The effective administration of inventories supported by techniques, methods and support instruments oriented to their systematization constitutes a catalyst factor in the optimization of the operational and managerial processes of the modern company, many organizations are unaware of the importance of implementing a systematized control of information flow. inventory or activities related to updates or adjustments.
What usually generates as a consequence the inaccurate possession of accounting and financial data, considerable losses in the year and an inefficient dynamics in relation to dispatch and supply chains.
This first stage of the publication aims to incorporate the basic concepts of technical inventory management, the second stage will propose software based on code standards specialized in the automation of the models and concepts presented here, as well as market intelligence techniques such as orders Suggested and inventory shots.
I Basic Notions of Inventories and Warehouse Management
1.1.- General Descriptions of Inventories and Warehouse Management Techniques
Inventory is a primary part of many companies. Essentially, inventory is the storage of goods that are supplied or dispatched to consumers or claimants in order to make a profit. In addition, in some cases, inventory also methods and technologies that a company uses to keep the business up and running.
There are different forms of inventory and any business can rely on one or more forms of inventory. First, the inventory of materials and components is mentioned: this type of inventory is the storage of the different parts for the manufacture of larger products. For example, an automaker has wheels or foot brake components in its inventory, available for use when it is necessary to add to a vehicle, that is in the manufacturing industry. Similarly, a web designer can have a variety of template and software applications that help create innovative Web sites.
Another form of inventory that a business may have is products that are ready for sale (Finished Product Inventory). For example, some companies buy their products from manufacturers and stockpile them in their warehouses: those facilities will require warehouse management in inventory. These products are ready for sale immediately and do not require assemblies, toys, household items, furniture, and office supplies are just a few of the many items that can be part of a finished product inventory.
If in a company or organization, the axis of business or operations is the storage of products for later use or storage of the parts that are subsequently used in the creation of products, said company must always know precisely what it has in his credit. If not, there is no way it can operate efficiently. Mismanagement of funds, loss of profits, and unlawful removal of items are some of the most common consequences of inventory mismanagement.
Regardless of the type of inventory that a company manages, its inadequate management constitutes a potential accelerator of excesses in the order of materials, and the loss thereof. Poor inventory management in a warehouse or in a company can even result in theft: storage items can be stolen without the knowledge of company management or even personnel linked to warehouse supervision activities, this is common in cases where adequate techniques, methods and support systems are not implemented for continuous inventory tracking.
If an entrepreneur does not know with optimal precision what they have in storage, they cannot know what to order. If the inventory balance is non-perishable, the items at the point of storage may be left in waste and the cost of the company's own funds could be better used. Also, excess nonperishable goods is not the best: the excessive presence of stocks can lead to few storage spaces and the need for unnecessary additional storage for stocks. Since storage space is a valuable asset in most cases, the use of storage space must be used efficiently.
Depleting inventory stocks can lead to dissatisfied consumers or inefficient rates in production time. You can assume the case of a company that does not have all the elements it needs to complete orders in a timely manner. In addition, imagining a company that has to pause production to unnecessarily wait for the complementary components that intervene in production to arrive at its warehouse, implies a situation in which the assembly line can find itself in inoperative situations and consumers completely dissatisfied with their bidders. Now take on a company that advertises certain products for sale and does not have balanced stocks to meet customer demand, once again dissatisfied and dissatisfied customers are the result.
Interestingly, good inventory and warehouse management can end situations such as those previously described and other issues, as well as ensure the appropriate level of productivity and efficiency. In essence, inventory management is a vital measure in almost all business processes involving the exchange of goods, thanks to the effective implementation and application of methods, technologies and support systems appropriate to the specific requirements of the administration of its Inventories, with a relatively lower level of human effort, companies can keep an adequate track of the losses that are claimed to be incurred during the tax time; You can maintain more than one balance sheet, by virtue of doubtful or illicit stocks and divestitures at a null or minimum level.
1.2.- Benefits of Effective Inventory Management
When a company embraces the benefits built into inventory management solutions, it can immediately appreciate the evolutionary changes that such solutions entail. Organizations that have firm control of their inventory know their commercial value, the value of their product, the changes to which such products will be susceptible in the future and precisely the amount of product that is needed in their stock for each of the items or classes of products that are handled in the warehouse. Companies that have a systematic understanding of their inventory also find that in the future they will never need additional storage space (except if the installed capacities of production, marketing or the business itself are expanded),since they efficiently managed the existing physical dimensions for inventory operations.
In addition to the aforementioned benefits, there are a number of added benefit factors that entrepreneurs can derive from applying appropriate inventory management measures. First of all, all business owners must be prepared for unforeseen events that can lead to huge losses. For example, damages as a result of claims, the company must initiate procedures related to its insurance contractors. If the company is not fully aware of what they have in their inventory they will not be in a position to file an accurate claim.
In addition to applying appropriate inventory updating techniques, business owners can also reorder simple products. Reordering is much more efficient when business management can determine in a brief or quick inventory inventory what they have. By subtracting the number of items dispatched or reduced from the initial inventory, the company can calculate the quantity of products that must be ordered.
Knowing the inventory value of a company greatly helps the achievement of operational and managerial objectives. In truth, like the inventory or existence elements or items, it is beneficial to inventory the set of basic goods that the company owns. In order to accurately calculate the values associated with financial aspects (accounting management) of the organization.
As mentioned earlier, one of the initial benefits derived from good inventory measurement can be identified in the fact that companies become more capable of effectively satisfying consumer demand. However, in marketing terms, such a benefit has a long-term advantage as well: when a company provides the consumer with the goods or services that the latter effectively need, the company will win the loyalty of the consumers.
1.3.- Generally Beneficial Practices in Effective Inventory Management
There is a wide range of measures that companies can use effectively to maintain their inventory in ideal control situations. First, the company needs to do a first count of all current inventory assets. The total of all items in stock (stock) must be fully documented, as well as all items that are ready for sale. A technical count and supported in support systems can guarantee accuracy. This will give the company a starting point for tracking their inventory. At this point, it may be an advantage for the owner company to use some type of computerized application (software) developed for inventory control and monitoring.
Then, at the moment that the inventories are effectively updated, the first thing that a titular company must do is check its quality. Are any of the elements in existence damaged or defective? If so, the possibility of returning to the supplier, definitive removal or submission to partial or total re-processing (recycling), as the case may be, will be evaluated. Then, depending on the updated inventory. The accounting account or accounts of the current inventory must be adjusted, thus contributing to the optimization of the administrative and financial processes of the business.
1.4.- An Approach to Order Analysis
Obtaining the correct amount of stock requires projections, calculations and a range of non-speculative estimates, the company cannot and should not guess how much it believes it can sell in the coming months in order to order the number of units of a certain inventory item that will be needed in stock.
Among other ways, by monitoring the dynamics of inventory behavior based on output volumes on a periodic chronological basis (weekly, biweekly, monthly, quarterly, quarterly or annually) the company will be able to identify the foreseeable patterns of use of a product, production component, raw material product and of course sales. They can then base their ordering process by supporting forecasting techniques based on the factors mentioned above. A common result is often that inventory stocks are minimized at the end of a period (monthly or financial), a situation to which attention should be paid.
Diligent and regular inventory tracking is recommended at all times. Also, when inventory is counted in a warehouse or companies, is it imperative that all calculations be correct? What use is inventory tracking if all calculations are poorly formulated or the results of estimates or projections do not match actual tangible management results? Basically, inaccurate inventory calculations result in significant time and money losses for a company.
As you can see, inventory management can turn out to be a full time process in itself. It is evident, based on all the aforementioned, that adequate inventory monitoring is necessary for the proper functioning of the company. With so many other things the company is responsible for, how can inventory management time be managed efficiently? Small inventories are generally fairly easy to manage, but what about warehouses and supplies whose volumes are classified as macro?
Since inventory management is not a process that can or should be avoided, it should be a good idea for business management to hire specialized personnel to handle large inventories. Many times, the duty of inventory management is handed over to the authority of a manager, who is responsible in certain periods of time for the inventory count and the ordering and valuation of products. This allows the company to focus on other aspects of operating the business.
