GLOBAL IDEA AND PRESENTATION
The objective of this work was to provide a precise idea of the different types of replenishment planning, for which I had to first address related topics such as Inventory Costs and all the sub topics that this generates.
Each of these topics was described and exemplified for your better understanding, hoping to have done an enjoyable, understandable and above all useful work.
INVENTORY COSTS
Inventory Management is an activity in which three types of Costs coexist
- Costs associated with flows Costs associated with stocks Costs associated with processes
This structure is proposed without prejudice to maintaining the classic structure of Costs by nature, as classified into the following two large groups.
- Operating Costs Costs Associated with the Investment
The former are those necessary for normal operation in achieving the End. While those associated with the Investment are those related to depreciation and amortization.
Within the scope of the flows, the Costs of the supply flows (transports) must be taken into account, although sometimes they will be paid by the supplier (in the case of contracts such as CFR, CIF, CPT or CIP, among others) and in other cases will be included in the price of the merchandise purchased. It will be necessary to take into account both the operating costs and those associated with the investment.
Costs associated with stocks, in this area all those related to Inventories should be included. These would be among other costs of storage, deterioration, loss and degradation of stored goods, among them we also have those of stock breakdowns, in this case they have a fundamental component the financial costs of stocks, all this will be explained later.
When you want to know, as a whole, the inventory costs will have to take into account all the indicated concepts. On the contrary, when it is necessary to calculate costs, for decision-making purposes, (for example, to decide the optimal size of the order), it will only be necessary to take into account the avoidable costs (which may vary in each case considered), since that unavoidable costs, by definition, will remain outside regardless of the decision made.
Finally, within the scope of the processes, there are numerous and important concepts that must be attributed to the Costs of the inventories. They are: Purchase costs, order launching and activity management. A paradigmatic case is the following. In general, transportation costs are incorporated into the purchase price (why not also include storage costs, or order management?), As a consequence of the fact that in most cases these are transports by supplier's account included more or less tacitly or explicitly in the purchase price. But even when the transport is managed directly by the buyer, this practice is maintained, although many times the price of the transport is not directly proportional to the volume of goods purchasedrather it depends on the volume transported in each order. In these circumstances the cost of transportation also becomes part of the cost of launching the order.
The purely logistical classification of Costs that has been cited so far is not the most frequently used in "the profession." We have already mentioned in the previous paragraph concepts such as "order launch cost" or "acquisition cost", which did not appear among the concepts initially exposed. Well, the usual cost classification used by inventory managers is as follows:
- Storage, maintenance or inventory holding costs Order launch costs Acquisition costs Out-of-stock costs
STORAGE COSTS.
Storage, maintenance or stock ownership costs include all costs directly related to the ownership of inventories such as:
- Financial costs of inventories Warehouse expenses Insurance Deterioration, loss and degradation of merchandise.
They depend on the storage activity, whether it is managed by the company or not, or whether the merchandise is stored under a warehouse regime by the supplier or whether it is owned by the manufacturer.
To record this complexity, a detailed list of the costs of storage, maintenance or possession of the stocks is included below in the most general case possible. However, a simplified method of calculating these costs (the annual "ad valorem" rate) that is used very frequently will be presented later.
The classification of storage costs that follows is classified by activity (storage and maintenance), by attributability (fixed and variable) and by direct and indirect origin.
DIRECT STORAGE COSTS
fixed costs
- Personnel Surveillance and Security Tax Burdens Warehouse Maintenance Warehouse Repairs Rentals Warehouse Amortization Amortization of shelves and other storage equipment Financial expenses of immobilization
variable costs
- EnergyWaterShelves MaintenanceReplacement materialsRepairs (related to storage) Deterioration, loss and degradation of merchandise.Financial Expenses of Stock.
DIRECT MAINTENANCE COSTS
fixed costs
- Personnel Insurance Amortization of handling equipment Amortization of computer equipment Financial expenses of fixed assets
variable costs
- Energy Maintenance of handling equipment Maintenance of computer equipment Repairs of handling equipment Communications.
INDIRECT STORAGE COSTS
- of administration and structure of education and training of personnel
There is an approximate method of valuing storage costs, known as the Annual Ad valorem rate.
CALCULATION OF THE ANNUAL RATE «AD-VALOREM«
This approximate method, which is widely used for planning Logistics Systems, consists of admitting that storage costs can be approximated by an annual rate applied to the value of the stored goods.
This hypothesis, which is evident in the case of the financial costs of Stocks, is generalized in this method to the other costs involved in storage (Investments, personnel, energy, deterioration, losses…) Assuming that the more expensive a commodity is more expensive is the cost of storage.
Let us suppose, for example, the case of a special cement trading company, located in a certain maritime port, to serve one of its clients, receives a 5,000 ton ship. With a shipment of special white cement of the same quantity, the price of which is $ 80 per Ton., it is transferred to a properly conditioned warehouse where it is stored.
The destination of this load is a factory that works Just in time, and that only admits 200 tons per day. The 5,000 Tns shipment. It will take 25 days to be withdrawn, existing throughout said 25 days an average Stock of 2,500 Tns. (5,000 on the first day and 0 on the last).
We have invested $ 400,000 (5,000 x $ 80), which we will not recover until the 25th. If we are able to obtain a return on our alternative money of 8% per year, the financial cost of the Stock that we have due to immobilization is 8%, this applied to the average Stock gives us (2,500 x $ 80) during the time that we have it immobilized (25 days).
| 1 / A | B | C | D | AND | F |
| two | 8% | Annual Yield | 16000 | (B3 x B5) x B2 | |
| 3 | 2500 | Average Immobilization | 1,095.89 pta | (E3 x B4) / 365 | |
| 4 | 25 | Average immobilized time | |||
| 5 | 80 | Unit price |
Well, the ad-valorem rate method is extended to the other costs that make up the storage of merchandise, admitting that in addition to the 8% per year that corresponds to the cost of Stock, there are other percentage points that correspond to the integration of the others costs that also intervene in storage, thus making rates higher than Stock storage, for example in Spain 25% was charged when the market rate was 15%.
It is also very important to note that these costs that we mention "extras" in storage, are always directly related to the type of merchandise in question, so it will not be the same to store sand, or firewood against money or caviar.
A reasonable structure for the composition of the fee is as follows:
Financial cost of Stocks 8% to 20%
Physical Storage 5% to 15%
Deterioration or Theft 2% to 5%
For the example of the storage of white cement, which requires careful storage but little maintenance, it can be valued with a rate that considers only the financial cost of storage without "Extras", in this case 18%.
The impact of storage costs is 0.49 per ton, which is added to the costs of primary transportation to the port of discharge, and the costs of capillary distribution to the customer.
ORDER LAUNCH COSTS
Order Launch Costs include all Costs that are incurred when a purchase order is launched. The Costs that are grouped under this heading must be independent of the quantity that is purchased and exclusively related to the fact of launching the order. Its components would be the following:
Implicit costs of the order: Cost of preparing the machines when the order is launched by production, Cost of getting "PLACE" in the receiving warehouse (movement of goods or transport to other locations, for example), transport costs exclusively linked to the order (the invoice of a «courier» in the case of an urgent replenishment, for example), costs of supervision and follow-up of the need to launch an order, etc.
Administrative costs linked to the order circuit.
Receiving and inspection costs.
Acquisition Costs
It is the total amount invested in the purchase of the merchandise, or the book value of the product when it comes to material in progress or finished products.
In the first case (raw materials or components), the acquisition cost will incorporate the non-recoverable items that the supplier will include in his invoice (for example, transport, if it is on the supplier's account, but not VAT). It should be taken into account that many suppliers apply volume discounts, so that sometimes the acquisition cost of an order will have an avoidable cost component and other times it will be entirely an unavoidable cost.
In the second case (material in progress or finished products), the determination of the acquisition cost is more complex, depending on the accounting practices of the company. In principle, it should incorporate the following concepts:
- Incorporated Materials Costs that, according to the company's accounting practices, can be valued according to the following criteria.
