Safety stocks serve as a kind of "emergency" source of supply in cases where the demand for this product exceeds expectations. In practice, the demand for goods can be accurately predicted extremely rarely. The same applies to the accuracy of predicting the timing of orders. From here there is a need of creation of insurance commodity-material stocks.

There are several reasons why entrepreneurs order more goods than currently required:

Delay in receiving ordered goods;

The ability to receive goods in an incomplete volume, which forces customers (especially intermediaries) to keep certain goods in stock for some time;

Providing discounts received by the customer when he purchases a large consignment of goods;

The same amount of transport, overhead and other costs, regardless of the size of the party. (For example, the cost of one container will be the same regardless of whether the container is fully loaded or not.)

The creation of reserves requires additional financial costs, so there is a need to reduce these costs by achieving an optimal balance between the volume of the stock, on the one hand, and financial costs, on the other. This balance is achieved by choosing the optimal volume of batches of ordered goods or by determining the economic (optimal) order size - EOQ (Economic Order Quantity), which is calculated by the formula

where A - production costs; D - average level of demand; - specific production costs; r- storage costs.

Determining the exact level of safety stock required depends on three factors:

1) possible fluctuations in the timing of the restoration of the level of stocks;

2) fluctuations in demand for the relevant goods during the period of implementation of the order;

3) the company's customer service strategy.

It is quite difficult to determine the exact level of necessary reserve stocks in the conditions of instability in the timing of orders, volatile demand for goods and materials. To find satisfactory solutions to the problems associated with reserve inventory, it is necessary to use modeling or simulation of various scenarios.

The optimal size of the batch of supplied goods and, accordingly, the optimal frequency of delivery depend on the following factors: volume of demand (turnover); transport and procurement costs; storage costs.

As an optimality criterion, the minimum amount of transport and procurement costs and storage costs is chosen. Transport- procurement costs with an increase in the size of the order, they decrease, since the purchases and transportation of goods are carried out in larger lots and, therefore, less frequently. Storage costs increase in direct proportion to the size of the order. To solve this problem, it is necessary to minimize the function representing the sum of transportation and procurement costs and storage costs, i.e. determine the conditions under which

where C total - total costs for transportation and storage;

From storage - the cost of storing the stock; With transp - transport and procurement costs.

Let's assume that for certain period time, the turnover value is Q. The size of one ordered batch is S. Let's assume that a new batch is imported after the previous one has completely ended. Then the average value of the stock will be S / 2.

Let's introduce the rate (A/) for storage of goods. It is measured by the proportion of the cost of storage for the period T in the value of the average inventory for the same period. The cost of storing goods for the period T can be calculated by the formula

The amount of transport and procurement costs for the period T is determined by the formula

where K - transportation and procurement costs associated with the placement and delivery of one order; - the number of orders for a period of time.

Substituting the data, we get:

The minimum of Ctot is at the point where its first derivative with respect to is equal to zero, and the second derivative is greater than zero. First derivative:

Let's find the value of S o bs (optimal order size), which turns the derivative of the objective function to zero:

