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]]>Any row which is concerned with only partial fulfilment of a purchase order is weighted accordingly.
For each row, for the purpose of testing the null hypothesis that the dates are correct, I assumed a lognormal distribution of supplier lead times, an example of which is shown in the following graph:
The estimation of the natural logarithms of the mean and standard deviation of the lead times was done separately for each row using all rows except the one concerned. That was necessary in order to prevent outliers or multi-modal lead time distributions from severely adversely affecting the hypothesis testing. Another thing which I did for the same reasons was to base the estimate of the standard deviation of the logarithms of the lead times on mean absolute deviation (MAD) because of its robustness.
Cells L4 and Q5 were calculated using the fact that the variance of the sum of independently and identically distributed random variables is equal to the sum of the variances of the individual variables. For manually set mean supplier lead times, it is assumed that the amount of historical data used in setting them is the same as in the spreadsheet.
The testing which I have done appears to show that the techniques which I have used are effective at ensuring that suspect lead times are flagged, either immediately or after the initially flagged rows are checked and corrected.
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]]>Transaction history held in your computer could be used for the lead time analysis if it is sufficiently reliable. Unfortunately, in most companies, it is not. Many ERP systems do not keep records of order dates and do not match up goods received with the purchase orders. It is essential for the records of order dates to be reliable if they are to be used for lead time calculations. Unless the dates of order placement and of receipt into store are reliable, I suggest that sample data be used. The sample should be small enough to enable it to be checked. Use of a small amount of reliable data is better than use of a large amount of unreliable data.
For the above-mentioned reasons, a spreadsheet analysis is appropriate. I have developed a spreadsheet for this purpose. There are four versions. The appropriate version should be downloaded by clicking on the appropriate link below. When the spreadsheet appears, click on the three dots near the top right hand corner and then click on “Download”. You will probably find that an “Enable editing” button appears, in which case, click on it.
Open document format with UK dates
Open document format with US dates
Excel 97 format with UK dates
Excel 97 format with US dates
These were updated on 19 February 2017.
Almost all modern spreadsheet software should be able to handle the open document format versions. It is recommended that you use that version unless you are using a pre-2013 version of Microsoft Excel, in which case, it is recommended that you use an Excel 97 version of the spreadsheet. All of the spreadsheets were developed using Libre Office.
The yellow cells are where you can enter data. The spreadsheet calculations cannot work with fewer than three rows of data. Some cells will show errors until three rows have been entered. The supplier (Cell B3) is just for your information. The item code (product code) can be entered in Columns A and B respectively for your information. Enter the order date and date received in Columns C and D respectively. It is important for these dates to be correct. In Column F, enter the quantity received in the shipment concerned. There is no need to enter the “order quantity” (Column E) if it is the same as the quantity received.
The “Comment” column (Column I) indicates action which needs to be taken.
The “rejection confidence” (Column H) is an estimate of the confidence with which it can be said that the row concerned contains an incorrect date. If it is greater than 90% then the dates in that row should be checked thoroughly. This situation is indicated by the word “Check” in the “Comment” column (Column I). The most important things to check are that
Use Column J (“Checked”) to indicate that the data in the row concerned has been checked thoroughly. Any corrections which you make will result in recalculation of all of the rejection confidences. As a result, some more rows might need to be checked. For that reason, it is important for you to use the “Checked” column (Column J) so that you know which rows have already been checked.
The results of the analysis are shown at the top of Columns K to Q. The spreadsheet is concerned with the supplier lead times (i.e. from order placement until receipt) which are only one component of the lead time. The lead time starts when the inventory position of the item concerned falls below the reorder point and ends when the replenishment stock is available for picking. The coefficient of variation is the standard deviation of the supplier lead times divided by the mean supplier lead time. However, when setting safety stocks, it is the standard deviation of the errors in forecasting lead times which should be used. This is higher than the standard deviation of the lead times. Consequently, the number in Cell L5 or Q5 should be used instead of the coefficient of variation in practice. The number in Cell Q5 is for use in relation to items for which the mean lead time has been set manually rather than using the mean supplier lead time in Cell L1. If less historical data is used in manual setting of a lead time than the amount of data in the spreadsheet then the number in Cell Q5 will be lower than it should be. When using the online Monte Carlo simulator which is accessed by means of the “Simulator” tab in the menu, the number in Cell L5 or Q5 as appropriate should be entered in place of the coefficient of variation.
Part 2 of this article will contain information concerning the mathematics involved in the spreadsheet and is intended for readers who have some knowledge of statistical mathematics.
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]]>The post Principles of Good Inventory Management appeared first on Inventory Management Advice.