-
- FIFO method (first in, first out). - (First in, first out) PEPS LIFO method (last in, first out). - (Last in, first out) LIFO is somewhat equivalent to a replacement price MIFO method (midle in, first out) is a weighted average Company standard prices Estimated replacement prices
-
- Direct production costs (MOD, depreciation, etc.) Indirect costs.
STOCK BREAKDOWN COSTS
The costs of breaking or breaking stocks include the set of Costs due to lack of stocks, these costs will not be absorbed by production in process, but will go directly to the income statement.
- Decrease in sales income: The lack of accounting integrity due to lack of references in an order placed, supposes a reduction in sales income, both due to the displacement in the type of billing date, as well as the absolute loss of the loss.
- Increase in Service expenses: This includes the contractual penalties for supply delays, stoppages in the production process, false freight, etc.
The valuation of these breaking costs is difficult and infrequent, it is only possible if the company is provided with an efficient quality management system, in general the inventory manager must comply with subjective estimates or Standard costs. In specialized literature these are considered between 1% and 4% of sales revenue, but this is also tentative.
REAPROVISION PLANNING
OF REAPROVISION
Once the objectives of the Inventory Management have been defined and the demand forecasting techniques described and the costs of the stocks determined, it is possible to expose the Inventory Management models used in planning.
MANAGEMENT MODEL: «JUST IN TIME»
In point XX we mentioned in the example for the calculation of the Ad Valorem rate the "Just in Time" method, then and as a way to complement the types of replenishment, we will describe what this method is about.
Just in Time or Just in Time was initially developed by Toyota and later moved to many other companies in Japan and the world, it has been the greatest factor contributing to the impressive development of Japanese companies. This has led companies from other latitudes to be interested in knowing what this technique is like.
The Just in Time more than a production system is an inventory system, where its goal is to eliminate all waste. Waste is generally defined as anything other than the absolute minimum of material, machine and labor resources required to add value to the product in process.
The benefits of JIT are that in most cases, the just-in-time system results in significant reductions in all forms of inventory. These forms include inventories of purchased parts, sub-assemblies, work in process (WIP), and finished goods. Such inventory reductions are achieved through improved methods not only of purchasing, but also of production scheduling.
Just-in-Time requires major modifications to be made to traditional parts sourcing methods. The preferred suppliers are chosen for each of the pieces to be obtained. Special contractual arrangements are structured for small orders. These orders are delivered at the exact times required by the user's production schedule and in the small quantities sufficient for very short periods.
Daily or weekly deliveries of purchased parts are not unusual in just-in-time systems. Suppliers agree, by contract, to deliver parts that meet pre-established quality levels, eliminating the need for the buyer to inspect incoming parts. The arrival time of such deliveries is of extreme importance. If they arrive too early, the buyer must keep a separate inventory, but if they arrive too late, stocks can run out and stop scheduled production.
Purchasers of these parts often pay higher unit costs to have them delivered this way. While the opportunity costs of structuring the purchase contract can be significant, the subsequent cost of sourcing batches of individual parts, daily or weekly, can be reduced to near zero levels. By not having to inspect incoming parts, the buyer can achieve higher product quality and lower inspection costs.
The production of parts to be manufactured is scheduled in such a way as to minimize work in process inventory (WIP), as well as stocks of finished goods. Just-in-time standards force the manufacturer to fix production bottlenecks and design problems that were previously covered by holding reserve stock.
Because the uncertainty has been eliminated, quality control is essential to the success of the "Just in Time" implementation. In addition, since the system will not function if frequent and long failures occur, it creates the inescapable need to maximize uptime and minimize defects. In turn, a vigorous maintenance program is required. Most Japanese plants operate with only two shifts, which allows full maintenance during non-productive time and results in a much lower rate of machine failure and deterioration than in the United States.
The pressure to eliminate defects is felt, not in maintenance scheduling, but in manufacturers' relationships with suppliers and in everyday work online. Just-in-time production does not allow for a close inspection of incoming parts. As such, suppliers must maintain high and consistent quality levels, and workers must have the authority to stop operations if they identify defects or other production problems.
INVENTORY MANAGEMENT MODELS
The models on which to base supply planning are grouped into two main categories, depending on whether demand is dependent or independent.
- Models for unscheduled Replenishment, in which the demand is independent, generated as a consequence of the decisions of many actors outside the logistics chain (customers or consumers), the most common model is the Economic Purchasing Lot.
- Models for scheduled Replenishment, in which the demand is dependent, generated by a production or sales program. They respond to Replenishment requests established by MRP or DRP based on optimization or simulation techniques.
In turn, non-programmed models are classified into two other categories:
- Continuous Replenishment Models, in which an order order is launched when inventories decrease to a certain magnitude or "order point". The quantity to be ordered is the "economic purchase batch". Periodic Replenishment Models, in which an order order is launched every certain time previously established. The quantity to order will be the one that restores a certain maximum level of stock to the target level.
These last models could, in turn, be subdivided according to the demand that is deterministic or probabilistic, constant or variable, which do not provide relevant methodological differences. The classic unscheduled Replenishment models were used for many years, which produced anomalous results and spread doubts in companies about the goodness of analytical models as substitutes for the good, intuitive work of inventory managers. Until the concepts of dependent demand and independent demand were defined in 1965, it was clear that the classical models were the only ones applicable to cases of unscheduled or independent demand.
SERVICE LEVEL AND SAFETY STOCK
The independent or unscheduled demand for a product is usually probabilistic. Rather, deterministic independent demands are in practice a resource of doctrine to complete classifications or to simplify the formulation of models. This random circumstance in the generation of demand can cause stock ruptures, with its associated costs and its undoubted losses in the quality of the service.
Consequently, it is necessary to have additional inventory in our warehouses over what is strictly necessary that our Replenishment model has established. Said safety stock will depend on the deviations that consumption will present during the period between the launch of an order and the receipt of the merchandise, that is, during the delivery period (Lead Time) or Critical Period.
Consequently, the determination of the Safety Stocks will be linked to the perception that we have of these deviations and the degree of reliability, or "level of service" that we are willing to offer to our clients. If we have the statistical perception of the deviations in the form of the standard deviation of demand, the safety stock will be the number of reserve standard deviations that we are interested in maintaining. In turn, that number of reservation standard deviations will define the level of service we are offering.
Set the "level of service" that we are willing to offer to our customers, expressed as a percentage of services without stock breaks (for example, we can set that there are no stock breaks at 97.72% of supplies).
Determine, on the basis of statistical laws, the number of reserve standard deviations that we must maintain, or "service factor", to guarantee that level of service (in the example above, and for a normal distribution, 2 standard deviations to ensure that level of service).
Calculate the safety stock by multiplying the standard deviation of the demand by the service factor (in the example shown whose monthly mean was 113.25 units and the standard deviation of 13.0125 units, the safety stock for a lead-time of one month would be 26 units).
Service levels and service factors
| Service level (%) | Service factor |
| 75.00 | 0.70 |
| 85.00 | 1.00 |
| 90.00 | 1.30 |
| 95.00 | 1.70 |
| 98.00 | 2.10 |
| 99.00 | 2.30 |
| 99.99 | 3.10 |
For the case in which the demand is explained by Poisson's law, the relationship between the service factor is taken from the previous table.
It is necessary to take into account in any of the cases that if the period of analysis of the demand (which was monthly in the previous example) does not coincide with the lead time, it is necessary to apply certain statistical corrections that are indicated below:
- if the period of origin for the calculation of the measures and deviations is:
- and the new period to consider (eg the lead time) is:
- the new measure will be:
- and the new deviation will be:
s q = s p. k
OPTIMAL ORDER SIZE
The next question that the manager usually asks when considering the replenishment is:
How much to order?
This is the main question that analysts have tried to answer since the importance of scientific stock management became apparent. The best known answer to this question is the famous "Wilson model formula" for the determination of the economic lot of purchases (LEC) or, in English, economic order quantity (EOQ).