The optimal batch size of the delivered goods and, accordingly, the optimal frequency of importation depend on the following factors:
volume of demand;
transportation and procurement costs;
inventory holding costs.
These factors are closely interrelated. Thus, the desire to save as much as possible the cost of storing inventory causes an increase in the cost of processing and delivering orders. Savings in repeat order costs result in wasted storage space and further reduce the level of customer service. With the maximum load of storage facilities, the cost of storing stocks increases significantly, and the risk of illiquid stocks is more likely.
It should be borne in mind that the interests of individual services within the organization in relation to the policy of stockpiling can vary significantly. So, the logistics service is interested, as a rule, in purchasing as many resources as possible, since this allows to achieve better conditions delivery of settlements, as well as to avoid claims of production units regarding untimely supply. Manufacturing departments are also interested in large inventory, as this allows them to quickly respond to incoming orders. From a sales point of view, large inventory is a means competition for the buyer. But at the same time, from a position financial department responsible for the rational management of the financial flows of the organization, large volumes of orders and, consequently, significant stocks mean an increase in the cost of their maintenance, service and financing.
The criterion for the optimal size of the ordered lot is the minimum total costs inventory management, which consists of order fulfillment costs and inventory holding costs. Both those and others depend on the size of the order, however, the nature of this dependence is different. Let's consider their behavior in more detail.
Order fulfillment costs (transport and procurement costs) are the overhead costs associated with the implementation of an order and depend on the size of the order.
The cost of fulfilling an order for a batch (C0) is determined by dividing the transport and procurement costs of the previous period (based on estimates of transport and procurement costs) by the number of orders placed during this period. The estimate of transportation and procurement costs includes the following costs: costs associated with the execution of a supply contract (travel, representation costs for negotiations, costs for developing the terms of delivery, the cost of document forms, costs for issuing catalogs, etc.), insurance costs, transportation costs, the cost of order fulfillment control, etc.
The order fulfillment costs for a certain period are calculated as follows:
G = C±
issue >
g
where g - batch size (pcs., kg); С^ - costs of fulfilling an order per unit of goods; q - the value of the turnover of goods for the period (pieces, kg); q/g - the number of product orders for a certain period.
The cost of order fulfillment both per unit of production (Co/g) and per volume for a certain period Svyp decreases with an increase in the size of the delivery lot (g) (Fig. 2).
Inventory holding costs include the costs associated with the physical holding of goods in the warehouse and possible interest on capital invested in inventory. They are expressed as a percentage of the purchase price for a certain time (i).
Provided that a new batch is imported after the previous one is completely exhausted, the average stock is g / 2. And, therefore, storage costs are determined by the average level of inventory.
With a constant sales intensity, the cost of holding inventory for a certain period of time is calculated as follows
g = Bg
°xp 2,
where i - storage costs, expressed as a share of the price of the goods; C - the purchase price of a unit of goods, rubles; C - the cost of storing a unit of goods.
The cost of holding stock increases linearly with an increase in the size of the delivery lot (Fig. 2).
Costs, C

order size, g
Rice. 2. Dependence of inventory management costs on the size of the order
The total cost of managing inventory over a given period is the sum of the cost of fulfilling orders and the cost of holding inventory.
C \u003d C + C \u003d ?ol + 4g
gen ex xp ~
g2
Another formula for calculating management costs is also used (taking into account the cost of goods)
C \u003d Qq + Shchd +. g2
The total cost curve is flat near the minimum point. This suggests that near the minimum point, the order size may fluctuate within certain limits without significant change general costs.
So, the criterion for the optimal size of the ordered batch is the minimum total cost of inventory management
Sob - Svyp + Save - 1: * min.
C0q + C/g g 2
The minimum total costs are where the first derivative with respect to g is equal to zero, and the second is greater than zero. Having carried out these operations, we determine that the total costs take on a minimum value if
2C0q 2С 0 Q
gapt=l1-CH or g opt="
where C0 is the total cost of fulfilling an order for a batch; q - the amount of goods sold for the period; C - the purchase price of a unit of goods; i - storage costs (in% of the price), Q = ^ - quantity of goods sold for the period in value terms (turnover)
The resulting value of the optimal size of the ordered batch is called the economic order quantity (Economic Order Quantity EOQ), it provides a minimum of total management costs. This formula for calculating the optimal order size is also known as the Wilson (Wilson) formula.
When determining the optimal order size, the following assumptions are used:
the total number of units constituting the annual requirement is known;
the quantity demanded is constant;
orders are executed immediately;
the cost of placing an order does not depend on the size of the batch;
prices for materials do not change in the period under review.
In the case of a delayed delivery, when the condition of instantaneous replenishment of the stock is replaced by the condition of replenishment of the stock for a finite interval, the replenishment of stocks occurs in each cycle during the time ti, and consumption occurs during the time ti + t2 or during the full cycle (Fig. 3). For such a mo- G h T h T 1 Fig. 3. Delayed Delivery Model
The optimal lot size increases as the average stock level is no longer equal to g/2, but less. In this case, the optimal batch size to be produced is calculated as follows:
S = , 2Coq
m
1Sch1 - q / p) where p - annual production.
In some cases, the intensity of consumption may increase material resources and there is a stock shortage. If it is comparable to the cost of maintaining stocks, then it is acceptable. In this case, the optimal order size is determined by
= C + h
Ss = SoptJh"
where h - costs due to shortages (penalties to consumers for late delivery, payment of idle time to workers, payment for overtime hours, losses associated with an increase in the cost of production, etc.).

