The optimal batch size is determined. Determining the optimal batch size
The EOQ model is based on the total cost (TC) function, which reflects the costs of purchasing, delivering and holding inventory.
p– purchase price or cost of production of a unit of inventory;
D– annual demand for reserves;
K– the cost of organizing the order (loading, unloading, packaging, transportation costs);
Q– volume of the delivery lot.
H– cost of storing 1 unit of inventory for a year (cost of capital, warehouse costs, insurance, etc.).
Having solved the resulting equation with respect to the variable Q, we obtain the optimal delivery quantity (EOQ).
Graphically this can be represented as follows:
In other words, the optimal delivery lot is the volume (Q) at which the value of the total cost (TC) function will be minimal.
Example. Annual requirement of the production company building materials in cement is 50,000 tons at a price of 500 USD. per ton. At the same time, the cost of organizing one delivery is 350 USD, and the cost of storing 1 ton of cement for a year is 2 USD. In this case, the size of the optimal delivery lot will be 2958 tons.
In this case, the number of deliveries for the year will be 16.9 (50000/2958). The fractional part of 0.9 means that the last 17th delivery will be completed by 90%, and the remaining 10% will be transferred to the next year.
Substituting the optimal delivery batch into the total cost function, we get 25,008,874 USD.
TC = 500*50000 + 50000*350/2958 + 2*2958/2 = 25008874 c.u.
For any other delivery lot size, the total costs will be higher. For example, for 3000 tons it will be 25008833 USD, and for 2900 tons 25008934 USD.
TC = 500*50000 + 50000*350/3000 + 2*3000/2 = 25008833 c.u.
TC = 500*50000 + 50000*350/2900 + 2*2900/2 = 25008934 c.u.
Graphically, inventory consumption can be represented as follows, provided that their balance at the beginning of the year is equal to the optimal delivery lot.
Taking into account the initial assumptions of the EOQ model about uniform consumption of inventory, the optimal delivery batch will be developed to zero balance, provided that the next batch will be delivered at this moment.
67. Operating lever and determining the strength of its influence;
Operating leverage manifests itself in cases where an enterprise has fixed costs, regardless of production (sales) volume.
The production leverage effect arises due to the heterogeneous cost structure of the enterprise. The change in variable costs is directly proportional to the change in production volume and sales revenue, and fixed costs over a fairly long period of time they hardly react to changes in production volume. A sharp change in the amount of fixed costs occurs due to a radical restructuring organizational structure enterprises during periods of mass replacement of fixed assets and quality
"technological leaps".
The strength of the production lever depends on the share of fixed costs in the total costs of the enterprise.
The production leverage effect is one of the most important indicators financial risk, since it shows by what percentage the balance sheet profit, as well as the economic profitability of assets, will change if the sales volume or revenue from the sale of products (works, services) changes by one percent.
In practical calculations, to determine the strength of the impact of operating leverage on a specific enterprise, the result from product sales after reimbursement of variable costs (VC), which is often called marginal income, is used.
Operating leverage is always calculated for a certain sales volume. As sales revenue changes, so does its impact. Operating leverage allows you to assess the degree of influence of changes in sales volumes on the size of the organization's future profit. Operating leverage calculations show by what percentage profit will change if sales volume changes by 1%.
Operating leverage effect comes down to the fact that any change in sales revenue (due to a change in volume) leads to an even stronger change in profit. The action of this effect is associated with the disproportionate influence of fixed and variable costs on the result of the financial and economic activities of the enterprise when production volume changes.
Operating leverage force shows the degree of business risk, that is, the risk of loss of profit associated with fluctuations in sales volume. The greater the effect of operating leverage (the greater the share of fixed costs), the greater the business risk.
Thus, modern management costs involves quite diverse approaches to accounting and analysis of costs, profits, and business risk. You have to master these interesting tools to ensure the survival and development of your business.
Production risk is associated with the concept of operational, or production, leverage, and financial risk is associated with the concept of financial leverage.