Wilson's model was formulated for the case of a very simple and restrictive situation, which has not been an obstacle to generalize its application, many times without the required scientific rigor, to other situations closer to reality.
Strictly the Wilson model is formulated for the category of continuous supply models, with deterministic and constant demand, in the following respective assumptions
Only storage and order launch costs are considered relevant, which is to admit that:
The acquisition cost of the Stock is invariable whatever the quantity to be requested, there being no quantity bonuses, for example, being therefore a non-avoidable cost.
Stock breaking costs are also not avoidable.
In addition, it is admitted that the delivery of the merchandise is instantaneous, that is, with no replacement period.
In these circumstances Wilson's reasoning is as follows:
- Let's adopt the following terminology:
«Q»: quantity to request of the analyzed product (in quantity or price)
"V": annual sales volume of the product (in quantity or price)
"A": the cost of storage expressed in an annual rate over the cost of the stored product
"B": The cost of launching an order.
«C»: The acquisition cost of a product, used exclusively to determine storage costs based on the aforementioned rate.
- Let us admit that stocks evolve, consistent with the hypothesis previously exposed, it follows immediately that:
- The number of orders launched per year is: V / Q The average stock is: Q / 2 The acquisition cost of the cyclical stock is: c * (Q / 2) The annual storage cost is: a * c * (Q / 2) The annual cost of the order launch is: b * (V / Q)
- Consequently, the total annual cost of the inventories in the hypothesis presented will be:
- The condition that the total cost is minimum would give the following value of the economic purchase lot
Which is the usual expression of Wilson's formula.
Let's consider the following example…..
A certain Company presents the following data:
- annual demand 1,359 units storage cost, expressed as an annual ad valorem rate 18% cost of launching an order $ 5 per order product acquisition cost $ 100
Applying Wilson's formula, it can be deduced that the optimal order size (LEC or EOQ) is 27.48 units (rounded to 28 units), so the company must launch about 49 orders per year. If instead of having used units for the calculation, we had used price data for annual sales, the optimal order size would also appear expressed in price.
The generalization of this formula to other assumptions closer to reality (such as, for example, variable transport costs with order size, volume discount, variable and probabilistic demands, etc.) is analytically simple, although with serious doubts in the most complicated cases about the mathematical rigor of the endeavor.
Considering the previous example adding a new condition:
-
- After 32 purchase units, the supplier applies a 5% discount on the total purchase.
In this case, the Wilson model hypothesis is modified in the sense that the inventory acquisition cost is no longer unavoidable and becomes relevant for the analysis.
At the cost implicit in Wilson's Formula, which was indicated in section d) above, the acquisition cost should be added. Consequently, the total cost of the economic purchase lot would be the following:
Now suppose that, instead of economic batch of purchase calculated above, we acquired the minimum number of units needed to get the discount, ie 32 units at $ 95 c / u, the total cost would be:
As the new total cost is lower than the previous one, the optimal decision would be to acquire in each order the number of units closest to 28 that gives rise to the discount offered, in this case 32 units.
In a case as simple as this, to avoid risks in the combined use of the economic purchase lot (28 units indicated above) and the new limit (which we are not sure is the optimal one) of 32 units, the ideal thing would be to simulate With the help of a spreadsheet the evolution of the total cost of Replenishment for different hypotheses of the order size, and choose the one that presents a minimum cost.
3.5 CONTINUOUS CHECKUP: THE ORDER POINT
Being able to calculate the optimal order size with relative simplicity, with the help of Wilson's formula, the next question that could be asked would be:
How much to order?
In continuous replenishment models, inventories are continuously monitored and the order is placed at the moment when inventories decrease to a certain magnitude or »order point». The quantity to order would then be the economic lot of purchases. (LEC or EOQ).
If the hypotheses on which the Wilson model is based are scrupulously respected (specifically, which establishes that the lead-time is zero), the order point would appear when the inventory level was equal to the safety stock. In a more general case, with a non-zero replacement period, the order point would appear when the inventory level was equal to the sum of the safety stock plus the demand that would foreseeably have to be met during the replacement period. That is to say:
3.6 PERIODIC REVIEW
In the case of periodic replenishment models, the answer to the question how much to order? It is apparently simple: an order is launched every certain time previously established (once a week, or once a month, for example), called the replenishment period. The quantity to order at that moment (in English "order quantity") will be the one that restores a certain maximum level of stocks, or "target level".
This restocking model tends to be used when there are low demands for many items and it is convenient to consolidate the requests for several of them into a single order to reduce launch costs or to obtain volume discounts.
The objective level of stocks would be, in the hypothesis of a null replacement period, that which guarantees supplies during the review period. That is, the expected demand in said period plus a safety stock associated with said period if the demand were (real case) of a probabilistic type. The quantity to order at each of the pre-established moments would be the difference between the existing stocks and the target stock.
If we now add the assumption that the replacement period is not zero, the previously calculated target level should be added to the expected demand during the replacement period, since if we only request at the time of the review the difference between the existing stocks and the previously defined target stock, at the time of order replenishment, a few days (or weeks) later, we would not reach that target. In summary we would have to:
The review period is usually set for practical reasons, related to the temporary management guidelines of the company, and that is why there are so frequent weekly, biweekly, monthly, quarterly review periods, etc. However, setting the review period should be related, seeking the optimum, with the concept of economic purchase lot (LEQ or EOQ).
According to this criterion, the review period should coincide or approximate as much as possible the average interval between two orders that corresponds to the economic purchase lot.
It may happen that the review period coincides with an exact unit of time (day, week, month, quarter), if not, the review will have to be adapted according to the good common sense of the person in charge.
Many times the order to be made is different from the economic batch of purchase. This means that inventory costs when using the periodic replenishment model are typically higher than the costs of the continuous replenishment model (obvious conclusion) and we will only apply the periodic replenishment model when it is very difficult or expensive to continuously track inventories or economies of scale arise by simultaneously ordering multiple references.
INVENTORY CONTROL
Until now, the "classic" ways of approaching Replenishment planning have been described and some fundamental tools for inventory management have been described, such as demand forecasting techniques and cost analysis.
Next, as a logical extension of the planning processes, some topics related to inventory control will be presented, such as measurement techniques and stock counts and generally accepted criteria for the classification of materials, necessary to optimally assign the efforts associated with the inventory management.
MEASUREMENT OF STOCKS
To adequately control stocks, the inventory manager must have a series of control measures and ratios that reflect as fully as possible the current asset situation and, where appropriate, the resources made available to them for that purpose. management.
The quantities to be measured can be grouped into the following categories:
Stocks
Movements
Rotation
Coverage
And in your case as before it was commented:
Means
The measurement of inventories is the quantification of the Current Assets available at all times (if the measurement system allows it) or at certain characteristic moments of the company's activity: Weekly inventories (those present on a specific and fixed day of the week), monthly (generally on the last day of each month), and annually or for the accounting year (in Europe it is usually on December 31; in other territorial areas it depends on generally accepted accounting practice). It is, therefore, an absolute measure, although it can be relativized based on average measures: annual, monthly or weekly average stocks, for example.
Stocks can be measured in physical units (what we have previously called "volume" of stocks, although in practice it can be units of volume itself, weight or discrete units), or in monetary units (dollars, euros, weights…..) this last valuation presents some definitional problems, as already stated when talking about the costs of inventories, so the inventory manager, without ever losing sight of the economic quantification of inventories, must focus your attention in the control of physical quantification.
The measurement of the movements of the working capital, that is, of the inputs and outputs of materials, is another fundamental aspect of inventory control, which generally requires the use of computer support tools. As in the previous case, this measurement can be made on the basis of physical or monetary units, with the same limitations and needs on the part of the inventory manager mentioned above. Inputs and outputs can be measured on an order-to-order basis, or in periodic terms: daily, weekly, monthly, or annual inputs or outputs, for example.