Computerized support systems such as specialized inventory management software can help control the amount of inventory a company handles. These applications allow the company, in addition to performing basic inventory management operations, to calculate and, in some cases, statistically analyze and estimate orders. Thus, software applications can minimize inventory handling time.
Curiously it has been possible to get to observe in current times, that many companies that lose the effective capacity to optimally manage their inventories, transfer such responsibilities to other companies or organizations specialized in the matter, this is known as outsourcing.
Certainly this type of corporate practices imply additional costs to the contracting figure, but in ideal cases there may be a reduction or minimization of losses in the long term.
1.5.- Towards the Automation of the Inventory Management Process
The most objective question related to this aspect would be: What type of inventory of software applications are available? A large number of companies use, among other supporting computer systems, barcode software to keep a technical control of their stocks. In addition, barcode management software can track all items that are shipped. Companies often use applications that integrate barcode management modules in inventory control because these applications can also minimize human error, since the price of the product will be added to the request, when a product runs through the registry, it never places an incorrect price. Too,Barcode recognition programs allow business owners to have a simple method of managing special discounts and sales of the products they handle.
Bar codes can be processed using special systems and devices and are a simplifying element of some processes related to inventory management: the items that are sold can be automatically reduced from stock and affect the accounting account of current inventory. Some software applications automatically create and print a document rearrangement. Other programs allow a barcode for electronic order submission.
In contrast, a business owner may want to invest in a software application that allows only the company's operating document, inventory registration and calculation document to be followed. Some programs also carry out inventory projections so that they can know exactly the current existence at the desired time.
1.6.- The Inventory Management Approach Based on Stock Origins
In business there is a reality recognized by many, but unfortunately rationalized and implemented by few "who buys well, sells or produces well." Having a good purchasing policy will allow a smooth management of the company and reduce its costs, which will obviously improve its profitability. Due to the above, it is necessary to study inventories from the moment the purchase is projected, that is, to involve them in the planning processes of the company and its mandatory counterpart, control.
In the broadest sense of the word, inventories are usable resources that are stored for later use at a certain time. Some authors define them simply as idle goods stored waiting to be used. Other authors define them as a current asset of vital importance for the operation of the company. There are multiple arguments to justify the holding or not of inventories.
What is indisputable is that inventories represent a high percentage of assets on the balance sheet and purchases are the same with respect to profits in the income statements, so if this reality is recognized from the financial point of view and appropriate management measures are not taken in order to improve their management, negligence is being incurred as far as company management is concerned.
II Inventory Management Techniques and Methods
2.1.- ABC Classification
Different products are used in each company, each one with its own characteristics, therefore, each one needs a particular handling, depending on its importance in the company's processes and the possibilities of acquisition. Thinking that all products should be controlled in the same way, is a limited vision of reality, which implies unnecessary wear and cost.
ABC analysis is a way of classifying products according to pre-established criteria, most of the texts that deal with this topic, take the value of inventories as criteria and give relatively arbitrary percentages to make this classification. For example, 10% of the products represent 60% of the company's purchases, therefore this is zone A, 40% of the products 30%, which would be those located in zone B, the rest (50% of products and 10% of purchases) are C products.
The above values are arbitrary, each company has its particularities, if someone decides to use this criterion, they must be aware of the realities of their company. One must think not only about costs, it is important to see other criteria, which is undoubtedly the main difficulty in this type of analysis. It is undeniable, however, that a small percentage of products, from any criteria, is essential for the operation of the company and / or to improve its profitability, these would be classified as typical A products, and according to this point of view they are selecting products from other areas; if one considers it appropriate, the possibility of adding a zone D could be considered, for really insignificant and very low-cost products.
The following graph gives us an insight into the ABC classification, percentages were not used explicitly, so as not to fall into the temptation to dogmatize about a particular value, the idea is that the products in zone A are looked for models that allow very strong control over the key criteria being handled and as products move away from this area, the models can be more flexible; This does not mean that the physical control of inventories is neglected, since, as mentioned in the introduction, this is not the objective of this booklet. See figure Nº 1.0
Figure 1.0 ABC Classification - List of inventories based on costs.
2.2.- Economic Order Quantity Model.
This model starts from a series of strong assumptions, which are softened as the theory progresses, however its applications and utility are important and the subsequent developments that it has allowed, make it an obligatory point of reference in all fields where inventories are discussed. So it is not strange to find mentions of this model in multiple books on costs, operations management, logistics, calculation and other topics. The assumptions on which this model is built are:
1. Demand is known with certainty and is constant.
2. The costs related to the model remain constant.
3. The order quantity per order is the same.
4. The order is received at the time it is ordered.
5. Inventory is restored the moment it runs out.
6. The supplier supplies the requested quantities in a single batch.
7. It is considered an infinite and continuous horizon in time.
Figure 2.0 Graph of the economic order quantity model.
In order to make a decision about: the height of the triangle (order quantity), the number of triangles (number of orders in the period), the base of the triangle (time between orders) and to know the value associated with these decisions, it is necessary to know the following data:
Demand, normally it works annually, although the model allows other management, it is calculated from the company's budgets.
Order cost, this is generated every time the company makes a purchase, in its calculation you must be involved from the time it takes to place the order, to the costs of transport and receipt of the merchandise, not forgetting to include the relevant administrative costs upon payment of the invoice.
Maintenance cost (conservation), this indicates how much it is worth to have the inventory unit in the warehouse, it must be taken into account from the cost of money, to the insurance in case of having it, that of the warehouse and that of the personnel that manages the inventories this cost must be given in the same unit of time in which demand is estimated.
The complex part of the model is precisely the definition of the previous costs, if they are objectively calculated the model gives valid results even if they are not absolutely exact, the objective of the model is not to minimize one of these costs, since its behavior is inverse and in In the case of minimizing one of them, the other is triggered so that the associated costs will be higher, the important thing is to minimize the sum of the costs of ordering and maintaining, which is known as the associated cost, in the The following graph shows how said cost in the values close to the minimum does not change considerably, however if they move away from this the costs can increase significantly, so the idea is to request a value very close to the economic quantity of order.
The symbology to be used is one of the many existing ones, in case you consult one of the cited authors or others it is possible to find different symbols, this is not a problem, the important thing is to have clear conceptual elements.
D: Demand
Co: Order cost
Cc: Conservation cost
Q *: Economic order quantity
N: Number of orders
Tc: Time between orders
CA: Cost associated with inventory policy
CT: Total cost, involves value of the items and the associated cost.
Calculating the first three variables the other values are automatically given, the demonstration of why the following formulas are used comes from the differential calculation:
Figure 3.0 Graph of the optimal order quantity point based on costs.
Example
A printer who is currently making a monthly purchase, studied the behavior of 70g book paper. in the last twelve months, he found that his demand was: 10, 11, 10, 9, 10, 11, 9, 10.5, 10, 9, 9 and 11.5 tons per month, he estimates the purchase price will remain at $ 2,300,000 per ton, its order cost at $ 500,000 and by policy charges 15% of the unit cost for inventory management plus $ 55,000 for warehousing, calculate:
1. The model to handle in these conditions.
2. If the supplier offers to give a 10% discount for purchases over 30 tons. and one of 11% for purchases of 60 tons, as my policy would change.
3. If, in addition to the discount, it is possible to obtain a term that makes our conservation cost be reduced only to the storage cost, as my policy would change.
The first thing to observe is the behavior of demand which is seen to be relatively constant, so it can be assumed that the model behaves according to the parameters of an economic order quantity model with the following data from input:
D = 120 tons year
Co = $ 500,000
C = $ 2,300,000 ton
Cc = $ 400,000 ton / year
Therefore:
As can be seen in this inventory purchase policy, the company saves more than 20% in the cost associated with the inventories that it would have if it made a monthly purchase (CA = 12 * 500,000 + * 400,000 = $ 8,500,000), which added to the savings that would be achieved with the different products that the company manages will allow significant improvements in profitability at the end of the year.