There are three main measures of operating leverage:
a) the share of fixed production costs in the total amount of costs, or, which is equivalent, the ratio of fixed and variable costs,
b) the ratio of the rate of change in profit before interest and taxes to the rate of change in sales volume in natural units;
c) the ratio of net profit to fixed production costs
Any major improvement in the material and technical base towards an increase in the share of non-current assets is accompanied by an increase in the level of operational leverage and production risk.
Method of controlling the level of fixed expenses- method for calculating the critical sales volume. Its meaning is to calculate at what production volumes in natural units the marginal profit (i.e. the difference between sales revenue and non-financial variable expenses or direct variable expenses) will be equal to the amount of conditionally fixed expenses. This method allows you to find the minimum volume of production that is necessary to cover conditionally fixed costs, i.e. expenses that do not depend on production volumes.
Among the indicators for assessing the level of financial leverage, two are most famous: the ratio of debt to equity capital and the ratio of the rate of change in net profit to the rate of change in earnings before interest and taxes.
As part of the overall financial strategy of a business entity debt management assumes preliminary analysis their attraction and use, adjustment of the attraction policy or development of a new policy. The analysis involves studying the volumes, dynamics, forms of attraction, types of loans, terms of attraction, lending conditions, composition of creditors, efficiency of use and repayment of borrowed funds. Borrowing policy includes the determination of: a) the reasons and prerequisites for such attraction; b) the targeted nature of the use of borrowed funds; c) limits (maximum volumes) of attraction; d) conditions (including terms and prices of attraction); e) general composition, structure; f) forms of attraction; g) creditors, etc.
68.Features of planning depreciation charges using the linear method;
Example No. 1. The store sells Q TVs daily. Overhead costs for supplying a batch of televisions to a store are estimated at S rubles. The cost of storing one TV in a store warehouse is s rub. Determine the optimal volume of a batch of televisions, the optimal average daily costs for storing and replenishing stocks of televisions in a warehouse. What will these costs be equal to for batch sizes n1 and n2 of televisions?
Download the solution.
The decision is made using the online calculator Optimal order size.
Example No. 2. Calculate the optimal order size for all components using Wilson's formula (c1=12;c2=0.3;q=1). Example No. 2(c1=5;c2=0.1;q=150).Example No. 3
(c1=1;c2=5;q=25).Example No. 4
(c1=22;c2=17;q=112).Example No. 5
(c1=150;c2=55;q=6).Example No. 6
(c1=20000;c2=150;q=3000).Example No. 7
(c1=200;c2=150;q=3000).Example No. 8
(c1=200;c2=150;q=3000).Example No. 9
(c1=20000;c2=1800;q=3000).Example No. 10
(c1=90;c2=10;q=73000).Example No. 11
(c1=90;c2=10;q=200).Example No. 12
(c1=9490.91;c2=5;q=113938.92).Example No. 13
(c1=1;c2=1;q=1).Example No. 14
(c1=3;c2=3;q=3).Example No. 15
(c1=1;c2=1;q=1).Example No. 16
(c1=1;c2=1;q=1).Example No. 17
(c1=1500;c2=20;q=30000).Example No. 18
(c1=1500;c2=20;q=3600).Example No. 19
Example No. 3. The intensity of demand is 1000 units of goods per year. Organizational costs are equal to 7 USD, storage costs - 6 USD, unit price - 6 USD. Determine the optimal batch size, number of batches per year, interval between deliveries and total costs. Create a stock chart.
Download solution
Example No. 4. Consider all the stages of solving the problem of the optimal size of the purchased batch of goods with the following data: Q = 72, C 0 = 3 thousand rubles / m, C 1 = 400 rubles / m, C 2 = 100 rubles / m.
Download solution
Example No. 5. The annual demand for valves costing $4 per unit is 1000 units. Storage costs are estimated at 10% of the cost of each product. average cost order is $1.6 per order. There are 270 working days in a year. Determine the size of the economic order. Determine the optimal number of days between orders.