The ratio or turnover rate is another magnitude, in this case relative fundamental for the control of inventories that relates outflows with inventories. It is defined as follows:
Turnover is usually measured in annual terms, placing in the numerator of the previous expression the total outflows for the year or financial year and in the denominator the stocks measured for said period. The result (for example, 8.5), means that for a reference, product family or total company, stocks have rotated for one year in our warehouses the number of times indicated. Monthly, weekly or daily rotations can also be measured, depending on the characteristics of the reference analyzed, but the control ratio par excellence is that of annual rotations.
In addition to this attention to the time period to which the turnover ratio refers, one must be extremely careful with the units used in the numerator and denominator of the previous expression. Both must be simultaneously physical or monetary and with the same units of measurement. The issue is especially perverse in the case of economic magnitudes: It is not uncommon to measure outflows at market prices and inventories at cost value, which would give a false financial turnover of stocks.
The inverse (nuanced) of the turnover ratio is the ratio or indicator called coverage. Coverage generally measures the number of days that cover the stocks available at any given time (or stocks measured for a certain period). The classic expression of this indicator is the following:
The result of applying this ratio will be a number of "days of stock" (for example: 23.7) that indicates that the stocks available at that time of a certain reference or family of products allow to cover the demand during the days indicated. If the measured stocks of a certain period (week, month, etc.) are placed in the numerator. instead of daily stocks, factor 365 will have to be adjusted by dividing it by the number of days in that period. For the rest, due attention will have to be paid to the problem of the units in the same sense that was exposed when talking about the turnover ratio.
Finally, another measure that may be of interest to the inventory manager is the degree of use or occupation of the available resources, generally the storage capacity. It is an eminently physical indicator that can be defined as follows:
For a given reference, if the annual average stocks are located in the numerator of the previous expression and the capacity dedicated to said reference in the denominator, the optimal degree of use would be 50%, since that means that it has not entered during the year analyzed a new order in the warehouse, until the stocks we had are exhausted. If the value of the index is greater than 0.50, this indicates that we have kept some other type of inventory in the warehouse in addition to those strictly necessary from a logistical point of view: for example, safety stocks, strategic stocks, or stocks speculative.
If the analysis is extended to multiple references and there are no capacities dedicated to a single product in the warehouses, but the capacity is shared, the indicator is less powerful, since a degree of utilization higher than 50% may be due to external effects to the pure logistics described above, or to careful management of the warehouse, in which gaps generated by outputs of a certain reference are used to locate other references that are entering at that moment.
4.2 CLASSIFICATION OF MATERIALS
The fact of classifying the materials that are part of our inventories is a common practice that aims to limit planning and control activities to a certain number of references, the most important. When there are thousands of references in an inventory, it is very difficult to extend these activities to all of them and it is necessary to optimally assign the real management capacity.
Classification of materials is usually approached on the basis of the following two criteria:
Outputs (in currency units)
Rotation
The classification by outputs is the most widespread, and groups the articles in the well-known "ABC" classification, sometimes called "XYZ" so as not to confuse the previous acronyms with the concept "Activities Based Costs", widely used in recent times.
The "ABC" classification is based on the well-known Pareto Law, and differentiates the articles between the important and scarce (category A) and the numerous and trivial (category C), with an intermediate group that does not participate in either of both denominations (category B). It is classic to consider the following groupings of articles:
TYPE A: 20% of the references 80% of the value
TYPE B: 30% of the references 15% of the value
TYPE C: 50% of the references 05% of the value
If we handle many references, the classification that we make according to the value of the outputs, and the number of articles available does not differ excessively from the table indicated. The "fine" management of inventories should progress from category A to categories B and C, depending on the real possibilities that we have.
The classification according to the turnover incidence is less generally defined than the previous one, depending on the characteristics of each company. Group the articles in the series of categories from highest to lowest rotation, according to the following or similar names:
- High turnover articles Normal turnover articles Low turnover articles Obsolete articles
Obviously, obsolete items are those with an extremely low turnover rate, close to zero, but the rest of the classification will depend on the usual practices of each company. Likewise, this classification, to be really useful, will have to be segmented into the following three fundamental types of stock:
- Raw materials and components Work in progress Finished products
On the other hand, as in the previous ABC classification, by outputs it was clear that we gave preference to the references of category A, rather than B and C, in this new classification, it may be important to focus attention on the products of the last steps in preference to the first, to avoid the risk of finding ourselves at some point with large quantities of obsolete products.
In any case, an adequate "mix" of both classifications would allow us to carry out a good control of our inventories, adapting it to the availability we have in terms of human resources and management tools.
4.3 STOCK COUNT
The inventory count, a fundamental activity within the control of inventories, consists of determining the means to periodically have viable data on inventories.
If the inventory manager has real-time and also reliable information on the movements of goods (inputs and outputs), it is relatively easy to also have real-time data on stocks, since:
This analytical or virtual count of stocks is based on the fact that the knowledge of the movements in real time of the merchandise is feasible since in general they are supported in accounting operations that generate delivery notes or invoices of entries and exits easily processable. However, in the case of materials in progress and, in general, of internal inventories, it is not so easy to have this type of information on movements, so the analytical count of stocks present some.
In addition to this last circumstance, there are accounting errors, loss of materials, damage and other circumstances that distort the analytical monitoring of stocks and that require physical (not virtual) counts of the goods to obtain data that can be used directly in management. or to periodically update the value:
Which are used for analytical monitoring of stocks in real time.
The physical stock count that is commonly used in the company is the cyclical count, which consists of counting the different products in warehouses periodically (every day, week, month, etc.). The allocation of the counting period to each product depends on its importance for the inventory manager depending on its place in any of the material classifications set out in the previous section 2.3.2. Articles classified as "A" can be counted daily or weekly, while articles in category "B" can be counted biweekly or monthly, and those of type "C" every two months, quarter, semester or even just once. year.
In order not to consume excessive human resources in these operations, the cyclical count of the Stocks must be materialized in a «counting list» in which the different references to be counted alternate so as not to have to carry out the simultaneous count of many of them. Suppose, for example, we have the following references.
Type "A": Item 001 with weekly count
Type "B": Article 002 and 003 with a fortnightly count
Type «C»: Article 004 to 007 with monthly count
In these circumstances, the »count list» should look like the one in the following table.
COUNT LIST
| Week | Items to count |
| one | 001-002-004 |
| two | 001-003-005 |
| 3 | 001-002-006 |
| 4 | 001-003-007 |
| 5 | 001-002-004 |
| 6 | 001-003-005 |
| 7 | 001-002-006 |
| 8 | 001-003-007 |
| 9 | 001-002-004 |
| 10 | 001-003-005 |
| eleven | 001-002-006 |
| 12 | 001-003-007 |
Thanks to the list, it is possible to perform the physical count of only three references each week, which allows optimizing resources.
- INTEGRATED INVENTORY MANAGEMENT
Up to now, the inventory planning techniques that have been described correspond to the «classical» typology, in which the demand that ultimately causes the stocks is implicitly considered to be an independent or unscheduled demand.
In the following pages, once the classical techniques of continuous replenishment and periodic replenishment have already been described, we will proceed to describe the replenishment techniques when the demand is of a scheduled type, techniques that are supported by MRP or DRP procedures. Regarding the latter, here we will focus the study on DRP (Distribution Resources Planning) procedures, as they are more recently implemented than MRP procedures.
5.1 RE-PROVISION WITH SCHEDULED DEMAND
Replenishment under conditions of dependent demand, based on MRP or DRP techniques, is characterized by the existence of a program of replacement needs, generally in the short term, whose simpler structure is of the following type:
Reference XXX:
Weeks: 1 2 3 4 5 6 7
Replacement need: 10 10 10 70 150 140 135
Accumulated IDs: 10 20 30 100 250 390 525
The problem consists, as in the cases described in the previous section, in deciding when and for how much quantity an order is launched.