Once the choice of a replenishment system has been made, it is necessary to quantify the size of the ordered batch, as well as the time interval through which the order is repeated.

The optimal batch size of the delivered goods and, accordingly, the optimal frequency of importation depend on the following factors:

volume of demand (turnover);

shipping costs;

inventory holding costs.

As an optimality criterion, a minimum of total costs for delivery and storage is chosen.

Rice. 59.

Both shipping costs and storage costs depend on the size of the order, however, the nature of the dependence of each of these cost items on the volume of the order is different. The cost of delivery of goods with an increase in the size of the order obviously decreases, since shipments are carried out in larger consignments and, therefore, less frequently. The graph of this dependence, which has the form of a hyperbola, is shown in Fig. 60.

Storage costs increase in direct proportion to the size of the order. This dependence is graphically presented in fig. 61.

Rice. 60.

Rice. 61.

Adding both graphs, we get a curve that reflects the nature of the dependence of the total costs of transportation and storage on the size of the ordered lot (Fig. 62). As you can see, the total cost curve has a minimum point at which the total cost will be minimal. The abscissa of this point Sopt gives the value of the optimal order size.

Rice. 62.

The task of determining the optimal order size, along with the graphical method, can also be solved analytically. To do this, you need to find the equation of the total curve, differentiate it and equate the second derivative to zero. As a result, we obtain a formula known in the theory of inventory management as the Wilson formula, which allows us to calculate the optimal order size:

where Sopt - the optimal size of the ordered lot;

O - turnover value;

St - the costs associated with delivery;

Сх - costs associated with storage.

26 Formation and planning of commodity stocks at the enterprise

With the transition to market relations, the importance of optimizing the volume and structure of commodity stocks in trade increases, taking into account the forms of ownership, the specifics of regions, links in the movement of goods, and types of enterprises. Inventory management includes planning their volume and structure in accordance with the goals set by the enterprise, control in order to ensure their continued compliance with established criteria. Inventory management also includes an analysis of the turnover and availability of goods, their rationing, formation and placement.

According to the instructions of the statistical authorities, in commodity stocks retail stocks of all goods owned by the company and listed on its balance sheet are taken into account - commodity stocks: 1) current storage, providing for the daily needs of trade; 2) seasonal storage (potatoes, vegetables, fruits), created to ensure trade in the seasons of the year; 3) early delivery, formed in hard-to-reach areas to ensure trade throughout the entire period between deliveries. The company's inventory includes goods available in the company's network, at small wholesale bases, distribution warehouses and bases, available at bases and warehouses owned by enterprises and organizations; goods purchased and paid for by this trade organization and left in custody with suppliers; goods handed over for processing and at the reporting date located at the enterprises of both their own and other organizations, agricultural products purchased at agreed prices.

Commodity stocks in the company are shown in the statements at retail prices, at which they are recorded on the balance sheet of these enterprises.

IN statistical reporting about commodity stocks in the company are not included: goods in transit - finished products at the auxiliary manufacturing enterprises trade organizations, the supplier's goods accepted by this trade organization for safekeeping against a safe receipt; goods accepted from the population and cooperatives for commission; free containers of all types (soft, hard, glass); goods of material and technical supply; goods of blanks passing through the balance sheet of procurement activities; raw materials and auxiliary materials obtained for industrial processing; goods shipped, for which settlement documents have been handed over for collection to banking institutions.

In the course of the analysis of commodity stocks, it is necessary to determine whether the actual stocks of goods correspond to the established norms in comparable terms and in days of turnover, to identify the reasons that influenced the deviations from the norm; find out to what extent commodity stocks satisfy the demand of the population and ensure the fulfillment of the planned target for retail trade whether inventory is correctly placed structural divisions; clarify the reasons for overstocking or interruptions in the sale of individual goods, the presence of low-quality goods. An important point in the analysis of inventory is to establish the impact of the effectiveness of the use of inventory on the amount of costs associated with their storage, and thus on the amount of profit of a trading enterprise.

The objectives of inventory analysis are:

determination of the level of provision of the enterprise with the necessary commodity resources; factors that determined their size, structure, change;

identification of excess or scarce types of commodity stocks;

establishing the degree of rhythm of deliveries, as well as their volume, completeness, quality, grade;

clarification of the timeliness of the conclusion of economic contracts for the supply of goods;

study of indicators of the effectiveness of their use and impact on financial results;

calculation of costs associated with the purchase and storage of stocks, and their impact on the profit of a trading enterprise;

preparation of the initial base for normalization and optimal control them, etc.