Solution: Download solution
Example No. 6. Grain is delivered to the warehouse in batches of 800 tons. The grain consumption from the warehouse is 200 tons per day. Overhead costs for delivering a batch of grain are 1.5 million rubles. The cost of storing 1 ton of grain for 24 hours is 80 rubles.
You need to determine:
- cycle time, average daily overhead and average daily storage costs;
- the optimal size of the ordered batch and the calculated characteristics of the warehouse in optimal mode;
To make the calculation, we use the basic formulas of the “ideal” warehouse operating model.
1) Cycle duration: T = Q/M = 800/200 = 4 days
average daily overhead costs: K/T = 1500/4 = 375 thousand rubles/day
average daily storage costs: hQ/2 = 80*800/2 = 28 thousand rubles/day
The optimal order size is calculated by Wilson's formula:
where q 0 – optimal order size, pcs.;
C 1 = 1,500,000, cost of fulfilling one order, rub.;
Q = 200, need for inventory items for a certain period of time (year), pcs.;
C 2 = 80, cost of maintaining a unit of inventory, rub./piece. 
T
Optimal average stock level: t
days
Example No. 7. The annual demand is D units, the cost of placing an order is C 0 rubles/order, the purchase price is C b rubles/unit, the annual cost of storing one unit is a% of its price. Delivery time 6 days, 1 year = 300 working days. Find the optimal order size, costs, re-order level, number of cycles per year, distance between cycles. You can get a b% discount from suppliers if the order size is at least d units. Is it worth taking advantage of the discount? The annual cost of lack of inventory is C d rubles/unit. Compare 2 models: basic and with a deficit (orders are fulfilled).
| Item no. | D | C 0 | Cb | a | b | d | Cd |
| 21 | 400 | 50 | 40 | 20 | 3 | 80 | 10 |
We obtain the solution using a calculator. First we find the cost of storing one unit, C 2 = 40 * 20% = 8 rubles. (introduced into the main model) and at a discount, C 2 = (1-0.03)*40*20% = 7.76 rub. (for discounted model)
1. Calculation of the optimal order size.
The optimal order size is calculated using Wilson's formula:
where q 0 – optimal order size, pcs.;
C 1 = 50, cost of fulfilling one order, rub.;
Q = 400, demand for inventory items for a certain period of time (year), pcs.;
C 2 = 8, cost of maintaining a unit of inventory, rub./piece. 
Optimal average stock level: 
Optimal replenishment frequency: 
(year) or 0.18·300=53 days.
Determining the optimal batch size
Dmitry Ezepov, purchasing manager at Midwest © LOGISTIC&system www.logistpro.ru
One of the most difficult tasks for any purchasing manager is choosing the optimal order size. However, there are very few real tools to facilitate its solution. Of course, there is the Wilson formula, which is presented in theoretical literature as such a tool, but in practice its use must be adjusted
The author of this article, working in several large trading companies in Minsk, never saw Wilson’s formula applied in practice. Its absence in the arsenal of purchasing managers cannot be explained by their lack of analytical skills and abilities, since modern companies pay great attention qualifications of their employees.
Let's try to find out why “the most common tool in inventory management” does not go beyond scientific publications and textbooks. Below is the well-known Wilson formula, using which it is recommended to calculate the economic order quantity:
where Q is the volume of the purchase batch;
S – need for materials or finished products for reporting period;
O – fixed costs associated with fulfilling one order;
C – costs of storing a unit of inventory for the reporting period.
The essence of this formula comes down to calculating what batch sizes should be (all the same) in order to deliver a given volume of goods (that is, the total demand for the reporting period) during a given period. In this case, the sum of fixed and variable costs should be minimal.