Regarding question 2:
Alternative 1:
Alternative 2:
Therefore, the 10% discount should be accepted, since in case of selecting the scale that provides an 11% discount, the inventory management costs are higher than the benefits that would be obtained with a lower purchase value.
Question 3, displays an aphorism, which is sometimes valid: "the price does not matter but the term"; In our case, when the conservation cost is radically changed, the entire model must be re-calculated with a conservation cost of $ 55,000, which will give the following results:
In this phase of this particular problem, it can be seen that with a reduction in the order cost, you can automatically order with a discount of 10% given the negotiated conditions, which would achieve savings of more than thirty million of weights with respect to the results obtained in the classic model, if the second scale of discounts is detailed, it is obtained:
In this case, the second scale of discounts must be accepted.
In summary, inventory management is undoubtedly a critical element, for the good development of the company, if this is not carried out correctly the possibility of having supply problems or higher costs is very high, which is why permanently The rules for its management within the company must be reviewed, being aware that it is in a reality where the only constant is change and that if an attitude consistent with this reality is not adopted, the possibility of ceasing to be competitive and leaving of the market is very high.
In administrative decisions, the expert's opinion is irreplaceable, however, a good use of quantitative instruments considerably facilitates his work, allowing him to make mistakes on paper, with which the company's profitability must improve considerably, in the example of Fascicle is played with only two possible variations, different options can be managed among which could be, as BONINI affirms to affiliate with buyers' clubs in order to obtain better negotiation conditions.
III Inventory Models
In order to meet demand on time, companies often maintain a certain level of inventory or stocks in their warehouses. This forecast is especially important when a product has a strongly seasonal demand or when the demand has to be served in a relatively short period of time. The purpose of this math-block is to present a series of models, all of them variants of the EOQ (Economic Order Quantity) Model that can be useful when making inventory decisions when demand is known.
Basically, these models will try to give an answer to the questions that the inventory management department normally asks: (1) When to launch a production or purchase order ?, and (2) What should be the optimal size of said order?
Figure 4.0 Stock Types.
3.1.- Types of Stock
Four types of possible stocks are distinguished according to the function they perform:
• Cycle stocks: Many times it does not make sense to produce or buy materials at the same rate as they are requested, since it is cheaper to launch an order purchase or production volume greater than the needs of the moment, which will lead to this type of stocks.
• Seasonal stocks: Some products have a highly variable demand throughout the year, increasing greatly in certain months and decreasing in others (toys, ice cream, soft drinks, etc.). Thus, it is logical that production is greater than demand in certain periods, so a seasonal stock will be generated.
• Safety stocks: They provide a guarantee against possible sudden increases in demand.
• Transit stocks: Its function is to act as a reserve in order to maintain the continuous flow of materials between the different phases of the production process
Even in those cases in which it is desired to maintain a constant inventory level, said level will vary when the requested demand (outputs) differs from the forecasts or when the input of material (inputs) does not coincide with expectations.
Figure 5.0 Existence balancing by input / output dynamics.
In any case, it will not always be desirable to maintain a constant level of stocks. Thus, for example, the production system could be supplied intermittently with a fixed quantity Q, which would be incorporated at regular intervals of T time units, while the output could be produced at a constant rate D.
3.2.- Characteristics of the Demand
The main characteristics of demand are summarized below: Continuous or Discrete The unit of measure for demand may vary depending on the environment and the presentation of the specific item (units, hundreds, liters, kilograms, etc.)
Deterministic or probabilistic There are cases in that future demand is assumed to be perfectly known; other times the demand values are assumed to be random
Dependent or independent. The demand for components will depend on the demand for final products, while the demand for the latter will be considered independent
Homogeneous or heterogeneous Demand is homogeneous if its value is constant over time
Deferred or Lost If demand is not satisfied (stock break) sometimes it will be possible to defer the
Notions on General Types of Applied Costs
The main costs associated with inventories are presented: Acquisition Cost It consists of a fixed part (cost of launching or issuing the order), and another variable part (variable cost of acquisition). The launch cost refers to the purchase of material from an external supplier (mail, telephone, administrative task, loading, transportation, etc.) and the preparation of orders for items manufactured in the same company (machine tuning, cleaning, etc.). The variable cost of acquisition results from multiplying the unit value of the item by the name of the items in the order (as long as there are no discounts depending on the quantities purchased)
Cost of Possession
Due to the creation and maintenance of warehouse capacity (rent, electricity, machinery, surveillance, etc.), material handling and administrative work, expenses arising from internal and external insurance, variations in the value of goods motivated by wear and tear, and at the opportunity cost of capital (money that is not earned due to keeping capital immobilized in stock instead of investing it)
Cost of Unsatisfied demand
Appears when it is not possible to meet the demand due to lack of stocks (rupture of stocks)
3.3.- Delivery and Replenishment Periods
3.3.1.- The delivery period (L)
It is the time that elapses between the detection of the need to place an order and the moment when the corresponding material is ready for consumption or use. Sometimes the delivery period is known, while the demand is not; other times both have a probabilistic character. This ignorance can give rise to undesirable situations such as those shown in the figure: at time A the need for material is detected and an order form is launched. The material will be available for consumption at time C; If the real need for material occurs at time B, a stock break will occur and demand will be unmet; if, on the other hand, the need arises at time D, then there will have been a hasty replenishment that will affect the costs of owning stocks.
Figure 6.0 Representation of the delivery period (L).
3.3.2.- The replenishment period (R)
It is the time during which the only protection available to the production system to face a possible rupture of stocks is the level of inventories. When a continuous control system is available and therefore the stock level is known at all times, the replenishment period coincides with the delivery period (R = L). When the information system is periodically reviewed, the replenishment period is equal to the revision period (T) plus the delivery period (R = L + T).
3.4.- Inventory Management Policies and Replenishment Methods
A stock management policy serves to define: (1) When should material be requested ?, and (2) How much material should be ordered ?.
For the first question, it is possible to resort to setting a reference level for the stock (order point, s), and launching an order each time the stock position falls below this value; Another alternative is to set a review period, T, and place an order at specific times. Regarding the second question, it is possible to always request a predetermined fixed quantity Q (lot measurement), or the difference between a fixed value S (coverage) and the stock position.
To describe a stock management policy, it will suffice to indicate, by means of an ordered pair, when and how much is requested. Thus, a policy (s, Q) will mean that a fixed size order Q is launched each time the stock position is less than units.
Other possible policies are: (T, S) with which an order is carried out every T time units, of size equal to the difference between coverage S and the level of detected stock; the policy (s, S), which implies the request for an order of a size sufficient to supply coverage S each time the stock position is lower than the order point s; and the policy (T, Q), in which a fixed order Q would be requested every T units of time.
3.4.1.- Replenishment Methods
One method of replenishment is to systematically apply a stock management policy with the support of an information or review system. The most commonly used methods are discussed below.
3.4.1.1- Replenishment methods
3.4.1.1.1.- Order point method with continuous review (s, Q):
The stock level will be known at all times. When due to consumption, a minimum level is reached (order point, s), a fixed measurement order Q (economic lot) will be issued. The order point attempts to balance the opposing costs of breaking and owning stocks, while the economic lot size is calculated to strike a balance between launch and holding costs. This is the method that EOQ models follow.
Figure 7.1 Representation of the continuous review request point method (s, Q)
3.4.1.1.2.- Periodic replenishment method with coverage (T, S):
A review is carried out at specific moments, after time intervals of equal length (review period, T). After the review, a purchase order is released, the quantity of which is determined from the difference between coverage S and the observed stock level.
Figure 7.2 Representation of the continuous replenishment method with coverage (T, S).
3.4.2.- Traditional Methods for Stock Determination
3.4.2.1.- PEPS method First to enter, first to exit.
This method basically consists of issuing inventory to those products that were purchased first, so that inventories will include those products most recently purchased.
In any of the methods, purchases are not very important, since they enter the inventory for the purchase value and do not require any special procedure.
In the case of purchase returns, this is done for the value that was purchased at the time of the operation, that is, the output of the inventory for the value paid in the purchase.