The order will be launched following criteria similar to those of the Continuous Replenishment described above: at the moment in which the inventories of the reference considered are reduced until they are equal to the sum of demand during the replacement period, plus the safety stock. In this case, the safety stock does not arise because it is the probabilistic demand, since it is now programmed, but because of the existence of possible delays and other risks in the development of the process (breakdowns, labor problems, etc.). The replacement period will refer to the delivery period of the goods by the suppliers, since the transfer periods to the destination of production cadens, commercial warehouses, etc.) will have already been taken into account when establishing the schedule.If we are at a point in the logistics chain far from the suppliers (for example, in a factory warehouse that must supply the majority), the replenishment period to determine our “order point” will be zero.
The order quantity is a matter of more complex analysis. It should be equal to the sum of the replacement needs for a certain number of program periods (one, two, three, four… weeks in the previous example), a number that will have to be determined with some optimization criteria. If we are at the beginning of the logistics chain, we will have to take into account the problems of the suppliers; if we are at the end the problems of the customers, and if we are in an intermediate point, the problems of the previous links (for example, production) and later (for example, wholesalers or retailers).
The way to approach this problem in a mathematically rigorous way is by means of OPERATIONAL RESEARCH techniques, specifically with dynamic programming procedures (Wagner-Withing method, for example). Some commercial MRP or DRP programs have exact algorithms of this kind. However, due to the difficulties inherent in these methods, the most frequent is to resort to other less exact techniques, such as simulation (testing various scenarios and choosing the best of those tested) or approximate algorithms such as Silver-Meal.
To apply this algorithm it is necessary to know a series of data similar to those that were needed to determine the optimal order size with the Wilson formula. That is to say:
The cost of storage, expressed in the form of an annual "Ad-Valorem" rate, which
we will assume for the example that it is 18%.
The cost of launching an order that we will assume for the example that is $ 5 per
order.
The acquisition price or the cost of the analyzed reference, which we will assume for the
$ 100 example.
Based on these data and on the programmed demand, the minimum cost accrual algorithm considers the cases in which the quantity to be ordered covers 1,2,3,4,…. periods and determines for each of these cases the sum of the costs of launching the period and storing the requested quantity during the periods in which it is not consumed. From this figure he obtains the unit costs per period or per unit of the reference and chooses the minimum cost option.
To apply this algorithm to the proposed example, we will admit that the first order will be placed in the initial week, with a null replacement period and safety stock.
CASE 1 : Period covering a single period.
Quantity to request: 10 units
Launch Cost: $ 5
Storage cost: $ 0 (because the merchandise is used immediately.
Total cost: $ 5
Average Cost: $ 5 per period or $ 0.5 per unit
CASE 2: Period covering two periods.
Quantity to request: 20 units
Launch Cost: $ 5
Storage cost: corresponding to the amount of the second period
for a period. That is: 0.18 * (1/52) * 10 * 100 = $ 3.46
Total cost: $ 8.46
Average Cost: $ 4.23 per period or $ 0.423 per unit
CASE 3: Period covering three periods.
Quantity to request: 30 units
Launch Cost: $ 5
Storage cost: that corresponding to the amount of the third period during
two periods, plus the amount of the second period during
a period. That is: 3.46 + 0.18 * (2/52) * 10 * 100 = $ 10.38
Total cost: $ 15.38
Average Cost: $ 5.13 per period or $ 0.513 per unit
CASE 4: Period covering four periods.
Quantity to request: 100 units
Launch Cost: $ 5
Storage cost: corresponding to the amount of the fourth period during
three periods, plus the amount of the third period during
two periods, plus the amount of the second period during
a period. That is: 10.38 + 0.18 * (3/52) * 70 * 100 = $ 83.07
Total cost: $ 88.07
Average Cost: $ 22,023 per period or $ 0.831 per unit
The procedure would continue to be carried out with the desired number of periods, although the Silver-Meal algorithm tends to be convergent and, once the inflection point of the average costs has been detected, it is not necessary to continue repeating the calculation. In the example it is clear that the first order to be placed should cover the first two periods and would therefore be 20 units. To define the next order, assuming that all the hypotheses adopted are maintained, we will place ourselves in the third period and we would apply the same calculation sequence again.
If we are at the beginning of the logistics chain, the results of the minimum cost accrual algorithm will be final, unless the suppliers have some specific condition (discounts for quantity, delivery limitations, etc.). However, if we are at another point in the logistics chain, the results of this algorithm will have to be weighed against the restrictions imposed by the previous link (for example, production), and the calculations repeated until a compromise solution is reached. For this reason, on many occasions it is preferable to directly use simulation techniques in which we already assume the restrictions of the different links in the logistics chain.
DRP TECHNIQUES: BROWN AND MARTIN METHODS
Resource planning techniques for distribution "DRP" aim to optimize within the logistics system of companies the relationships between the physical distribution subsystem (including transport and storage) and the production subsystem.
Consequently, the DRP must determine with optimal criteria the following aspects of logistics:
The needs to replace merchandise at the various interruption points in the flow of materials (factory and warehouses) in accordance with the pre-established basic conditions (production batches, replacement period, order point, etc.).
The resource needs associated with physical distribution (means of transport, storage capacity, etc.) in such a way as to ensure the pre-established quality of service and the best degree of use of the available means.
In other words, DRP techniques consist of the following:
A system (obviously computerized), for evaluating the needs for replacement of materials at the distribution points, coordinated with another specific system of control of production and inventories (such as MRP or others).
That serves as a link between the external demand for products by customers and the supplies provided by the master production plan (MPS).
There are various DRP procedures and packages on the market, generally marketed by their authors or consulting firms. At the level of general theoretical approaches, there are two main methodologies of «Distribution resources planning»:
Brown's method: according to which, the demand at the distribution points determines the gross needs of merchandise to be obtained from production and the needs for means of transport.
Martin's method: According to which, the distribution points are satisfied on the basis of scheduled batches to be obtained from production, which also determines the needs of means of transport.
In the tables, an example of the way of working of the Brown and Martin methods is represented respectively.