The problem being solved has at least four initial conditions: 1) a given volume that needs to be delivered to its destination; 2) specified period; 3) equal batch sizes; 4) pre-approved composition of fixed and variable costs. This formulation of the problem has little in common with the real conditions of doing business. No one knows the capacity and dynamics of the market in advance, so the sizes of ordered batches will always be different. There is also no point in setting a period for planning purchases, since commercial companies usually exist much longer than the reporting period. The composition of costs is also subject to change due to the influence of many factors.
In other words, the conditions for applying the Wilson formula simply do not exist in reality, or at least occur very rarely. Do commercial companies need a solution to the problem with such initial conditions? I think not. That is why the “common tool” is implemented only on paper.
WE CHANGE THE CONDITIONS
In market conditions, sales activity is inconsistent, which inevitably affects the supply process. Therefore, both the frequency and size of purchased lots never coincide with their planned indicators at the beginning of the reporting period. If you focus solely on the plan or long-term forecast (as in Wilson’s formula), then one of two situations will inevitably arise: either an overflow of the warehouse or a shortage of products. The result of both will always be a decrease in net profit. In the first case, due to an increase in storage costs, in the second, due to a shortage. Therefore, the formula for calculating the optimal order size must be flexible in relation to the market situation, that is, based on the most accurate short-term sales forecast.
The total costs of purchasing and storing inventories consist of the sum of these same costs for each purchased batch. Consequently, minimizing the cost of delivery and storage of each batch separately leads to minimization of the supply process as a whole. And since calculating the volume of each batch requires a short-term sales forecast (and not for the entire reporting period), then necessary condition The flexibility of the formula for calculating the optimal lot size (OPS) in relation to the market situation is fulfilled. This condition of the problem corresponds to both the goal of a commercial company (minimizing costs) and the real conditions of doing business (variability of market conditions). Definitions of fixed and variable costs for the supply minimization approach on a lot-by-lot basis are provided in the “Types of Costs” box on page 28.
ACTUAL CALCULATION
If we assume that the loan is repaid as the cost of inventory decreases at planned intervals (days, weeks, month, etc.) (1), then, using the formula for the sum of the terms of an arithmetic progression, we can calculate the total cost of storing one batch of inventory (usage fee credit):
where K is the cost of storing inventory;
Q – purchase batch volume;
p – purchase price of a unit of goods;
t is the time the stock is in the warehouse, which depends on the short-term forecast of sales intensity;
r – interest rate per planned unit of time (day, week, etc.).
Thus, the total costs for delivery and storage of the order batch will be:
where Z is the total cost of delivery and storage of the batch.
There is no point in minimizing the absolute value of the cost of delivery and storage of one batch, since it would be cheaper to simply refuse purchases, so you should move on to relative indicator costs per unit of inventory:
where z is the cost of replenishment and storage of a unit of stock.
If purchases are made frequently, then the sales period for one batch is short, and the sales intensity during this time will be relatively constant2. Based on this, the time the stock is in the warehouse is calculated as:
where is a short-term forecast of average sales for a planned unit of time (day, week, month, etc.).
The designation is not accidental, since the forecast is usually average sales in the past, taking into account various adjustments (shortages in stock in the past, the presence of a trend, etc.).
Thus, substituting formula (5) into formula (4), we obtain the objective function for minimizing the cost of delivery and storage of a unit of inventory:
Equating the first derivative to zero:
we find (ORP) taking into account short-term sales forecast:
NEW WILSON FORMULA
Formally, from a mathematical point of view, formula (8) is the same Wilson formula (the numerator and denominator are divided by the same value depending on the adopted planned unit of time). And if the sales intensity does not change, say, during the year, then, replacing the annual demand for goods and r - the annual interest rate, we will get a result that will be identical to the EOC calculation. However, from a functional point of view, formula (8) demonstrates a completely different approach to the problem being solved. It takes into account the current sales forecast, which makes the calculation flexible relative to the market situation. The remaining parameters of the ORP formula, if necessary, can be quickly adjusted, which is also an undeniable advantage over the classical formula for calculating EOP.