If what is returned is a product sold to a customer, this is entered into the inventory again for the value in which it was sold, since it is assumed that when the sale was made, those products were assigned an exit cost according to the method of inventory valuation managed by the company.
Example:
With the following data, taken from the accounting books, calculate the value of the inventories:
• On January 2, 2001, there were 1,000 units in stock, whose unit cost was $ 10.oo.
• On January 3, buy 500 units at a unit cost of $ 12.oo.
• On January 4, it sells 1,100 units at a unit price of $ 20.oo
• On January 15, it buys 600 units at a unit cost of $ 15.oo.
• On January 28 buy 500 units at a unit cost of $ 18.oo.
· On January 31, it sells 1,200 units at a unit price of $ 22.oo.
The procedure is as follows: the initial balance is placed, which is 1,000 units at $ 10.00 each. On January 3, a purchase of 500 units is made at $ 12.oo each. This information is placed in the input column and passed to the balance column. On January 4, a sale of 1,100 units is made. So the first ones that entered are the inventory ones, which were 1,000 units at $ 10.00 each. As these units are not enough, 100 units are taken from those purchased on January 3, at a cost of $ 12.oo each, completing the total units sold and leaving 400 units valued at the last cost, which is $ 12.oo. This action is repeated every time there is a sale.
When making all transactions, 300 units remain in inventory at a cost of $ 18.oo for a total of $ 5,400.oo. Cost of sales is the sum of the exits for the period, which amounted to $ 28,600.oo
Note that each time a sale is made, a simple line is placed on the balance before the sale to separate the previous situation from the new one.
By using this method of inventory valuation, an effect is given on the financial results of the company, both by the amount of the cost of sales and by the value of the ending inventory. We know well that taking out the units that were purchased first means that the last units purchased remain in the final inventory, and these units were generally purchased at a higher cost. Now the cost of sale when determined by taking out the first units purchased, which were generally cheaper, has a relatively lower cost of sale, which means that it will have less effect on profit, resulting in it being more higher than if other inventory valuation methods were used.
As can be seen generally, this method makes profit less and that the Balance Sheet is slightly overvalued by containing a somewhat more expensive final inventory of merchandise. The Income Statement is also affected, to the extent that a lower cost of sale is incorporated as a result of paying with the first units of raw materials purchased.
3.4.2.2.- UEPS Method:
In this method, what is done is to give out the products that were recently bought, with the aim of keeping those products that were bought first in the final inventory. This is a very useful method when product prices are constantly increasing, which is very common in countries with inflationary trends.
The treatment that is given to returns on purchases is the same as that given in the PEPS method, that is, it is issued from the inventory for the acquisition value, this because as it is hardly logical, the product is returns for the value paid at the time of purchase. We must also remember that the different valuation methods are valid to pay for sales or departures, since purchases already have an identified cost that is the value paid for them.
In the case of the return in sales, these enter the inventory again for the value or cost with which they left at the time of making the sale.
Example:
Using the following data, taken from the ledgers, calculate the value of the inventories:
On January 2, 2001, there were 1,000 units in stock, the unit cost of which was $ 10.oo.
On January 3, she buys 500 units at a unit cost of $ 12.oo.
On January 4 he sells 1,100 units at a unit price of $ 20.oo
On January 15 he buys 600 units at a unit cost of $ 15.oo.
On January 28, she buys 500 units at a unit cost of $ 18.oo.
On January 31, it sells 1,200 units at a unit price of $ 22.oo.
Solution.
The above information is recorded on the control card (Kardex) as follows:
The procedure is as follows: the initial balance is placed, which is 1,000 units at $ 10.00 each. On January 3, a purchase of 500 units is made at $ 12.oo each. This information is placed in the input column and passed to the balance column. On January 4, a sale of 1,100 units is made. So the last ones that came in are those of the first purchase on January 3, which were 500 units at $ 12.oo each. As these units are not enough, 600 units are taken that are in the initial inventory, at a cost of $ 10.oo each, completing the total of units sold, leaving 400 units valued at the first cost, which is $ 10.oo. This action is repeated every time there is a sale.
When making all transactions, 300 units remain in inventory at a cost of $ 10.oo for a total of $ 3,000.oo. The cost of sales is the sum of the outputs of the period, which amounted to $ 28,600.oo. Note that each time a sale is made, a single line is placed on the balance before the sale to separate the old situation from the new one.
Financially, the use of this method implies a higher cost of sale value because it is determined based on the latest units purchased, which are generally more expensive; Likewise, on the coast, based on the last units purchased, it means that in the final inventory the first units remain, which in most cases are cheaper, which means that they are of a lower value.
In conclusion, it can be said that this method is used by companies in countries where inflation is high, with the aim of recognizing such increases in the income statement, since with the UEPS the profit is lower as it has higher sales costs., and another effect is seen in the Balance Sheet as it is somewhat undervalued for having the ending inventory with old prices.
3.4.2.3.- Simple Mathematical Determination of Stocks.
It is carried out is through a manual count one of its forms is that of minimum stocks; in this system the amount of replenishment time (q) is constant, while the time (t) between the replenishment periods is variable, since the minimum stocks (Em) are those that determine the issuance of a new order (q) units, as follows:.
Em = ER + dt
Where:
Em = minimum stocks
ER = reserve stocks
D = average consumption
T = average waiting time in days between period and receipt
In this case,
EM = ER + Q / 2
Where:
EM = larger stocks
Q = replacement order quantity
3.4.1.1.3.- The Basic EOQ Model or Harris Wilson's Model
The assumptions on which this model is based are the following:
1) The time horizon that affects inventory management is unlimited (ie: the process continues indefinitely).
2) The demand is continuous, known and homogeneous in time (ie: if the consumption rate is D units / year, the monthly demand is D / 12 units / month, etc.).
3) The delivery period, L, is constant and known.
4) Stock breaks are not accepted (ie, there must always be enough stock to satisfy the demand).
5) The acquisition cost, CA um / unit, is constant and does not depend on the size of the lot (there are no discounts for large volumes of purchase).
6) The batch entry to the system is instantaneous after the delivery period has elapsed.
7) It is considered a launch cost of CL um / order and a cost of possession of stock equal to CP um / unit and year.
Under these hypotheses, what is more economical is to organize the orders in such a way that a batch enters the system at the moment when the stock level is zero; therefore, orders for the issuance of orders must be carried out at times when the stock level is the minimum necessary to satisfy demand during the delivery period.
The order point S must be: S = D * L.
Furthermore, all lots must be the same size, since the model parameters remain constant over time, and the horizon is unlimited.
If each order is of a volume equal to Q, to satisfy the annual demand D it will be necessary to order D / Q orders / year (replenishment frequency N); the inverse of this value will represent the time between two consecutive inputs to the system (TC provisioning cycle time).
Since the cost of launching an order is CL um, the annual cost of launching KL will be:
This cost is related to the lot size Q, so that if said size grows, the number of launches is reduced and, for Consequently, the annual launch cost will decrease.
The annual KA acquisition cost depends on the units requested; As the annual demand D is known and it is assumed that all units have the same unit value, CA, regardless of when it is requested and the quantities required (there are no discounts), the acquisition of D units will cost KA = CA * D.
Figure 8.0 Graphical representation of the EOQ cost model.
The annual cost of owning KP stock is related to the average level of stock held throughout the year. Under the assumptions considered, the stock level ranges from 0 to Q. Since demand is homogeneous and stock breaks are not allowed, the average inventory level will be equal to Q / 2; As keeping a unit of product in stock for a year has a cost of possession of CP um, the annual cost of possession will be:
KP = CP * Q / 2
Note that as lot size Q increases, the annual cost of KP possession.
The total annual cost of stock will be the sum of the three previous costs. In any case, the relevant costs in inventory management (those on which our decisions can influence) are the annual cost of launch, KL, and the annual cost of ownership, KP, since the annual cost of acquisition does not depend neither the size of the lot or the dates on which orders are ordered.