The analysis of commodity stocks includes the analysis of the general condition of commodity stocks and commodity turnover, distribution of commodity stocks, structure and composition. The most reliable results are given by weekly, operational and full analysis based on the results of the month. Such a period for analysis is recommended based on foreign experience and experience of domestic firms operating on the terms joint venture. Analysis for such a period allows you to take certain effective actions to accelerate the turnover, which corresponds to the idea of inventory management.

Once the choice of a replenishment system has been made, it is necessary to quantify the size of the ordered batch, as well as the time interval through which the order is repeated.

The optimal batch size of the delivered goods and, accordingly, the optimal frequency of importation depend on the following factors:

volume of demand (turnover);

shipping costs;

inventory holding costs.

As an optimality criterion, a minimum of total costs for delivery and storage is chosen.

Rice. 59. Two-bunker inventory control system

Storage costs increase in direct proportion to the size of the order. This dependence is graphically presented in fig. 61.

Rice. 60. Dependence of transportation costs on the size of the order

Rice. 61. The dependence of the cost of storing stocks on the size of the order

Rice. 62. Dependence of the total costs of storage and transportation on the size of the order. Optimal order size S opt

where Sopt - the optimal size of the ordered lot;

O - turnover value;

St - the costs associated with delivery;

Сх - costs associated with storage.

Questions for knowledge control

1. Define the concept of "inventory".

2. List the costs associated with the need to maintain inventories.

3. What are the main reasons that force entrepreneurs to create inventories.

4. List the types of inventories known to you.

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2. Practical part
Task 1
Task 2
Task 3
Task 4

1. Determination of the optimal order size

volume of demand (turnover);

transportation and procurement costs;

inventory holding costs.

As an optimality criterion, choose the minimum amount of costs of transport and procurement and storage.

Transport and procurement costs decrease with an increase in the size of the order, since the purchases and transportation of goods are carried out in larger lots and, therefore, less frequently.

Storage costs increase in direct proportion to the size of the order.

To solve this problem, it is necessary to minimize the function representing the sum of the costs of transport and procurement and storage, i.e. determine the conditions under which

Common \u003d Save + Transp,

where Сtot is the total cost of transportation and storage; Store - the cost of storing the stock; Stsp - transport and procurement costs.

Suppose that for a certain period of time, the turnover is Q. The size of one ordered batch S. Let's say that a new batch is imported after the previous one has completely ended. Then the average value of the stock will be S / 2. Let's introduce the tariff (M) for the storage of goods. It is measured by the proportion of the cost of storage for the period T in the value of the average inventory for the same period.

The cost of storing goods for period T can be calculated using the following formula:

Save = M (S / 2).

The amount of transport and procurement costs for the period T will be determined by the formula:

Store = K (Q/S)

where K - transportation and procurement costs associated with the placement and delivery of one order; Q/S - number of orders for a period of time. Substituting the data into the main function, we get:

So6sch \u003d M (S / 2) + K (Q / S).

The minimum Ctot is at the point where its first derivative with respect to S is equal to zero, and the second derivative is greater than zero.

Let's find the first derivative:

Once the choice of a replenishment system has been made, it is necessary to quantify the size of the ordered batch, as well as the time interval through which the order is repeated.

The optimal batch size of the delivered goods and, accordingly, the optimal frequency of importation depend on the following factors:

volume of demand (turnover);

shipping costs;

inventory holding costs.

As an optimality criterion, a minimum of total costs for delivery and storage is chosen.

Rice. 1. Dual bin inventory control system

The graph of this dependence, which has the form of a hyperbola, is shown in Fig.1.

Both shipping costs and storage costs depend on the size of the order, however, the nature of the dependence of each of these cost items on the volume of the order is different. The cost of delivery of goods with an increase in the size of the order obviously decreases, since shipments are carried out in larger consignments and, therefore, less frequently.

The graph of this dependence, which has the form of a hyperbola, is shown in Fig. 2.

Storage costs increase in direct proportion to the size of the order. This dependence is graphically presented in fig. 3.