The company's purchasing policy is also influenced by other, often more significant factors than the intensity of sales (current balances in the company's own warehouse, minimum batch size, delivery conditions, etc.). Therefore, despite the fact that the proposed formula eliminates the main obstacle to calculating the optimal order size, its use can only be an auxiliary tool effective management stocks.
A highly professional purchasing manager relies on a whole system of statistical indicators, in which the ORP formula plays a significant, but far from decisive role. However, the description of such a system of indicators for effective inventory management is a separate topic, which we will cover in the next issues of the magazine
1- In reality this does not happen, so the cost of holding inventory will be higher. 2- In reality, you need to pay attention not to order frequency, but to the stability of sales within the short-term sales forecast period. It’s just that usually, the shorter the period, the less seasonality and tendency appear.
With this article we open a small series of publications devoted to determining the optimal batch size of parts put into production. Obviously, this value affects economic indicators, therefore it is important for each manufacturer to determine it correctly. We want to talk about the history of this issue, the methods used and the latest trends.
As soon as any product is produced in quantities of more than one piece, a choice arises: either we can first completely make all the dissimilar parts of one product and only then proceed to the next one, or we make the same (or similar) parts for all products at once. The second method provides many advantages: specialization of jobs, rational use technology, quality stability, increased productivity.
When producing a small quantity of goods, the number of identical parts is equal to the number of finished products. As production volume increases, production costs associated with setting up equipment, installing fixtures, and changing tools fall. But this happens up to a certain limit. Further growth leads to increased costs for storing raw materials, semi-finished products in workshops and finished products; significant funds are frozen in unfinished products.
This problem becomes noticeable even for a small artisanal workshop: “Where to place additional raw materials, where to put finished goods before they are bought and exported, where to get additional funds to buy more material?” But for a large enterprise everything is much more serious - additional warehouses, buffer zones, and this means not only additional space, but also equipment, people, heating, organization of logistics, accounting.
The solution is to split the total number of parts into separate batches. Production of products based on launch-release batches is called batch production.
People began to think about how many identical parts to put into production almost immediately after the transition from the manual method of manufacturing goods to the machine one. The development of high-volume and mass flow production in the early 20th century stimulated the development of theories for optimizing part lot sizes. These models have been improved over the years. At the end of the 20th and beginning of the 21st century, production began to change fundamentally, which also required new approaches to the distribution of products among production batches.
Obviously, as the batch size increases, the frequency of equipment changeovers, equipment and tool changes, and production preparation operations decreases, which means the costs of changeovers fall. At the same time, warehousing costs are increasing. The graph of total costs versus batch size has a minimum point. The nature of changes in costs is shown in the figure.
Determining the batch size that corresponds to this minimum cost is an optimization problem. Methods for calculating this point were developed at the beginning of the 20th century, and not without intrigue.
Historically, the first to propose a formula for calculating the optimal batch was the American Ford W. Harris. In 1913 he published his calculations. Frankly, derivation of the optimal batch size formula did not represent any theoretical breakthrough in mathematics. This is a fairly simple problem of finding the minimum of a function. Practical knowledge of the peculiarities of production economics was valuable. Harris worked as an engineer for an electrical engineering firm and used his experience to inform his analysis. Moreover, he did not have a diploma - he only graduated high school. Self-taught, he was phenomenally successful - he published 70 articles and registered 50 patents.
Over the next decades, publications by other authors appeared on the topic of optimal batch size in manufacturing. Since these studies were applied, there was no tradition of citing primary sources, as is customary in fundamental science.
In 1934, a new publication appeared in the Harvard Business Review, in which the author R.H. Wilson (Wilson or Wilson) again gives a formula for the optimal batch size without reference to previous works. And by a strange coincidence, it was his name that gave the name to the formula and became entrenched in subsequent history. Some researchers believe that there was competition between various publications and business schools (Harvard and Chicago), which supported only their authors. As a result, Harris' priority was forgotten after some time. It was only in 1990 that an attempt was made in the United States to understand the priority and date of the first publication on this topic.