Therefore, the relevant annual cost K will be: K = KL + KP um If K = K (Q) is considered, it is immediate to verify that this function takes a minimum value K * associated with an optimal lot size (Q *):
This Q * quantity is called the Economic Order Quantity. Furthermore, in this model, the economic lot is precisely the value that equals the annual costs of launching and possession1.
In the formula above, the unit cost of ownership, CP, is often expressed as the product of a maintenance cost rate i, by the unit unit value of the item, CA. Rate i therefore represents the cost (in US $) of keeping material stock worth US $ 1, and may encompass concepts such as the interest rate that the company could obtain in an alternative investment of similar risk, the percentage of annual losses resulting from the storage and handling of products, theft losses, the cost of insurance that covers the stocks, etc.
Next, an inventory management example based on this model will be solved with the help of the EOQ.xls file, created with the EXCEL spreadsheet. A service station sells 1,740 liters of gasoline per month. Every time the station asks for a tank to fill its tanks, it has to pay US $ 50 for transportation plus US $ 0.70 for each liter it requests. The annual cost of maintaining a liter of gasoline is US $ 0.30.
You want to determine the optimal lot size and the number of annual orders that must be placed in order to minimize total costs. What would be the order point if the delivery period were two weeks? What if it was ten weeks?
Figure 9.0 Treatment of cost EOQ model with commercial electronic spreadsheet.
Although the sheet is sufficiently explanatory in itself, it is appropriate to observe the following:
• To determine the Cp (box B23) it is only necessary to complete box B21 or B22, since cell B23 = MAX (B21; B22 * B18).
• When determining the order point (box E15) the following formula is used: E15 = YES (B15 * B16 / 365 <= E23; B15 * B16 / 365; WASTE (B15 * B16 / 365; E23)). In other words, the order point will be L * D as long as L * D ≤ Q *. Otherwise it would not make sense to take s = L * D since the stock level would always be below the order point, so this would not serve as an indicator. In such situations, the division L * D between Q * will be carried out and s will be taken as the rest of it.
The "output" says that the ideal would be to order 4,000 liters of gasoline each month, which will suppose a relevant annual cost of 1,200 US $ (note that in the optimum, CL = CP). In addition, orders should be placed when the fuel level in the tanks reaches 1,841 liters. If the delivery period increased to 70 days, the order point would be 1,205 liters, obtaining this figure as the rest of the L * D division between Q *.
3.6.- Stock Management and Economies of Scale
It could be seen previously that K * = K * L + K * P = (CL * D / Q *) + (CP * Q * / 2) is the expression of the minimum annual relevant cost. Substituting Q * = (2 * CL * D / CP) 1/2 in the previous equation we have: K * = (2 * CL * CP * D) 1/2 um this formulation of the minimum annual relevant cost will be used to explain in part the competitive advantages of large companies when they are capable of generating sufficient demand. Suppose two traders, A and B, have the same demand, D, and identical costs CL and CP. If you both optimize inventory management costs, each will cost K *. What would happen if they decided to jointly manage their respective stocks? Would they reduce costs or, conversely, would they increase the total cost?
The initial situation in which each merchant acts separately assumes a total cost: K * A + B = K * A + K * B = 2K * um / year. If the merchants decide to create a joint stock, the annual demand of the new company will be 2D and, therefore, the total cost will be: K * AB = (2 * CL * CP * 2D) 1/2 = 21 / 2K * CU / year, which means that the business merger will have reduced management costs. In addition to reducing costs, a decrease in the average level of stock would also be achieved: in the initial situation, the average level of stock would be Q * / 2 + Q * / 2 = Q *, whereas once the merger was completed would be Q * AB / 2 = / 2 = 21 / 2Q * / 2.
Given that it is difficult to accurately estimate the real values of the variables D and CP (or alternatively i), it is very interesting to know that the total costs are “robust” against small variations in the value of Q *, ie, if the value obtained from Q * does not differ much from its actual value (which would be obtained with the exact values of D and CP), so the actual total cost will not differ much from the predicted one.
Figure 9.0 Stock management nomenclature and economies of scale.
These results can be extended to the case where the demand for an item is doubled as long as the company is able to meet it. Thus, a situation of economies of scale is entered: identical and progressive increases in demand imply decreasing increases in the costs of inventory management.
In general, if a demand K corresponds to a cost K, a demand nD will be associated with a cost n1 / 2K (as long as the rest of the parameters remain constant).
3.7.- The EOQ Model with Discounts for Acquisition Volume
Suppliers often offer discounts on the prices of the product served if purchased in large quantities. Such discounts must be taken into account when deciding what quantity should be purchased and when orders should be placed. We will therefore be facing a different model from that of Harris-Wilson: CA will no longer be constant, but will depend on the volume of the lot purchased, which will affect both the unit cost of ownership CP = i * CA, and the total annual cost KT = KA + KL + KP.
3.7.1.- Uniform Discounts Uniform
discounts imply the same discount on all units purchased, a discount that will be of greater or lesser magnitude depending on the interval or section in which the quantity requested is found. An example of a uniform discount would be:
Given that in each of the n sections the acquisition cost CA is constant, in reality this case is reduced to applying the basic EOQ model to each of the intervals, with which a minimum annual cost will be obtained for each section considered KT (i) = KA (i) + KL (i) + KP (i). Obviously, the Q * associated with the least of these n minimum total costs will be selected.
However, an important observation should be made: now Q * will be the order size that minimizes the relevant costs K (Q) = KL + KP within the considered interval (optimization with restrictions). Therefore, if when doing the calculations it turns out that the Q * obtained according to the formula of the previous model does not belong to the interval in which it is, the end of the interval that is closest to the obtained value should be taken as Q *, since this will be the optimal value restricted to this section (since the function K (Q) is convex with respect to the origin).
The EXCEL commercial electronic calculation sheet will be used again to exemplify the previous concepts by solving the following case:
A management agency orders rewritable CDs from a large warehouse. The discs go in boxes of 10 units, and their price depends on the number of boxes requested as shown in the previous table (the one used as an example of uniform discounts). The agency estimates that it will need about 10,000 discs a year. The launch cost of each order is US $ 100, while the annual maintenance fee is estimated at i = 0.20. It is about determining the optimal lot size, the costs associated with it, and the number of annual orders that should be made.
In the new spreadsheet that is applied (called Uniform Discounts), the ends of the section to be studied at each moment must be specified, as well as the acquisition costs associated with said interval. The results for each of the three sections are shown below. Of the three Q * that will be obtained, the one whose associated total cost (KT) is lower will be selected (in this case Q * = 300, which carries an estimated total cost of US $ 50,288.33).
Figure 11.0 Spreadsheet for computational treatment of uniform discounts.
As you can see, the structure of this new sheet is very similar to the one used to solve the basic EOQ model. The only significant difference lies in the determination of Q *, which will now be given by
E23 = SI (ROOT (2 * B19 * B14 / B23) <= B16; B16; MIN (ROOT (2 * B19 * B14 / B23); B17)),
Expression that comes to say the following: “If the Q * you obtain is within the considered interval, then it is valid. Otherwise, take as Q * the end of the interval that is closest to the value obtained ”.
3.7.2.- Gradual Discounts
Gradual discounts or incremental discounts are characterized in that the price reduction is not applied equally to all the units purchased, but rather the units of different tranches of quantities have different prices. Consider the following example:
Figure 12.0 Tabulated relationship of gradual discounts
Suppose you need to buy 120 units (section 3 of the previous table). In such a case, an “accumulated” acquisition cost of US $ 9,500 (50 * 100 + 50 * 90) plus an “extra” cost of 20 * 80 = US $ 160 will have to be met.
Note, therefore, that if you decide to purchase a lot of size Q belonging to a section whose lower end is Qmin, the cost of acquiring the order can be decomposed as the sum of two costs: Accumulated Cost + Extra Cost = A + CA * (Q - Qmin + 1), where CA represents the acquisition cost for each unit of the section considered.
Based on the above, for an order of Q units, the average acquisition cost per unit can be defined as CAM = / Q. As orders will be placed at the end of the year, the annual acquisition cost will be KA = D / Q *.