Rice. 2. Dependence of transportation costs on the size of the order

Rice. 3. The dependence of the cost of storing stocks on the size of the order

Adding both graphs, we get a curve that reflects the nature of the dependence of the total costs of transportation and storage on the size of the ordered lot (Fig. 4). As you can see, the total cost curve has a minimum point at which the total cost will be minimal. The abscissa of this point Sopt gives the value of the optimal order size.

Rice. 4. Dependence of the total cost of storage and transportation on the size of the order. Optimal order size S opt

Thus, the problem of determining the optimal order size, along with the graphical method, can also be solved analytically. To do this, you need to find the equation of the total curve, differentiate it and equate the second derivative to zero.

As a result, we obtain a formula known in the theory of inventory management as the Wilson formula, which allows us to calculate the optimal order size:

where Sopt - the optimal size of the ordered lot;

O - turnover value;

St - the costs associated with delivery;

Сх - costs associated with storage.

The resulting formula, which allows you to calculate the optimal order size, is known in the theory of inventory management as the Wilson formula.

The task of determining the optimal order size can be solved graphically and analytically. Consider the analytical method.

"To do this, it is necessary to minimize the function representing the sum of transportation and procurement costs and storage costs from the size of the order, i.e. to determine the conditions under which:

With total = From storage + transp. Min

where, C total. - the total cost of transportation and storage of the stock;

From storage - the cost of holding stock;

With transp. - transportation and procurement costs.

Suppose that for a certain period of time the turnover is Q. The size of one batch ordered and delivered is S. Let's say that a new batch is imported after the previous one has completely ended. Then the average value of the stock will be S / 2.

Let's introduce the size of the tariff M for stock storage. M is measured by the share that storage costs for period T make up in the cost of the average stock for the same period. For example, if M = 0.1, then this means that the cost of holding the stock for the period amounted to 10% of the cost of the average stock for the same period. We can also say that the cost of storing a unit of goods during the period amounted to 10 5 of its value.

Now you can calculate how much it will cost to store goods for period T:

From storage = M x S/2

The amount of transportation and procurement costs for period T is determined by multiplying the number of orders for this period by the amount of costs associated with the placement and delivery of one order.

With transp. = K x Q/S

Where

K - transportation and procurement costs associated with the placement and delivery of one order; Q/S - the number of deliveries for a period of time.

Having performed a number of transformations, we will find the optimal size of a one-time delivered lot (S opt.), at which the total cost of storage and delivery will be minimal.

With total = M x S/2 + K x Q/S

Next, we find the value of S, which turns the derivative of the objective function to zero, from which a formula is derived that allows you to calculate the optimal order size, known in inventory management theory as the Wilson formula.

Consider an example of calculating the optimal size of the ordered batch. We take the following values as initial data. The cost of a unit of goods is 40 rubles. (0.04 thousand rubles).

Monthly warehouse turnover for this item: Q = 500 units/month. or Q = 20 thousand rubles. /month The share of costs for storing goods is 10% of its value, i.e. M = 0.1.

Transport and procurement costs associated with the placement and delivery of one order: K = 0.25 thousand rubles.

Then the optimal size of the imported lot will be:

Obviously, it is advisable to import goods twice a month:

20 thousand rubles / 10 thousand rubles = 2 times.

In this case, transport and procurement costs and storage costs:

With total \u003d 0.1 H 10/2 + 0.25 H 20/10 \u003d 1 thousand rubles.

Ignoring the results obtained will lead to inflated costs.

An error in determining the volume of the ordered batch by 20% in our case will increase the monthly costs of the enterprise for transportation and storage by 2%. This is commensurate with the deposit rate.

In other words, this mistake is tantamount to the unacceptable behavior of a financier who kept money without movement for a month and did not allow them to "work" on a deposit."

The reorder point is determined by the formula:

Tz \u003d Rz x Tc + Zr

where, Pz is the average consumption of goods per unit of order duration;

Tc - the duration of the order cycle (the time interval between placing an order and receiving it);

Зр - the size of the reserve (guarantee) stock.

Consider an example of calculating the reorder point.

The company buys cotton fabric from a supplier. The annual volume of fabric demand is 8,200 m. We assume that the annual demand is equal to the volume of purchases. At the enterprise, the fabric is consumed evenly, and a reserve supply of fabric equal to 150 m is required. (Assume that there are 50 weeks in a year).