But while the Americans were figuring out who was the first to learn how to calculate the optimal size of parties, the Germans, agreeing with Harris’s primacy, claim that their compatriot Kurt Andler really developed this topic for the first time in 1929 and call the corresponding formula after him , while no mention is made of Wilson.
Andler's formula for the optimal batch size of parts in its simplest form is as follows:
where y min is the optimal batch size,
V — the required volume of products over a period of time (sales speed),
Cr — costs associated with changing batches (conditionally - for setup),
Cl— specific warehousing costs over a period of time.
Wilson's formula for the optimal batch of goods to be ordered to a warehouse (for sales or for processing) looks similar. But its components have a slightly different meaning and different designations (in the classical form):
where EOQ is the economic order quantity (EOQ)),
Q — quantity of goods per year (Quantity in annual units),
P — costs of order implementation (Placing an order cost),
C — the cost of storing a unit of goods per year (Carry costs).
By the way, Americans easily remember this formula using the mnemonic phrase: “The square root of two Q uarter P unders with C heese.” The phrase is easy to translate,
or - “the square root of two quarter pounders with cheese.” Here, for Russians and in general everyone except Americans, an explanation is required. Americans call a McDonald's cheeseburger a “quarter pound,” which traditionally weighs a quarter pound—113.4 grams.
Outside the United States, this type of hamburger has different names, and in this regard, one can recall the famous dialogue between two killers Vincent and Jules from Tarantino’s film “Pulp Fiction.” One of the bandits, played by Travolta, talks about his trip to Europe, that in Paris you can buy beer at McDonald’s and other “miracles”:
— Do you know what they call Quarter Pounder with cheese in Paris?
- Why don’t they call him Quarter Pounder?
- No, they have the metric system, and they don’t know what ... (omitting profanity) a quarter pound is. They call it the Royal Cheeseburger.
— Royal Cheeseburger??? What do they call a Big Mac then?
“Big Mac is Big Mac, but they call it Le Big Mac.”
- Le Big Mac?! Ha ha ha...
So Vincent and Jules could easily remember the formula for the optimal volume of goods and apply it in their activities.
The classical Andler-Wilson optimal batch model is based on a number of initial assumptions: production without capacity limitations, without intermediate warehouses, demand is stable, the ability to divide materials into any batch size, warehouse costs are constant, a warehouse of unlimited volume, an unlimited planning horizon, implementation goods occurs immediately after production, etc.
Each such assumption is at the same time a limitation for the application of the model in certain specific production conditions and can serve as the basis for the development and complication of the model.
However, the results of calculations using the simplest classical formula can still serve as basic values for the initial assessment - the accuracy of the assessment largely depends on how fully and accurately we take into account the costs associated with launching a new batch and storage costs.
The furniture industry has recently become increasingly individualized; work is increasingly based on orders - if not from end customers, then from a dynamically replenished warehouse, which practically acts as a customer. In this regard, the trend of the last decade has been to work according to the Losgrösse 1 principle - that is, the batch size is from one piece. We will dwell on this in more detail in the following articles.
Batch size- this is the amount of sequentially produced goods without interruptions or switching in the technological process .
What is the importance of determining the optimal batch size?
The optimal batch size leads to a reduction in warehouse losses, interest on property, and reconfiguration costs. Consequently, dividing the volume of goods produced per year into shares leads to a significant reduction in costs.
The best lot size for the manufacturer is counteracted by the best lot size for distribution. With this option, reconfiguration costs become costs for order registration.
What is the peculiarity of mass production?
Serial production is optimal for groups of goods with similar manufacturing processes. After some time, there is a need to reconfigure to produce a different product. The above figure shows that products A, B, C are produced sequentially on the same production line.