For its part, the average cost of possession per unit will be given by CPM = i * CAM, so the annual cost of possession will be: KP = i * CAM * Q / 2.
Finally, the annual launch cost will be: KL = CL * D / Q.
The objective will be to minimize the total annual cost KT (Q) = KA + KP + KL = D / Q * + i / 2 * + CL * D / Q, convex function with respect to the origin. Deriving this function and equating to zero, we obtain the lot size that minimizes the total costs:
Q * = 1/2
As was done with the uniform discounts, the idea will be to calculate the Q * associated with each section, and then choose the one with the lowest associated costs. When calculating each Q *, a distinction should be made between the case in which the result obtained by applying the formula belongs to the interval considered (then this number will be Q *), or the case in which it does not (if this happens, the closest end, being the convex total cost function).
Suppose you have an annual demand for 500 items and our supplier offers the prices shown in the table above. If the maintenance fee is 20%, and the launch cost is US $ 50, what would be the optimal lot size? What are the costs associated with this size?
Again, the EXCEL commercial electronic spreadsheet is used to design a sheet that allows calculations to be made quickly (in this case they will be called Graduated Discounts). The results associated with each of the sections are shown below:
In this sheet, the most significant formula is the one that calculates the Q * based on the equation deduced previously. Thus, the corresponding box will be:
E23 = YES (ROOT (B14 * (B18-B19 * B16 + B19 + B20) / (B22 / 2 * B19)) <= B16; B16; MIN (ROOT (B14 * (B18- B19 * B16 + B19 + B20) / (B22 / 2 * B19)); B17)).
3.8.- The EOQ Model of Continuous Entry
On many occasions, part of the items that are stored are produced by the company itself instead of being purchased from another company. In such situations, the assumption 6 that the batch entry to the system is instantaneous is meaningless, since it is not possible to produce all the articles at once, especially if long production series are considered. Rather, it will happen that the production process brings items to the warehouse gradually.
Thus, the items produced will become part of the inventory in transfer lots, which will be smaller than the volume of the series produced. In our case, it will be assumed that the transfer lot is equal to the unit. Obviously, the hypothesis will be that the annual productive capacity P will be greater than the annual demand D, since otherwise it will not be possible to satisfy said demand indefinitely.
Both demand and production will be considered to be homogeneous over time, with rates equal to D and P units per year respectively. Representing this process, it will be observed that during the production cycle the stock level increases progressively at a constant rate equal to the difference between both rates P – D; once said cycle is over, the maximum stock level, Imax, will be reached; from this moment the inventory level will be reduced progressively according to a D rate until reaching level 0; point at which another new cycle will begin.
Figure 15.0 Graph of the EOQ model in continuous input.
In each production cycle, Q units will be manufactured in a time period of Q / P years, since it will take 1 / P years to produce each unit. During this period, the stock level (starting from 0) increases at a constant rate P – D units / year. Thus, the maximum level that will be reached will be given by the equation: Imax = (P – D) * Q / P. From this point on, it will take Imax / D years to return to the starting level (stocks 0).
In this model, the annual launch cost will continue to be: KL = CL * N = CL * D / Q um
If it is assumed that the unit acquisition (or production) cost CA is constant (there are no discounts for large production volumes), the annual acquisition cost will be, KA = CA * D um, which does not depend on Q and therefore is not relevant in minimizing costs.
Finally, the annual cost of ownership will be given by the expression: KP = CP * Imax / 2 um, since now the average level of the stock will be Imax / 2.
In conclusion, the relevant annual cost will be K = KL + KP um, which will be minimized for a production volume.
Q * = 1/2.
The spreadsheet corresponding to this model (continuous EOQ) is shown on the next page, in which the solution to the following case appears:
A factory needs to produce 10,000 vehicle chassis per year, each of which has a production cost of $ 2,000. The annual production capacity of the plant is 25,000 chassis, the launch cost per production order being US $ 200. Knowing that the maintenance rate is 25%, determine the optimal batch size to produce. How many production orders must be released over the course of a year?
3.9.- The EOQ Model with Stock Rupture
In many real-life situations, demand is not met on time due to a lack of stock (stock breaks). When this happens you can be in front of a deferred demand, or in front of a lost demand. Both options represent a cost for the company, which is much higher in the second case (loss of sale, possible loss of customers, bad image, etc.). However, if the customer agrees to defer the delivery of his order, it makes sense to consider possible stock breaks of a certain size seeking that the cost of deferring deliveries outweighs the costs of holding inventory. In the following it will be assumed that the cost of delaying the delivery of a unit for one year on CD um can be estimated
The image above represents the evolution of stocks when considering the possibility of deferring demand. Assuming that the batch instantly enters the system, the inventory level will vary between a negative minimum value, -M (maximum unsatisfied demand) and a maximum value equal to QM. Starting from this maximum value, the stock level is progressively reduced at the rate set by the annual consumption rate D; after a time equal to (QM) / D years, level 0 is reached, at which time the stock break occurs; During a period equal to M / D years, units are no longer served, and the stock position falls to the minimum value –M; At this moment a new batch of size Q arrives at the system, the deferred demand is delivered and the inventory level returns to its maximum value.
In this model, both the annual launch cost and the annual acquisition cost are identical to the basic EOQ model. The annual cost of ownership, however, is different. This is due to variation in the average level of possession. In addition, when calculating the total cost function, the annual cost of deferring the KD demand must be considered. The time of each cycle (time between two consecutive entries of a batch) is equal to Q / D years.
Two periods per cycle can be distinguished: the period without break has a duration equal to (QM) / D years, and presents an average stock of (QM) / 2 units; for its part, the period of rupture is equal to M / D years and during the same its average stock is 0, oscillating the level of rupture between 0 and M. Thus, it will be assumed that the average stock in each cycle will be (QM) 2 / (2D) units, while the average breakdown level per cycle will be M2 / (2D) units. As there will be D / Q cycles per year, the average annual level of stocks will be (QM) 2 / (2Q), and the average annual level of rupture M2 / (2Q).
The relevant annual cost will therefore have the expression: K (Q, M) = KL + KP + KD = CL * D / Q + CP * (QM) 2 / (2Q) + CD * M2 / (2Q). It can be shown that this multivariable function is convex, so it will reach its minimum value when: ∂K / ∂Q = ∂K / ∂M = 0. Solving this system of equations we obtain the optimal sizes of the batch and the level of rupture:
Q * = 1/2 M * = 1/2
If the CD cost is made to infinity, M * will tend to zero and Q * will tend to the value that would be obtained with the basic EOQ model. This is logical, since in such a case the cost of deferring delivery would become prohibitive and, therefore, it would not be feasible to consider stock breaks.
Suppose an optical clinic estimates your annual eyeglass frame sales at 10,000 units. The clinic orders from a supplier who charges $ 15 for each frame plus $ 50 for each shipment. The manager of the optician considers that the monthly cost of deferring the delivery of the requested frames is US $ 1.25 (due to the loss of future sales).
Knowing that the annual maintenance rate is 30%, determine the optimal lot size to purchase, as well as the maximum level of inventory breakdown.
3.10.- Silver - Meal Heuristics for Variable Demands
In all EOQ models, it has been assumed that the demand was homogeneous throughout the year. However, this hypothesis will not always be true: in real life there are many cases in which demand, although deterministic in nature, is variable due to various factors, the main one being seasonality.
Figure 19.0 Computational treatment of inventory management with SILVER-MEAL heuristics.
Following is a method that will help determine if the assumption of homogeneity is reasonable or not. If so, the previous EOQ models may be used.
But if this is not the case, other procedures (such as Silver-Meal) should be used to estimate the batch size that best suits our needs. Suppose that the observed demands in n time periods are: D1, D2n. Define the Variability Coefficient of the random variable demand D as: CV = Var / E2, where Var and E represent respectively the variance and the expectation of path D. Well, practice says that if CV ≤ 0.20 it will be lawful consider that the variance is homogeneous, but if CV> 0.20, then use the Silver-Meal technique explained below with the help of the Silver Meal sheet from our EOQ.xls file:
In this example, as VC> 0.20 Silver-Meal will be applied: suppose that the fair quantity is requested to satisfy the demand of the first period (Q1), that is, that 500 units are requested. The relevant cost associated with the first period, K1, would be US $ 750. Note that this cost will be exclusively due to the launch cost, since the order would be served immediately to customers (there is no cost of possession).