The average consumption of fabric per unit of order duration will be:

Rz = 8200 m. / 50 weeks = 164 m.

The reorder point will be equal to:

Tz \u003d 164 m. X 1 week. + 150 m. = 314 m.

This means that when the level of stock of fabric in the warehouse reaches 314 m, the next order should be made to the supplier.

It is worth noting that many enterprises have an affordable and very important information, which can be used in the control of TMZ. Groupings material costs should be carried out for all types of inventory in order to identify the most significant among them.

As a result of ranking by cost certain types raw materials and materials among them, a specific group can be distinguished, the control over the state of which is of paramount importance for the management working capital enterprises. For the most significant and expensive types of raw materials, it is advisable to determine the most rational order size and set the value of the reserve (insurance) stock.

It is necessary to compare the savings that can be obtained by the enterprise due to the optimal order size, with the additional transportation costs that arise when implementing this proposal.

For example, the daily supply of raw materials and materials may require the maintenance of a significant fleet of trucks. Transportation and operating costs can exceed the savings that can be obtained by optimizing the size of stocks.

transportation size order commodity

At the same time, it is possible to create a consignment warehouse of used raw materials near the enterprise.

In the management of stocks of products in a warehouse, the same techniques can be used as in the management of goods and materials, in particular the ABC method.

Using the methods presented above, as well as on the basis of an analysis of consumer requests and production capabilities, the most rational delivery schedule can be determined. finished products to the warehouse and the size of the safety stock.

The costs of storage, accounting and other costs associated with ensuring the rhythm of the supply of manufactured products must be weighed against the benefits that come from the uninterrupted supply of traditional buyers and the fulfillment of periodic urgent orders.

2. Practical part

Task 1

Plot an ABC analysis curve for the following set:

Let's sort all the objects in the table according to the share of the object in the total contribution, while calculating the share of the object on an accrual basis. We divide all materials into groups as follows: objects belong to group A, while specific gravity cumulative total will not reach 80%; in group B - 95%, the rest of the objects will be assigned to group C.

ABC analysis

primary list	ordered list
object number	Object Contribution	item number	Object Contribution	The share of the object in the total contribution,%	Share of cumulative total, %

Task 2

The annual demand is D units, the cost of placing an order, rubles/order, the purchase price, C rubles/unit, the annual cost of storing one unit is a % of its purchase price. Delivery time 6 days, 300 working days a year. Find the optimal order level, costs, reorder level, number of cycles per year, distance between cycles. Compare two models: the main one and the one with a deficit (bids are fulfilled).

1) The basic model of inventory management.

Optimal order level:

Thus, during each order cycle, it is necessary to place an order for 86 units of products.

The annual total variable cost of orders is determined according to the formula:

The sales volume for 6 days of delivery will be:

Reorder level 16 units.

That is, new stock is supplied when the stock level is 16 units. Number of cycles per year

Distance between cycles

2) Consider a model with a deficit (orders are fulfilled).

Planned deficit

Optimal order level:

In this situation, it is necessary to submit orders of 116 units.

Maximum deficit:

The total variable cost per year is defined as follows:

Compared to the basic model, the savings are

1396.42-1073.26 = 323.16 rubles per year.

Thus, if we use the deficit planning model, then we can achieve savings in the total variable cost of inventory, equal to 323.16 rubles per year.

Task 3

The table shows the coordinates of eight consumers, the monthly turnover of each of them is indicated. Find the coordinates of the supply center.

consumer number	X coordinate	Y coordinate	Cargo turnover

We will solve the problem of choosing the location of the supply center for a distribution system that includes one supply center. The main factor influencing the choice of the location of the supply center is the size of the cargo turnover of each of the eight consumers. Costs can be minimized by placing a supply center in the vicinity of the center of gravity of cargo flows.

Coordinates of the center of gravity of cargo flows (X center, Y center), i.e. - the points where the distribution warehouse can be located are determined by the formulas:

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

Xi, Yj are the coordinates of the i-th consumer.

The point in the territory that provides the minimum transport work on delivery, in the general case does not coincide with the found center of gravity, but, as a rule, is located somewhere nearby. To select an acceptable location for the supply center will allow the subsequent analysis of possible locations in the vicinity of the found center of gravity. At the same time, it is necessary to assess the transport accessibility of the area, the size and configuration of the possible site, as well as the plans of local authorities regarding the intended territory.

