same period, other elements of multitude (Aj) of in-bound flow parameters cannot be equal to the appropriate elements of multitude (Bj) of out-bound flow parameters (see Fig. 1, c).

So, the warehouse changes or transforms some of the flow parameters mentioned before.

(about 40), which are fulfilled with cargoes in warehouses.

The objective of these operations is to transform characteristics of material flows as it has been explained earlier. So, warehouses are organized in the points of transport networks, where transformation of material flows is necessary. But then a question arises: why and what for does this necessity appear?

Transport network consists of a lot of different transport systems with their own specific constructions, performance, organization, functioning and some sort of activity and control. Going through these different transport systems the cargoes, goods, products on their way from manufacturers to customers adopt specific characteristics of these systems.

So, the flow of finished products comes to a factory finished product warehouse by means of inner factory transport with some multitude of parameters. These parameters are suitable for products manufacturingand industrial transport, but do not match the railway or outer road transport that has to deliver these goods to the Logistic Center or directly to a shop or supermarket. And this multitude of the goods parameters can be not suitable also for these shops or supermarkets

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(for example, as concerning the amount of goods in the transport batches, their contents and goods denominations, dimensions of separate packages and parcels, time, type of transport tare and packing, time of dispatching, including other conditions of goods delivering etc.).

Therefore, the finished products warehouse of a factory has to transform the products flow so as it would conform to all requirements of goods receivers and transport of delivery. That will be its purpose and assignment - to adapt parameters of the goods flow outgoing from the warehouse for the best following transportation of the goods.

In the same manner a freight terminal at a railway station or a marine port, a warehouse of the Logistic Centre, warehouses of raw materials and components, semi-finished components at a factory etc. can be considered.

To the warehouse of raw materials, parts and components of a factory these materials come by rather big transport batches, in transport packages or containers and not very often (not every day, for example). These characteristicsof the in-bound material flow almost always do not match the technological proceeding of a factory, which needs the raw materials and unfinished components to be supplied in lesser batches, completed according to the technological process and delivered to the particular point in determined time. Therefore, the warehouse of materials and unfinished components should change the parameters of the material flow in such a way that they in the most degree would appropriate to the needs of the technological process of the factory. So in this case, the objective of the warehouse is to transform the flow for the best consequentusing of the materials and unfinished components, arrived to the factory.

So, we can declare that warehouses of various types and assignments are created in the points of interaction of different transport

and industrial systems with an objective of material flow transformation for the best consequent transportation and/or using goods. Temporary storage and handling cargoes at the warehouse are just some of its proceeding operations fulfilled for changing the parameters of the materials flows.

Transformation of a material flow is only one side of a warehouse objective. The other one is to make this transformation in the most efficient way, i. e. with the least spending of 6 main resources, which we have in our real natural environment: space, time, materials, energy, labor and money. This part of the warehouse objective is reached by competent professional projecting of the warehouse, which is known to experts in this field of knowledge.

According to TWS, a warehouse should be analyzed (existent warehouse planned to be reconstructed) and created (new warehouse) as a technical system consisting of the following elements-technological areas (see Figure 2):

• Area of unloading cargoes from transport, delivering them to the warehouse (unloading dock ) - UD;

• Area of temporary storage of cargoes, which arrived to the warehouse and for some reasons cannot yet be received by the authorized storage in the main stock (TSA);

• Area of reception and sorting of arrived cargoes with quantity and quality(RSA);

• Main storage area (MSA);

• Area or subsystem of picking and retrieval ofdispatched goods (PRA);

• Area of picking and completing of orders with dispatched goods (PC A);

• Area of temporary storage and preparation of goods for dispatching from the warehouse (TSD);

• Area of loading to transport the cargoes dispatched from the warehouse (loading dock) - LD;

• Inner warehouse transport, that moves the cargo through processing between

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technological areas and therefore unites all these areas in a system (IWT);

Subsystem of automatic control (SAC).

Fig. 2. Structure of a warehouse as a facility for material flow transformation consisting of elements - technological areas

Practically, this interaction of the warehouse system with the environmental systems represents mutual transferring material and informational flows, which makes the warehouse pass under this influence from one of its states to another. The number of these states may be very large, and they are characterized with types and amount of technological operations to be carried out at the moment, cargoes to be stored and processed, delivered to and from the warehouse, picked, sorted etc.

Every one of these components of a warehouse system has its own technology, equipment and purpose of functioning. But there is one general system objective which all the components operate for. This is the united objective of creating the warehouse to transform the determined material flow in a specific way with the least spending of 6 resources mentioned above. This is known as a synergetic effect in the General Theory of Systems.

While operating, the warehouse system interacts with the environment, which consists of a number of outward systems. This interaction with surrounding systems should be planned so as to help the warehouse system to reach its main objective of material flow transformation.