DRP: Brown method
| Point 1 | ||||||||||
| Replacement space: 1 day | ||||||||||
| Day | one | two | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sales forecast | 10 | 10 | fifteen | fifteen | 17 | 17 | twenty | twenty | 30 | twenty |
| Stock (initial stock 59) | 49 | 39 | 24 | 9 | -8 | -25 | -Four. Five | -65 | -95 | -115 |
| Replacement Needs | twenty | twenty | twenty | twenty | twenty | twenty | ||||
| Stock after restocking: | 49 | 39 | 24 | 9 | 12 | fifteen | fifteen | fifteen | 5 | 5 |
| Point 2 | ||||||||||
| Replacement place: 2 days | ||||||||||
| Day | one | two | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sales forecast | fifteen | fifteen | twenty | twenty | 22 | 22 | 25 | 25 | 35 | 25 |
| Stock (initial stock 94) | 79 | 64 | 44 | 24 | two | -twenty | -Four. Five | -70 | -105 | -130 |
| Replacement Needs | 30 | 30 | 30 | 30 | 30 | |||||
| Stock after restocking: | 79 | 64 | 44 | 24 | two | 10 | fifteen | twenty | fifteen | twenty |
| Point 3 | ||||||||||
| Replacement place: 3dias | ||||||||||
| Day | one | two | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sales forecast | 7 | 7 | 12 | 12 | 14 | 14 | 17 | 17 | 27 | 17 |
| Stock (initial stock 37) | 30 | 2. 3 | eleven | -one | -fifteen | -29 | -46 | -63 | 90 | 107 |
| Replacement Needs | 10 | 10 | 10 | twenty | twenty | twenty | 25 | |||
| Stock after restocking: | 30 | 2. 3 | eleven | 9 | 5 | one | 4 | 7 | 0 | 8 |
| Point 4 | ||||||||||
| Replacement space: 1 day | ||||||||||
| Day | one | two | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sales forecast | fifty | Four. Five | 65 | 55 | 65 | 65 | 65 | 55 | 55 | 55 |
| Stock (initial stock 285) | 235 | 190 | 135 | 80 | fifteen | -fifty | -115 | -170 | -225 | -280 |
| Replacement Needs | 80 | 70 | 60 | fifty | fifty | |||||
| Stock after restocking: | 235 | 190 | 135 | 80 | fifteen | 30 | 35 | 40 | 35 | 30 |
| Factory Warehouse | ||||||||||
| Day | one | two | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Departures for replacement | 10 | 10 | 10 | 70 | 150 | 140 | 135 | 125 | 115 | 90 |
| Stock (initial stock 285) | 295 | 285 | 275 | 205 | 55 | -85 | -220 | -3. 4. 5 | -460 | -550 |
| Replacement Needs | 275 | 275 | ||||||||
| Stock after restocking: | 295 | 285 | 275 | 205 | 330 | 190 | 55 | 205 | 90 | 0 |
DRP: Martin's method
| Point 1 | ||||||||||
| Replacement space: 1 day | ||||||||||
| Day | one | two | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sales forecast | 10 | 10 | fifteen | fifteen | 17 | 17 | twenty | twenty | 30 | twenty |
| Stock (initial stock 59) | 49 | 39 | 24 | 9 | -8 | -25 | -Four. Five | -65 | -95 | -115 |
| Replacement Needs | fifty | fifty | fifty | |||||||
| Stock after restocking: | 49 | 39 | 74 | 59 | 42 | 75 | 55 | 35 | 55 | 35 |
| Point 2 | ||||||||||
| Replacement place: 2 days | ||||||||||
| Day | one | two | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sales forecast | fifteen | fifteen | twenty | twenty | 22 | 22 | 25 | 25 | 35 | 25 |
| Stock (initial stock 94) | 79 | 64 | 44 | 24 | two | -twenty | -Four. Five | -70 | -105 | -130 |
| Replacement Needs | 60 | 60 | 60 | |||||||
| Stock after restocking: | 79 | 64 | 44 | 84 | 62 | 40 | 75 | fifty | fifteen | fifty |
| Point 3 | ||||||||||
| Replacement place: 3 days | ||||||||||
| Day | one | two | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sales forecast | 7 | 7 | 12 | 12 | 14 | 14 | 17 | 17 | 27 | 17 |
| Stock (initial stock 37) | 30 | 2. 3 | eleven | -one | -fifteen | -29 | -46 | -63 | 90 | 107 |
| Replacement Needs | Four. Five | Four. Five | Four. Five | |||||||
| Stock after restocking: | 30 | 2. 3 | 56 | 44 | 30 | 51 | 44 | 27 | Four. Five | 28 |
| Point 4 | ||||||||||
| Replacement space: 1 day | ||||||||||
| Day | one | two | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sales forecast | fifty | Four. Five | 55 | 55 | 65 | 65 | 65 | 55 | 55 | 55 |
| Stock (initial stock 285) | 235 | 190 | 135 | 80 | fifteen | -fifty | -115 | -170 | -225 | -280 |
| Replacement Needs | 100 | 130 | 140 | |||||||
| Stock after restocking: | 235 | 190 | 135 | 180 | 115 | fifty | 115 | 60 | 5 | 90 |
| Factory Warehouse | ||||||||||
| Day | one | two | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Departures for replacement | 0 | 110 | 145 | 0 | 110 | 175 | 0 | 110 | 185 | 0 |
| Stock (initial stock 285) | 305 | 195 | fifty | fifty | -60 | -235 | -235 | -3. 4. 5 | -530 | -530 |
| Replacement Needs | 265 | 265 | ||||||||
| Stock after restocking: | 305 | 195 | fifty | fifty | 205 | 30 | 30 | 185 | 0 | 0 |
APPLICATION OF “DPR” TECHNIQUES
In order to develop the application examples of the DRP techniques indicated in the previous tables, a small simulation model has been developed (on a spreadsheet) that reflects in a simple way the relationships between demand at points of sale, transport and production and it allows us to appreciate the efficiency of the methodologies that, like the DRP, serve to optimize the relationships between such subsistence and elements of the logistics system.
The simulation model presents the same situation as the previous tables, although extending the analysis period and introducing economic data. Thirty-five reference time periods are considered, which in the example are thirty-five days (5 weeks), which could be weeks or months, depending on the planning period that needs to be considered. The numerical comparisons are made in the example considering only the three central weeks of the entire simulated period, to avoid distortions associated with the effect of the initial or final days.
In the proposed model, as in the previous examples, the replenishments of merchandise at points of sale # 1 and # 4 are assumed to take one day to be carried out, from the moment the replacement order is sent to the factory warehouse.. At point of sale # 2 the replacement period is two days and at point of sale # 3 it is three days.
Sales forecasts have been extended to thirty-five days at each of the four final destination points for the goods that make up the practical case. By adding these sales forecasts, the total expected sales are obtained that serve to establish the master production plan, certain hypotheses have also been established on storage costs and on transport costs, which can be varied in order to simulate new situations.
Regardless of whether, according to what has been said, various simulations can be addressed with the model, two examples are included below that provide the following limit situations:
CASE 1
It is the next to the Martin method. Replenishment at the points of sale is carried out by means of a single weekly shipment, to be received on Monday, calculated on the basis of the sales forecasts of the 5 weeks that have been considered. In turn, production is scheduled on the basis of weekly batches that are also sent to the factory warehouse on Mondays. Both at the points of sale and in the factory warehouse, a safety stock of 10 units is kept to attend to possible unforeseen events or emergencies. The following indicates the assumptions made regarding storage and transportation costs and the main results of the analysis. Other cost concepts are not considered to overcomplicate the model.
CASE 2
It is the closest to the Brown method. Replenishment at the points of sale is carried out daily, requesting the points of sale from the factory warehouse for each day the amount of merchandise that is expected to be sold on that day. Production is scheduled, on the other hand, based on daily batches of the same quantity, calculated on the basis of the sales forecasts for the 5 weeks that have been considered in the practical case. All other hypotheses are analogous to those established for the previous case. The table shows, in addition to the calculation hypotheses, the main results of the analysis.
It can be seen, comparing both cases, that the total stock corresponding to case 2 is 10% of the total stock of case 1, and that the logistics costs that have been reduced, also in case 2 with respect to case 1, by reducing the size of the shipment, but the costs of the stocks, much lower in case 2 than in case 1, largely make up for the difference.
Based on these results of the physical flow simulation, the great potential of the tools that facilitate the processes of relationship between the Physical Distribution and Production activities can be verified.
DYNAMIC SIMULATION OF REAPROVISIONING STRATEGIES
In the last exercise of the preceding section, dedicated to studying the integration of inventories in the logistics chain, the simulation of the two replenishment alternatives was already carried out. In the following tables a new approach to these tools (simulation techniques) is made, which are remarkably effective for decision-making in the matter of replenishment, but in this case a powerful and very suitable methodology for the case of the inventories, such as the Dynamic Simulation of Systems and the existing commercial software in this regard.
INTEGRATION OF INVENTORIES INTO THE LOGISTICS CHAIN
BASIC DATA OF THE EXAMPLE
Dynamic Simulation OF SYSTEMS
In 1961, Jay Forrester published the book «Industrial Dynamics», from this publication the dynamics of systems and the associated simulation techniques became part of the tools of the mathematical analysis of the company's problems.
Systems dynamics, the field in which the »Industrial Dynamics» proposed by Forrester is integrated, is the generalization of systematic analysis to real world problems, giving special relevance to the study of the relationships between the elements of systems and introducing in this analysis the differential characteristics that the real problems present with respect to the simplified or theoretical approaches.
Real processes are characterized, from the point of view of systemic analysis, by the following aspects:
- These are dynamic processes Relationships between elements are not always linear There are regulatory effects Processes are affected by delays
The dynamics of systems introduces these aspects in the analysis to be able to explain the behavior of the systems seeking a greater approximation to reality. Once the elements of the system have been identified and their relationships and attributes established on the basis of these plans, simulation techniques are applied that allow us to predict the behavior of the system in changing situations.