Let's make a drawing for the task.

Find the coordinates of the center of gravity of cargo flows.

X center = 21.7

Y center = 17

Let's put a point with such coordinates on the drawing.

Task 4

Select a supplier if the dynamics of prices for the supplied goods is known. The data are given in the table.

Dynamics of prices for supplied goods

Price growth rate for i-th variety goods from the j-th supplier

where C ij2 is the price of the i-th product from the j-th supplier in the second quarter;

C ij1 - the price of the i-th product from the j-th supplier in the first quarter.

Under the conditions of this problem, for the first supplier for goods A, B and C, respectively

For the second supplier for goods A, B and C, respectively

The share of the i-th product in the total supply of the j-th supplier

where S ij is the amount for which the goods of the i-th type j-th supplier

G ij - the volume of supply of goods of the i-th type by the j-th supplier;

УS ij - the amount on which all goods j supplier.

The share of goods of type A in the total supply of the first supplier

The share of goods of type B in the total supply of the first supplier

The share of goods of type C in the total supply of the first supplier

The share of goods of type A in the total supply of the second supplier

The share of goods of type B in the total supply of the second supplier

The share of goods of type C in the total supply of the second supplier

The weighted average price growth rate of the j-th supplier

Then the weighted average price growth rate of the first supplier.

The weighted average price growth rate of the second supplier.

The growth rate of the price reflects the increase in the negative characteristics of the supplier, so preference should obviously be given to one of them, whose rating is lower. IN this example preference should be given to supplier No. 1.

List of used literature

1. Anikin, B.A. Logistics: Textbook [Text] / B.A. Anikin. M.: INFRA - M, 2008.

2. Gadzhinsky, A.M. Logistics: Textbook [Text] / A.M. Gadzhinsky - M.: "Dashkov and Co", 2008. - 484 p.

3. Nerush, Yu.M. Logistics: Textbook [Text] / Yu.M. Nerush. - M.: Prospekt, TK Velby, 2008. - 520 p.

4. Workshop on logistics / Ed. B.A. Anikina. - M.: INFRA - M, 2007. - 280 p.

5. Chudakov, A.D. Logistics [Text]: Textbook / A.D. Chudakov. - M.: RDL Publishing House, 2003. - 480 p.

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The optimal batch order depends on. Determination of the optimal order size

Send your good work in the knowledge base is simple. Use the form below

1. Determination of the optimal order size

volume of demand (turnover);

transportation and procurement costs;

inventory holding costs.

As an optimality criterion, choose the minimum amount of costs of transport and procurement and storage.

Transport and procurement costs decrease with an increase in the size of the order, since the purchases and transportation of goods are carried out in larger lots and, therefore, less frequently.

Storage costs increase in direct proportion to the size of the order.

To solve this problem, it is necessary to minimize the function representing the sum of the costs of transport and procurement and storage, i.e. determine the conditions under which

Common \u003d Save + Transp,

where Сtot is the total cost of transportation and storage; Store - the cost of storing the stock; Stsp - transport and procurement costs.

The cost of storing goods for period T can be calculated using the following formula:

Save = M (S / 2).

The amount of transport and procurement costs for the period T will be determined by the formula:

Store = K (Q/S)

where K - transportation and procurement costs associated with the placement and delivery of one order; Q/S - number of orders for a period of time. Substituting the data into the main function, we get:

So6sch \u003d M (S / 2) + K (Q / S).

The minimum Ctot is at the point where its first derivative with respect to S is equal to zero, and the second derivative is greater than zero.

Let's find the first derivative:

Once the choice of a replenishment system has been made, it is necessary to quantify the size of the ordered batch, as well as the time interval through which the order is repeated.

The optimal batch size of the delivered goods and, accordingly, the optimal frequency of importation depend on the following factors:

volume of demand (turnover);

shipping costs;

inventory holding costs.

As an optimality criterion, a minimum of total costs for delivery and storage is chosen.

Rice. 1. Dual bin inventory control system

The graph of this dependence, which has the form of a hyperbola, is shown in Fig.1.

The graph of this dependence, which has the form of a hyperbola, is shown in Fig. 2.

Storage costs increase in direct proportion to the size of the order. This dependence is graphically presented in fig. 3.