At the same time, the state of the warehouse system influences on the busycondition of its personnel,forklift trucks, cranes, conveyors, occupation of its stock, racking and other warehouse equipment. Ability of the warehouse system to be in some state Wcan be valued with its appropriate probability P(Wi).

Procedures of warehouse systems transitions from one state to the other ones are illustrated in Figure 3 in a simple form, where only 4 states are shown, which are explained also in Table 1.

P(Wi)

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P(W4— W2)

W4

P(W4- W3)

P(W4)

Fig. 3. Graph of states and transitions of a warehouse system (4 states and 8 transitions illustratively)

and their appropriate probabilities

TABLE 1. Four main states of a warehouse system (without taking into account the inner warehouse operations)

Code of state Description of states Designation of states Operations having been carried out Probabilities of states

Loads reception Loads dispatch

1 There is no work at a warehouse W1 0 0 P(WX)

2 Only unloading is fulfilled W2 1 0 P(W2)

3 Only loading is fulfilled W3 0 1 P(W3)

4 Loading and unloading are fulfilled at the same time W4 1 1 P(W4)

Functioning of the warehouse system can n

also be represented in a formulized form as a r = Z r ■ p(w,)-

matrix of transition probabilities: 1=1

P11 P12. . P1i .. . Pn

P21 P22 . .. P2i . .. P2n

Pj = P1 P 2. .. P . .. Pn

Pn1 Pn2 . .. Pni . .. Pnn

Probabilities disposed in the main diagonal of the matrix can be used for calculation of the possibilities of the warehouse system to remain in the same states.

This method of formalization of warehouse system functioning can be used for its research and optimization.

Using the formal representation of the warehouse system activity shown in Table 1, it is possible to compute the required quantity of the material handling equipment, for example - fork lift trucks for a warehouse:

where r - number of fork lift trucks or other equipment; n - number of states of a warehouse (in this example n = 4); P(W) -the probability of the i-state of the warehouse system.

Here is an example of application of this method to computation of the number of forklift trucks under ever changing conditions of cargo loading and unloading at a warehouse (Table 2).

Under these conditions it is necessary to furnish the warehouse with 4 forklift trucks.

The results of the warehouse system operation should be compared with the objective set when it was being projected.

So, the main stages of analyzing or projecting a warehouse as a complex stochastic technical system are the following:

• Objective setting (it should be single);

• Selecting and determination of elements - technological areas (including options);

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• Selecting and determination of a warehouse structure as various connections between the system elements (including options);

• Research and analysis of the system functioning (including its simulation);

• Research and analysis of the system interaction with environmental systems (also with its simulation);

• Analysis of the results of the warehouse system performance and operation in comparison with the objective having been set.

TABLE 2. An example of forklift trucks number computation at a warehouse which changes its states during operation

State Codei Description of states Hours of states? State Probability Pt= T/24 Trucks number in states ri Real trucks number Tri-Pi

1 No work at warehouse 7 0,29 0 0

2 Only cargo unloading 3 0,13 5 0,65

3 Only cargo loading 9 0,37 3 1,11

4 Loading & Unloading 5 0,21 7 1,47

Total 24 1,00 - 3,23

In is interesting to point out that this general methodology can be used while creating or analyzing other technical and social objects in various fields of industry or society, which receive a flow of some objects with one set of parameters, proceed it through its structure and give it out with some other values of parameters.

There are plenty of such objectsin many kinds of industries, trade, building, transport, social spheres etc. (e. g. railway stations, marine ports, parking lots, garages, sport and cultural objects, shops and markets etc.). These objects do not produce any new products, but all the same they are very useful and important in their sectors of

References

1. Business Logistics: New Specific Approach to the Concept / O. Malikov // Proceeding of The Forth International Railway Logistics Seminar. -Kouvola, Finland, 2008. - PP. 39-52.

2. Warehouses& Freight Terminals / O. Malikov. - St. Petersburg, Russia, 2005. - 650 p.

3. Business Logistics / O. Malikov. - St. Petersburg, Russia, 2003. - 240 p.

economy and in Logistics Chains. Profound analysis, however, shows that all these objects are very much alike in their nature and action and can be considered, created and optimized by using the same approach. These objects may be named «transforming systems» and they should be considered on the base of the same methodological principles as warehouse and storage systems.

Certainly, for every specific kind of the transforming systems some more profound research and descriptions should be required because of their wide variety and peculiarities. Further scientific works and researches would allow to discover more features of this new methodology.

4. Warehouses of Industrial Enterprises / O. Malikov, A. Malkovich. - St. Petersburg, Russia, 1990. - 676 p.

5. Warehouses of Flexible Manufacturing Systems / O. Malikov. - St. Petersburg, Russia, 1986. - 186 p.

6. Designing of Automatic Warehouses / O. Malikov. - St. Petersburg, Russia, 1980. - 240 p.

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