The basic importance given to temporal aspects in system dynamics makes this analysis an approximation to differential calculus. The dynamic evolution of the system is established in successive incremental periods of time (which, in practice, depending on the temporal scope of the analysis, we can associate minutes, hours, days, weeks, months or years), characterizing the system in each one. of the incremental periods of time by the "instantaneous" values that take in them a series of characteristic variables, or "state variables". These state variables can be associated with the «stock» type elements of a system, in accordance with the definitions that have been set forth at the time when describing the Logistics System. These aspects are discussed in greater detail later.
CHARACTERISTICS OF THE REAL PROCESSES
The real processes represent some differential characteristics with respect to the usual simplified or theoretical models that try to reproduce this reality. The characteristics are described below.
Dynamic Processes: time is a relevant variable of the process. The initial situation and the final situation of a certain period of analysis of the process influence the process itself or its continuation in the following period.
Non-Linearities: Relationships between elements cannot always be converted to linear relationships. Even some relationships cannot be expressed in the form of equations, but in the form of an empirical graph or numerical list.
Feedback (feed-back): There may be process variables that are affected over time by the values that the final result of the process takes, producing changes in its temporal development, which can lead to a situation of stability and instability.
Delays: The continuity of a process can be affected by the existence of temporary delays between its various phases, which can enhance situations of instability.
The system dynamics considers all the characteristics. Or, more precisely, if a system is not modeled giving absolute priority to the characteristics that have been described, we will not be using the System Dynamics methodology.
ELEMENTS OF A DYNAMIC SYSTEM
Until now we have classified the elements of the logistics system into three categories, which were very useful when modeling the system:
"Stock" elements
«Flow» type elements
"Process" type elements
If we now consider a dynamic system, this classification of elements continues to be valid, although some qualifications and redefinitions of them must be made, which we will address below.
- "Stock" type element: These are the fundamental elements for the person responsible for inventory management and also for the doctrine of Dynamic Simulation of Systems. Thus, in the specific terminology of system dynamics, the elements of the "stock" type are called "state variables" of the system. The values that these elements take are often called "Levels". The level of a state variable is the value that said variable takes at a given moment (in one of the time periods to which the dynamic situation extends).
-
- "Flow" type elements: They represent the variation over time of a state variable. The state variables are, therefore, accumulators or flow counters at a given moment. «Process» type elements: From the point of view of System Dynamics, these are combinations of stock flow, which are they add delays and other restrictions (such as capacity restrictions). These "process" type elements can be classified as follows:
- Continuous processes Discontinuous processes Waiting lines
- "Flow" type elements: They represent the variation over time of a state variable. The state variables are, therefore, accumulators or flow counters at a given moment. «Process» type elements: From the point of view of System Dynamics, these are combinations of stock flow, which are they add delays and other restrictions (such as capacity restrictions). These "process" type elements can be classified as follows:
Continuous processes: These are ordered accesses of flows that generate successive stocks also ordered (they cannot be mixed). There is a parameterized time lag (continuous process time) from when a flow accesses the process and becomes a stock until it leaves the continuous process again in the form of a flow of a different nature
(transforming the process).
Discontinuous processes: There is a capacity restriction in the process
(Capacity limitation) and an access restriction of other flows for the duration of the process. There is a parameterized time lag
(Discontinuous process time) from when the flow enters the process and becomes stock until it comes out of the discontinuous process again in the form of a flow of a different nature (the process transformed), then giving way to the next one.
Waiting lines: Orderly accumulation of Stocks waiting for another process (they cannot be mixed). There is a time lag
(Waiting time) from when the flow enters the waiting line and becomes stock until it leaves the waiting line again in the form of another flow of the same nature.
In addition to the Stocks, flows and processes, which are the fundamental elements, conceptually speaking, of a system, there are other auxiliary elements that are necessary to successfully approach the monetization of a dynamic system. Said auxiliary elements are described below.
-
-
- Auxiliary variables: They are quantities with a certain physical meaning in the real world and with an instantaneous response time, which operates on values of the fundamental elements of the system. Constants or parameters: System quantities that do not change in value over time. Conditions contour: These are variables outside the analyzed system, which represent actions of the environment on the system. There are two types of boundary conditions:
- Sources and sinks Exogenous variables
- Auxiliary variables: They are quantities with a certain physical meaning in the real world and with an instantaneous response time, which operates on values of the fundamental elements of the system. Constants or parameters: System quantities that do not change in value over time. Conditions contour: These are variables outside the analyzed system, which represent actions of the environment on the system. There are two types of boundary conditions:
-
Sources and Sinks: These are state variables (stock-type elements or, in other words, flow accumulators) outside the system, inexhaustible (not affected by the system), which contribute or withdraw flows from it.
Exogenous variables: They are auxiliary variables whose evolution is different from those of the rest of the system.
SYMBOLOGY
The following figure shows the symbology commonly used to present the fundamental and auxiliary elements until now, defining a dynamic system.
It is basically the symbology provided by Jay W. Forrester in his book "Industrial Dynamics", with some improvements introduced by various recently developed dynamic simulation programs on graphic support (such as the STELLA, I'THINK, POWERSIM and others).
The following figure shows, following the Forrester symbology, a dynamic model that represents the Continuous Replenishment method (with order point) previously described in point 4.4
The basic objective in this model, which is repeated on multiple occasions when replenishment strategies are modeled, is constituted by a stock-type element (I) that represents existing inventories, which vary over time, and by two flow-type elements, (E and S) that respectively represent the incoming and outgoing goods.
Other elements that appear in the model are auxiliary variables and parameters, as well as the source and sink of the goods (suppliers and customers respectively). One of the auxiliary variables represents the calculation of the order point (PP), which is based on the values of the inventory itself (I), and of the safety stock (SS). The latter is another variable to use, which is calculated based on the standard deviation of demand, (ds). This value, as well as the average demand (m) and the economic purchase lot (eoq), are parameters of the model.
The graphical representation indicated in the figure must be materialized in a series of equations that must be defined. The main part of the model is a differential equation that expresses the variation over time of inventories:
Other serious equations represent the inputs and outputs based on auxiliary variables and parameters, such as:
Finally, the equations that end the values of the auxiliary variables should be formulated, with expressions of the following type:
The formulation of these expressions, which in the text have been indicated simply in a symbolic way, is relatively simple knowing the "internal mechanics" of the process and having adequate software that allows the introduction of conditions such as "yes…" And random calculations. The exposition of the existing software in this regard will be the subject of the next section of this work.
Once all the equations have been formulated, a calculation method will be applied by finite increments, giving successive values to dt and concatenating the calculation of the variables that depend on each other. This process can be done using a simple spreadsheet, or using more sophisticated integration techniques, such as the Euler or Runge-Kutta methods. The results of the application of the dynamic model would be the evolution over time of each of the variables considered, which would allow us to make decisions by adjusting parameters or reformulating some expressions.
The model can be complicated as much as desired to more accurately represent reality or to obtain management indicators. For example, the economic purchase batch has been considered a model parameter, but it could also be an auxiliary variable dependent on other parameters, such as the cost of launching an order and the cost of storage. Likewise, we could have obtained an indicator of the cost of the inventory, adding in another auxiliary variable the accumulated costs of launching the orders that are being made and of storing existing inventories at all times.
System dynamics simulation software
Various commercial simulation programs developed specifically for dynamic system models are available on the market, such as the DYNAMO, POWERSIM, WITNESS, STELLA and I'THINK programs, among others. Its basic characteristics are described below.
The DYNAMO program, developed by Jay W. Forrester himself, from the moment the first digital computers were marketed, is the most classic in the field of dynamic simulation of systems, having served as a reference for other computer packages, in a similar way as does the IBM MPSX program, with respect to linear programming software. The vast majority of dynamic system models published in the specialized scientific literature up to about ten years ago have used the language of the DYNAMO program. However, since it is not a program that works in a Windows-type graphical environment, it has been losing positions in recent years to programs with friendlier interfaces such as those mentioned at the beginning.