A break in the technological process to launch production of a new product leads to downtime and the appearance of costs not related to the batch size - constant serial costs. These are the costs of reconfiguring and adjusting production facilities.
As batch size increases, fixed serial costs also increase. On a per-unit basis, these costs are reduced as batch sizes increase and are produced without interruptions or changeovers. technological process- digressive behavior of costs.
Serial production requires precise coordination of production volume, series and sequence of production of goods. Requirements for various goods must be fulfilled by the enterprise without delay.
What are the options for meeting the annual demand for a product?
A businessman has several options for satisfying the need for a product throughout the year:
1) A single batch equal to the volume of annual demand:
- an increase in proportional serial costs, namely warehouse costs and interest on property;
- single costs for reconfiguration;
- low level of fixed serial costs;
- the likelihood that needs for other types of goods will not be satisfied.
2) A certain number of batches that satisfy the annual need:
- reduction of warehouse and property costs;
- increase in reconfiguration costs.
So, the main task is to find the most effective batch size, at which a unit of goods produced will bring minimal constant and proportional serial costs.
What are the main costs for mass production?
When mass producing goods at an enterprise, costs arise that require more complete consideration:
A) Warehouse costs:
- warehouse expenses - wages, costs of maintaining the functionality of warehouse space;
- calculation interest is an expense that correlates with the volume of property stored in a warehouse.
Both positions can be reduced through a planned reduction in the volume of goods in stock. The lower limit in this case is the safety stock.
Reducing warehouse costs and calculation interest causes resistance from the increasing costs of reconfiguring the technological process and the likelihood of not saturating the need for a certain type of goods. The way out of this situation is to find the optimal batch size.
B) Reconfiguration costs:
- depend on the duration of the reconfiguration process;
- do not depend on the size of the batch;
- in terms of unit of goods decrease with increasing batch size;
- consist of: 1) downtime costs; 2) costs for necessary technical means and equipment; 3) wages; 4) support costs.
Steps to finding the optimal batch size
To find the most appropriate batch size option you need to:
1. Find the number of games:
where n is the number of batches, M is the annual volume of goods sold, m is the most acceptable batch size, produced without interruption or reconfiguration of the technological process.
2. Calculate the constant serial costs of all series:
where K F is the total fixed costs for reconfiguring all batches, K f is serial costs for one batch.
where K L is the amount of total warehouse costs, K l is the rate of warehouse costs and calculation interest in terms of per unit of goods for the period.
4. Determine total costs (K):
5. Minimizing total costs leads us to the function:
6. The most acceptable batch size (m) is found by reducing the equation to differential form:
7. Setting the condition
8. Solving the equation for m
Consider this with an example. Projected sales next year will be 400,000 units of product T. The amount of fixed serial costs reaches 6,000 DM. Warehouse costs are equal to 20 DM per unit of goods per year. Let's calculate the most acceptable batch size option.
So, cost minimization will be achieved with a batch size of 15,491 pieces. goods.
Are there any assumptions in the formula for calculating the optimal batch size?
Assumptions in the formula for calculating the most acceptable lot size:
- infinity of speed of the production process;
- constant speed of implementation;
- warehouse losses were not taken into account;
- constancy of fixed serial costs;
- directly proportional change in other production costs;
- restrictions on warehouse space were not taken into account.
Is calculating the optimal batch size feasible today?
You should not refuse to calculate the optimal batch size under the pretext of excessive expenditure of labor resources. Of course, there is no need to determine the optimal lot size for each type of product, but for goods A and B these calculations are necessary.
To begin with, the optimal batch size is calculated for A-products, which make up 5 percent of the volume of all products, but give about 75 percent in terms of profitability. Improved planning and regulation of the production of A-products will lead to a significant reduction in costs.
Implementing batch size optimization in combination with ABC analysis will significantly reduce production costs. This effect will be more significant when efficiency increases and warehouse costs decrease.
The widespread and active use of personal computers facilitates the task of finding the optimal batch size.