Now assume that you are ordering a batch capable of meeting the demand for the first two periods. The requested quantity would be 3,600 units. Of these, 500 would be served immediately and the rest would be delivered at the beginning of the second period; therefore, there would be a stock of 3,100 units during a period (they will assume a cost of possession as indicated by the maintenance fee). Thus, an average cost per period of K2 = 685 US $ will be obtained. It will be noted that it is cheaper to request this last lot than the one that only covered the first period.
If a quantity is requested to satisfy the first three periods, the lot size would be 4,200 units. Of these, 500 would be served immediately and 3,700 would be stored during the first period. Much of these 3,700 units, specifically 3,100, would be delivered at the beginning of the second period, leaving 600 in stock until the beginning of the third. The average cost per period would be K3 = US $ 536.67. As can be seen in the “output” above, this will be the best option. Therefore, an order of 4,200 units will be ordered, which will cover the demands of the first three periods. The total relevant cost of this operation will be US $ 1,610.
Once the first decision was made, it would be expected at the beginning of the fourth period to have more information about future demand.
IV Inventory Systems
4.1.- Inventory / Production Systems
In general, in production systems a final product is manufactured from a series of components, each of which is produced in one location. For this reason, the production systems are usually convergent, that is, at the beginning of the system there are many facilities, and as one progresses along the system the number of locations decreases. Taking into account that normally the first components have less value than the last ones that are closer to the final product, it is logical that the maintenance cost is usually lower in the first levels of the production chain. Therefore, it is usually more convenient to store more stock in the first locations of the system than in the last ones.
The following figure represents a production system in which each location has a single successor. These types of systems are called assembly systems.
4.2.- Inventory / Distribution Systems
In distribution systems each location has a single predecessor that supplies the items. In turn, each facility meets the demand of the immediately succeeding locations. Locations that do not have successors are responsible for meeting the external demand of customers and those that do not have predecessors obtain the items from an external supplier. An example of these systems is shown in Figure Nº 20.0
Figure 20.0 Inventory system based on distribution dynamics
As seen in the previous Figure, the structure of distribution systems is divergent. The simplest distribution system is the one with only two levels, known as the 1-warehouse and N-retail system. See Figure 7. In these systems, retailers have to meet customer demand, and the central warehouse has to meet the demand of all retailers. Note that when N = 1 the system is reduced to a series system.
4.3.- Echelon inventory
The concept of cost and leveling stock was first introduced by Clark and Scarf (1960). For location j, the level stock is defined as the number of units in the system that are or have passed through location j, but have not yet been requested by external customers. Thus, for example, for serial systems, the leveled cost of location j, denoted by, is defined as where hj is the conventional cost of maintaining location j.
The idea of leveled stock is to take into account the stock of all successive locations. For a series system with two facilities, the levels of conventional and level inventories are shown in Figure 8 and Figure 9, respectively. Obviously, the calculation of maintenance costs is much easier if inventories and level costs are used. Thus, in this chapter, serial inventory, assembly and distribution systems are formulated, using level costs. In all these systems we assume that the demand, d, is constant and that breaks are not allowed. In addition, in each installation there is a maintenance cost and a fixed replacement cost denoted by The objective is to determine the optimal replacement quantities, 4.4.- Distribution systems
The structure of distribution systems is just the opposite of that of assembly systems. In practice, the locations of a distribution system represent both the central factory of a product and regional and local warehouses and / or retailers. In particular, we focus on two-tier distribution systems, that is, 1-warehouse and N-retailer systems. For two-tier assembly and serial systems we have seen that optimal policies are nested and stationary. However, for two-tier distribution systems the optimal policy does not have to be nested or stationary. In particular, the optimal policy for this type of system can be very complicated, so much so that it would not even be possible to apply it in practice.
For this reason, typically, simpler, close-to-optimal policies are discussed, such as nested and stationary policies.
4.4.1.- Logistics Cost Reduction Opportunities in Warehouse Management Systems
4.4.1.1.- Application to Distribution Systems.
Supply chains are increasingly customer-oriented. These seek the constant increase in the quality of the service, but it must also be achieved that customers perceive this quality, that they see it. But what do customers understand by quality? Agility, flexibility and responsiveness to change in demand are essential values and proper inventory management can lead to new strategies in the supply chain to achieve this.
In the supply chain, customers are primarily looking for orders to arrive on time, as well as correctly and completely. To achieve this, an approach must be applied not only in the scope of the order, but also in the line of order. In the modern company and especially in the supply chain to which it belongs, all activities that do not really add value to products must be analyzed and eliminated or reduced in time and costs. An example of this would be inventories, since no customer is going to pay more for a company to have more stock in storage than is actually required.
On the contrary, a client does value and may end up paying more if they are met and the delivery times and terms, and if they also manage to be faster. To achieve this, the company must rely on good inventory management, which will help to be faster and not incur high storage costs, since the necessary stocks will be available just in the amount required at all times, when and where they should be in the Supply Chain.
4.4.1.2.- Pull Replenishment System
In this traditional system, the supplier determines the inventory needs based on forecasts and pushes the product towards its distribution center. In this model, the supplier owns the product in the Distribution Center, until the buyer pulls the product downstream of the Supply Chain.
This creates higher inventory costs for the supplier since he owns it for a longer time throughout the chain and also the risk is greater. The buyer always wants more inventory at the Distribution Center, so he increases the result of the forecast and thus gives it to his supplier.
This really should not happen, and information should be shared to create a more competitive and efficient supply chain. Forecasts must be shared but providers must also forecast demand.
4.4.1.3.- Min-Max replenishment
To follow this methodology, the company establishes maximum and minimum inventory levels for each item and in each warehouse in the supply chain. Why can this system become a supply chain strategy? The client asks the supplier, with the Min-Max levels that it has given him, to try to keep the client's inventory in this range and manage the client's stocks himself.
To be able to carry out this system and implement it, it is necessary that both the provider and the client are coordinated and integrated and for this they need a good computer system that:
a.- Provide real-time information on On Hand inventory levels, forecasts, scheduled receptions, launch of orders to our suppliers, and promised orders to customers. All of this information helps suppliers plan their and the company's replenishment more efficiently.
b- That it has a system of indicators such as a traffic light that warns for each item what the current inventory level is, red if it is below the minimum, and must be restocked, and green if it is not necessary to resupply this item.
In this strategy it is not necessary that the supplier owns the product until it reaches the customer. Inventory savings as well as Service Level improvements will be generated while helping the supplier minimize inventory and create more efficient production and transportation schedules.
It is important to highlight that the maximum and minimum inventory levels must be readjusted depending on the type of company or the characteristics of the product, weekly, quarterly or annually. To be successful with the min / max methodology, you need very good planners, and good information systems that allow you to have information that is as real and up-to-date as possible.
4.4.1.3.- Virtual Inventory
This system can be used both in the distribution of finished products and in multistage production. Can be used to relocate orders that are in transit, assign new ones
orders to expeditions, assign new routes and new inventory shipments to other locations or distribution centers, etc. Companies that resupply customers who are in their VMI (Vendor Management Inventory) system, when the supply time is low and there are also large transit times, should negotiate that the inventory in transit is considered as available inventory, so they can relocate it "on time" and take it directly to the customer's house, for example. In this way, companies that apply this system, can work with a few days of supply time and also manage to reduce inventory costs.
4.4.1.4.-Postponement
This strategy usually occurs in the final product configuration stage. An example of “Postponement” would be the purchase of T-shirts, which are colored or printed according to the customer's orders and not before they occur.