The POWERSIM program is a package for personal computers developed by a Norwegian software company, powersim AS, to run on the windows platform and with similar characteristics to the I'THINK program, which will be described later, although reinforced. It is designed as a “business simulation” tool to create “dashboards” or “navigation charts” for business management. Its main areas of application are the following:
-
- Strategic planning Resource management Process reengineering
The latest version of the POWERSIM 2.5 program, incorporates multimedia features, object galleries and color effects to make presentations of a certain spectacular for users, not so advanced, for example those offered by the WITNESS program, but superior to relatively flat presentations of the I'THINK.
The price of the basic single license of powersim 2.5 is around $ 9,000.
The witness program is also a package for personal computers developed by the English company Lanner Group, which in turn was formed from AT&T Istel. It is a program aimed essentially at the dynamic simulation of industrial production processes, more restricted than the other packages described from the point of view of system dynamics, but equipped with multiple tools for its main function. It can model on the basis of these tools all kinds of activities related to fluids and has specific monetization elements for the oil industry, such as tanks, pipes, etc.
It has a great capacity for graphical visualization of the models and the simulation results, reaching characteristics of "dynamic visualization", with integrated animation, import with CAD and even virtual reality. For example, the layout of the simulated plant and the movements of personnel and goods in it can be represented.
This computational power and especially its great showmanship when it comes to presenting results, has as a counterpart a relatively high price compared to other software options. The price of the witnes basic individual license is around $ 30,000.
All the existing software, perhaps the best known and most widespread among the experts in dynamic system simulation are the stella and i'think packages, both developed by high performance systems inc. From New Hampshire, USA, a company founded by followers and students of Jay W. Forrester, the creator of systems dynamics, who at age 81 still teaches classes as emeritus professor at the Sloan School of Management at (MIT).
In reality, both stella and i'think are the same computer development although specifically prepared for different work environments. Thus, stella is designed for scientific and social science applications, while i'think is designed to support applications in the business environment.
Due to the very origins of its creation, i'think scrupulously respects the doctrine of system dynamics by Forrester, and its use as a simulation tool is mathematically justified. The resolution by the procedure of the finite increments of the differential equations that the models generate is based on the Euler and Runge-Kutta methods.
It is a program for personal computers, to run under the OS. Windows. The visualization of the models scrupulously follows the Forrester symbology described above, without aesthetic concessions such as those provided by the powersim and especially witnes programs. Thus, the model corresponding to the previous example case (Continuous replenishment model), if modeled with the help of the i'think program, would have the appearance indicated in the figure below.
The equations that reflect the relationships between elements are obtained with the help of i'think almost automatically, using monitoring systems. These equations will be shown after the following graph.
The latest version of the i'think 5.1.1 program incorporates some "friendly" graphical display of results of the "flight simulator" type and greater computing power.
Finally, other dynamic simulation programs on the market are simply cited, such as Taylor, Vensim, Simulink.
6.6 application of simulation techniques
In order to make the power of dynamic system simulation tools fairly clear, something that has already been advanced on a smaller scale with the exercise outlined in the previous pages, a more complex application example is now presented, which is modeled with the i'think program.
The example is as follows:
- A liquor manufacturer is going to start operations in a new location. It plans to sell 800,000 bottles per year. It will have a factory, with a warehouse in the corresponding factory, located at the production site and a warehouse located in the center of Your target market The bottles will be produced packed in packs of 3 units The packs will go in boxes at a rate of 36 packs per box, in three layers Primary transport between the factory warehouse and the distribution warehouse is carried out in full trucks that support 38 boxes Each one. Capillary distribution is carried out from the distribution warehouse with the necessary means of transport for each type of order from its customers. The problem that the manufacturer is considering at the moment is to size the factory and distribution warehouses. That is to say,estimate the maximum volume of Stocks that will need to be stored and the number of boxes storage cells that will need to be available so that there is no excess or lack of storage space Considering that both the factory and the distribution warehouse will be operational 250 days a year Consequently, the average demand will be 3,200 bottles per day, equivalent to 29 or 30 boxes per day. The production of bottles will adjust to this average demand, as the capacity of the primary transport trucks exceeds the daily production, and not every day will a truck go to load,estimates that the factory warehouse should accommodate at least the production of two trips (equivalent to 60 holes per box) and in the distribution warehouse it must have space for the unloading of a full truck and for unsold surpluses from the previous truck (that is, just under 50 holes per box), however. Do not trust this crude estimate, because just as production can be scheduled and adjusted quite a bit to the average demand of 3,200 bottles per day, the actual demand is random and can vary from day to day. Even production can have ups and downs due to material supply problems or labor problems. In principle, it considers that both production and real demand will have a normal distribution and will be approximately equal to the average demand, but with standard deviations of,respectively plus / minus 5% and 20% It is also concerned that trucks cannot have an exact arrival sequence, due to the difference between the truck's load capacity and production, which is not exactly predictable either. There will be trips in which there will be enough quantity to load a truck and others in which they cannot be filled, and you must notify the carrier not to go until the next day. Given these circumstances, the manufacturer has chosen to simulate the behavior of the two warehouses in the circumstances indicated, and size them according to the results obtained by the simulation of an adequate number of trips.Due to the difference between the load capacity of the trucks and the production, which is not exactly predictable either. There will be trips in which there will be enough quantity to load a truck and others in which they cannot be filled, and you must notify the carrier not to go until the next day. Given these circumstances, the manufacturer has chosen to simulate the behavior of the two warehouses in the circumstances indicated, and size them according to the results obtained by the simulation of an adequate number of trips.Due to the difference between the load capacity of the trucks and the production, which is not exactly predictable either. There will be trips in which there will be enough quantity to load a truck and others in which they cannot be filled, and you must notify the carrier not to go until the next day. Given these circumstances, the manufacturer has chosen to simulate the behavior of the two warehouses in the circumstances indicated, and size them according to the results obtained by the simulation of an adequate number of trips.The manufacturer has chosen to simulate the behavior of the two warehouses in the circumstances indicated, and to size them according to the results obtained by the simulation of an adequate number of visits.The manufacturer has chosen to simulate the behavior of the two warehouses in the circumstances indicated, and to size them according to the results obtained by the simulation of an adequate number of visits.
The simulation is carried out with the help of i'think, and the resulting model can be seen in the following figure on the next page.
In the upper line of the model, all the parameters (that is, the starting values) that will be used in the equations are located, these parameters are:
annual sales
annual working days
bottles per pack
pack per box
box per truck
production standard deviation
typical deviation of demand
The "core" of the model is made up of two stock-type elements, which measure the inventories (with the cash unit) located in the two warehouses that make up the logistics system. This stock is called:
warehouse manufactures
warehouse distribution
The stock-type elements feed each other with three flow-type elements, which represent the physical movements between the two warehouses, the inputs from production and the outputs to customers. These flows are called:
production
primary transport
demand
The model is completed with a series of auxiliary variables. In four of them intermediate calculations are carried out and are called:
dairy produce
daily demand
boxes entering the factory warehouse
boxes leaving the distribution warehouse
The other two auxiliary variables are the output data of the model for decision making, whose evolution over time can be visualized in the form of graphs or tables generated by the i'think program. These variables are called
vault holes in factory warehouse
box gaps in distribution warehouse
The equations that link these elements of the model, whose definition is monitored by the i'think program itself, can be seen in the following table.
The dynamic situation is carried out by the EULER method, in daily intervals during a period of one year, being able to observe for each one of the simulations the evolution of any of the variables included in the model throughout the mentioned year. You can perform as many simulations as you wish to obtain conclusions from the analysis.
- bibliography:
- "LOGISTICS MANAGEMENT TRAINING PROGRAM" School of Industrial Organization, Madrid - Spain. Gonzalo alvares lastra. "LOGISTICA EMPRESARIAL" boixereu editores, 1989 Eduardo a. Arbones malisani «STOCK MANAGEMENT» R. Laumaille »Well Done in America» Peter C. McGraw-Hill, 1991