Rice. 2. Dependence of transportation costs on the size of the order

Rice. 3. The dependence of the cost of storing stocks on the size of the order

Rice. 4. Dependence of the total cost of storage and transportation on the size of the order. Optimal order size S opt

Thus, the problem of determining the optimal order size, along with the graphical method, can also be solved analytically. To do this, you need to find the equation of the total curve, differentiate it and equate the second derivative to zero.

As a result, we obtain a formula known in the theory of inventory management as the Wilson formula, which allows us to calculate the optimal order size:

where Sopt - the optimal size of the ordered lot;

O - turnover value;

St - the costs associated with delivery;

Сх - costs associated with storage.

The resulting formula, which allows you to calculate the optimal order size, is known in the theory of inventory management as the Wilson formula.

The task of determining the optimal order size can be solved graphically and analytically. Consider the analytical method.

"To do this, it is necessary to minimize the function representing the sum of transportation and procurement costs and storage costs from the size of the order, i.e. to determine the conditions under which:

With total = From storage + transp. Min

where, C total. - the total cost of transportation and storage of the stock;

From storage - the cost of holding stock;

With transp. - transportation and procurement costs.

Suppose that for a certain period of time the turnover is Q. The size of one batch ordered and delivered is S. Let's say that a new batch is imported after the previous one has completely ended. Then the average value of the stock will be S / 2.

Now you can calculate how much it will cost to store goods for period T:

From storage = M x S/2

The amount of transportation and procurement costs for period T is determined by multiplying the number of orders for this period by the amount of costs associated with the placement and delivery of one order.

With transp. = K x Q/S

Where

K - transportation and procurement costs associated with the placement and delivery of one order; Q/S - the number of deliveries for a period of time.

Having performed a number of transformations, we will find the optimal size of a one-time delivered lot (S opt.), at which the total cost of storage and delivery will be minimal.

With total = M x S/2 + K x Q/S

Next, we find the value of S, which turns the derivative of the objective function to zero, from which a formula is derived that allows you to calculate the optimal order size, known in inventory management theory as the Wilson formula.

Consider an example of calculating the optimal size of the ordered batch. We take the following values ​​as initial data. The cost of a unit of goods is 40 rubles. (0.04 thousand rubles).

Monthly warehouse turnover for this item: Q = 500 units/month. or Q = 20 thousand rubles. /month The share of costs for storing goods is 10% of its value, i.e. M = 0.1.

Transport and procurement costs associated with the placement and delivery of one order: K = 0.25 thousand rubles.

Then the optimal size of the imported lot will be:

Obviously, it is advisable to import goods twice a month:

20 thousand rubles / 10 thousand rubles = 2 times.

In this case, transport and procurement costs and storage costs:

With total \u003d 0.1 H 10/2 + 0.25 H 20/10 \u003d 1 thousand rubles.

Ignoring the results obtained will lead to inflated costs.

An error in determining the volume of the ordered batch by 20% in our case will increase the monthly costs of the enterprise for transportation and storage by 2%. This is commensurate with the deposit rate.

In other words, this mistake is tantamount to the unacceptable behavior of a financier who kept money without movement for a month and did not allow them to "work" on a deposit."

The reorder point is determined by the formula:

Tz \u003d Rz x Tc + Zr

where, Pz is the average consumption of goods per unit of order duration;

Tc - the duration of the order cycle (the time interval between placing an order and receiving it);

Зр - the size of the reserve (guarantee) stock.

Consider an example of calculating the reorder point.

The average consumption of fabric per unit of order duration will be:

Rz = 8200 m. / 50 weeks = 164 m.

The reorder point will be equal to:

Tz \u003d 164 m. X 1 week. + 150 m. = 314 m.

This means that when the level of stock of fabric in the warehouse reaches 314 m, the next order should be made to the supplier.

It is worth noting that many enterprises have an affordable and very important information, which can be used in the control of TMZ. Groupings material costs should be carried out for all types of inventory in order to identify the most significant among them.

It is necessary to compare the savings that can be obtained by the enterprise due to the optimal order size, with the additional transportation costs that arise when implementing this proposal.

Consider an example of calculating the optimal size of the ordered batch. We take the following values as initial data. The cost of a unit of goods is 40 rubles. (0.04 thousand rubles).