Instead of storing finished product and ready to be shipped to the customer, un-customized product is stored and adapted to customer needs once orders are generated. Homogeneous and highly standardized products are usually stored, which undergo a final process, of short duration, which allows that once the customer order has been generated, the order is processed in a short time, thus reducing the time supply to the customer within days. Inventory management tools are used in this system to determine where, when and how to postpone and what products.
4.4.1.5.- Inventory optimization in Multilevel systems
Supply chains, in an environment as globalized as today, need to work with tools, methodologies and strategies that allow them to be more flexible, more agile and more efficient. It will be determined where we should store stocks and how much we should store, what type of product (raw material, semi-finished or finished) so that the supply chain in which we are located makes us position ourselves in one strategy or another (speed versus efficiency).
The optimization that is achieved takes into account the position of the inventories taking advantage of Postponement or Push-pull tools to minimize investment in stocks. In addition, the level of customer service is optimized with less investment in inventory, because it is used where it is really needed.
4.4.1.6.- Risk assessment
The risks are determined by having more capital invested in stocks instead of disposing of it, by the costs of obsolescence and opportunity, among others. To know which strategy is the most appropriate in each case, a risk analysis must be performed, calculating cash flows, payback or return on investment (ROI), or VAN (Net Present Value), which will finally indicate which projects it is advisable to proceed according to the evaluated conditions.
V Warehouse Management in Warehouse Based on Costs and Demand
The reason why the first warehouses were created was the need to satisfy a practically constant demand for basic necessities with seasonal and variable production (some examples are food, heating…) Sometimes, on the contrary, production can be so stable as desired, while demand is variable. This is the case of umbrellas or toys.
In addition, since production and demand are stable, different economic reasons prevent buying the product in the right quantity. Transport costs from the production center to the consumption center can force the purchase of raw materials on a periodic basis (monthly, quarterly…). It is also possible that you want to store products because it is thought that in the more or less near future, the products will rise in price, which will earn the difference. It is said that in times of inflation the important thing is to have products. The financial reason also appears when large purchases are made at the end of a tax period to decrease accounting benefits.
Although the demand is stable, it may happen that for some reason it is not strictly constant but varies with a certain randomness. The same can be said of production, the machine or the supplier can stop (breakdown, strike, etc.). Protection against such randomness is another reason why it should be stored. Finally, production requirements can force the existence of stocks. For example, if the demand for several similar products is covered using the same machine (detergents, paper…), it is necessary to create manufacturing batches and therefore stocks. Thus it can be summarized that 6 are the basic reasons for the existence of stocks:
• Variation in supply compared to stable demand
• Variation and seasonality of demand
• Economic restrictions
• Financial or speculative reasons
• Protection against irregularities
• Regulation of production
Based on these reasons, the inventory can be broken down into six basic components:
1. CYCLE STOCK: It is the result of applying the different order policies, and is determined by the frequency of orders and the quantity requested each time.
2. SECURITY STOCK: It is the one that is kept as protection against the uncertainty of demand (and sometimes also of supply).
3. ANTICIPATION STOCK: It is the accumulated in anticipation of a need or because a special offer proposes it (Promotion Stock), or also to get advantages in the market linked to the rise in prices (Speculation Stock).
4. STOCK IN TRANSIT: It is the one in transit between suppliers and customers and can be identified separately. In the present study, the cycle stock will be considered fundamentally (result of the order batch and the occurred demand); the safety stock, created to protect against uncertainty, and the transit stock as an inevitable effect of the delivery time.
The anticipation stock will not be considered, since it is part of different management concepts. It can be admitted from the outset that the stocks represent a fixed asset without profitability, except in the case of speculation stock. In addition the costs of maintenance, obsolescence, etc. they can represent a significant part of the cost of storage.
5.1.- Cost of capital immobilization.
There are two ways to approach the definition of this cost. The first pretends that the stock is financed by an external activity (bank or similar) to which we must pay a certain interest. The second part of the fact that the company that invests money in stock does not invest it in other more productive concepts.
In the first case, it must be distinguished whether our company is capable of financing the stock in the “Long Term” or that it is obliged to finance it in the “Short Term”. It is common for financial institutions to consider the stock as a short-term investment (due to its more or less perishable nature) although it is an investment that, rotating, usually lasts with the production process. In general, long-term financing is cheaper than short-term financing.
In the second case, the cost of storage due to the immobilization of capital is equal to the rate of return on investment set by the company. If either option is taken, the cost of capital immobilization is usually the most important.
5.2.- Other costs.
5.2.1.- Warehouse maintenance cost.
Sometimes the warehouse is rented, so the definition of this cost is simple. However, the warehouse is generally its own, so it is necessary to estimate a cost to be passed on by the use of facilities, energy, etc.
It does not cost the same to store frozen products as some type of sand that requires only a tarp on top to avoid being blown away by the wind. Also, insurance premiums can be incorporated at a value that will generally range between 0.5% and 2% of the stored cost.
5.2.2.- Maintenance cost.
The movement of materials (personnel, machinery, etc.) is the object of this cost. Generally it is not proportional to the quantity stored but to the activity of the warehouse. Large variations are allowed depending on the sector and the company, although some authors estimate this expense between 4% and 6% per year of the stored value.
5.2.3.- Impairment cost.
It depends on the nature of the stored products and they are particularly high for fragile products such as crystals, laboratory equipment, etc. A cost can be determined for each category varying between 0.2% and 5%. 3.2.2.4 Looting cost.
Some products are more likely than others to “disappear” in the course of work (eg in alcoholic beverage warehouses). Sometimes it is cheaper to assign a cost and let it continue to disappear than to establish a theft prevention system. These costs vary greatly in companies, although they are very easily evaluable.
5.2.4.- Cost of expiration and obsolescence.
The nature of these cost types is similar. In the first case, expiration, the duration of the product is determined by itself (food, sanitary, etc.). In the second case, obsolescence, it is the market or the sector that causes the obsolescence (electronic products, fashion…). These costs can range between 0% and 15% of the stored value depending on the volatility of the sector and the management policies used.
5.3 Classification of the Demand in Inventory Management.
Independent Demand / Dependent Demand: Independent demand is one that is not affected by more elements than the market itself. Dependent demand is that which is linked to the manufacture of another product (For example, the demand for bicycle wheels is dependent on the demand for bicycles).
Random / Predictable Demand: An item is said to have predictable demand when the quantity and timing of delivery are committed, while random demand is one that depends on uncontrollable factors. Stable demand: Stable demand is one in which, although the value of the demand varies, it does so around a constant figure over time.
5.3.1 Demand with trend
It is one in which the average value of demand varies over time, showing an increasing or decreasing trend.
5.3.2.- Seasonal demand
A seasonal demand model is one that shows a variation in average demand at different points in the planning cycle, and this variation can be related to certain market factors.
5.3.3 Demand for fast or slow movement.
The classification of fast or slow moving demand does not depend so much on the value of the demand, but on the frequency of the demand over time and, therefore, on the form of the distribution of the demand. In the case of fast-moving demand, it is assumed that demand has a statistical distribution of normal type, while slow-moving demand is more like a Poisson or composite Poisson.
5.3.4 Demand Established by Periods.
It is one in which the demand is known in advance and divided into periods (hours, days, weeks). It is generally associated with dependent demand.
Figure 25.0 Ordering dynamics in the demand direction.
6. References
Abdul-Jalbar, B., J. Gutiérrez, J. Puerto and J. Sicilia, 2003. Policies for Inventory / Distribution Systems: The efect of centralization vs. decentralization.
International Journal of Production Economics, 81-82, 281-293.
Abdul-Jalbar, B., J. Gutiérrez and J. Sicilia, 2004a. An integrated inventory model for the single-vendor two-buyer problem. Submitted to International Journal of Production Economics.
[Abdul-Jalbar, B., J. Gutiérrez and J. Sicilia, 2004b. Policies for a single-vendor multi-buyer system with finite production rate. Submitted to Operations Research.
Abdul-Jalbar, B., J. Gutiérrez, and J. Sicilia, 2005. Integer-ratio policies for distribution / inventory systems. International Journal of Production Economics,
93-94, 407-415.
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