]]>In order to reduce investment in inventory and improve the service level, there are a number of things which need to be looked at. Initially, it is better to tackle all of the important ones to some extent than to just concentrate on a few of them. More work can then be done in those areas which will lead to further cost-effective improvement. Things which will result in improvement include the following:
I will now elaborate on several of the above.
1. Ensure that the data used for inventory management purposes is accurate and up to date.
The reasons for this are obvious. However, achieving this objective in a cost-effective manner is far from being simple. See the article entitled “Data Accuracy“.
2. Ensure that the computer provides adequate and appropriate exception reporting.
Whenever, for any reason, action needs to be taken, that fact should be brought to someone’s attention promptly, thereby facilitating prompt appropriate action. However, too many false alarms can greatly reduce the benefits of exception reports.
3. Ensure that any problems are identified and dealt with when they occur.
This can be greatly facilitated by good exception reporting (See “2” above). The exception reporting needs to be prompt and acted upon promptly. Adequate monitoring of indicators of overall inventory system performance should also be carried out. Such indicators include total inventory value, total value of orders on suppliers and customer service level. The reasons for any unexpected changes in any of these should be investigated thoroughly.
4 Reduce the average effective lead time.
The lead time is the time taken to obtain replenishment supplies. It effectively starts when the item should be ordered. It effectively ends when the replenishment supplies are available for issue. The greater the lead time, the greater are the errors in forecasts of lead time demands and, consequently, the required amount of safety stock. The risks of being left with obsolete stock and of deterioration are also affected. See the articles entitled “Reducing Lead Times“, “Reducing Reorder Review Periods” and “Reducing Ordering Delays“.
5. Reduce the amount of variation in lead times.
Uncertainty in future lead times contributes to the uncertainty in the lead time demand and, consequently, to the required safety stock.
6. Improve the forecasting of lead times.
Part of each reorder point is the forecast lead time demand. In order to forecast that, one of the requirements is a forecast of the lead time. Averaging recent lead times is helpful in this regard. However, if for any reason, future lead times are likely to differ from those in the past, this needs to be taken into account. If there have been few purchases of the item from the supplier then the past lead times are likely to be of little use. For that reason, the historical lead times of all items obtained from the same supplier might provide useful information. As in any forecasting, it is better to forecast the distribution of future lead times rather than producing a forecast as a single number. For example, if, on average, the lead time for an item is 15 days but it is longer than 40 days on 10% of occasions, that information is useful. Unfortunately, what can be done in this regard is probably limited by data availability.
7. Use the supplier as the stockist when appropriate.
This benefit of this in terms of your investment in inventory is obvious.
8. Improve the forecasting of demands.
If the demands are, to some extent, predictable then you should be able to achieve a very high turnover ratio (i.e. a small amount of inventory in relation to sales). If the demands are unpredictable, as is usually the case, then they should be forecast as accurately as possible given the information available. Demand history, market knowledge and market indicators should all be used as appropriate. Good results can, as a general rule, only be achieved by choosing a forecasting technique on the basis of the peculiarities of your own company. Use of whatever forecasting technique is supplied with your inventory software will not usually produce good results, even if it is an adaptive technique (such as focus forecasting). As with lead time forecasting (See “6” above), it is helpful to produce each forecast as a distribution rather than a single number. In relation to forecasting of demands, see the articles entitled “Evaluating Forecasting Algorithms” and “Demand Rate Estimation“.
9. Do not aim at providing the same service level for all items.
This is usually a major source of potential improvement. The cost of providing good service is not the same for all items. Also, the effects of shortages are more serious for some items than for others.
10. Setting of safety stocks
Safety stock is the stock which is held in case of higher than expected demand and/or a longer than expected lead time. Appropriate setting of safety stocks is the main, but not the only, means by which the service levels are controlled. Improving the manner in which they are set is usually a major source of potential improvement.
11. When setting order quantities, take into account the risks of obsolescence and deterioration.
For some types of items, this is particularly important. Large order quantities can result in stock being on the shelves for a long time. This can be a problem for perishable items. Also, if an item becomes obsolete, there could be a substantial amount of “dead” stock as a result. One of the shortcomings of the classical “economic order quantity” formula is that it does not take these problems into account.
12. When considering cost saving measures such as quantity discounts and consolidation of orders, take into account the effects on the investment in inventory.
Such cost saving measures are often very tempting. They should only be used after a realistic analysis of both the short and long term effects on your inventory levels.
No mention has been made so far in this article about distribution through multiple stores. Achieving near optimal inventory management under these circumstances is far more complex than in a single store operation. However, the principles mentioned above can be extended to multiple store operations. In a multiple store operation, several of them are often even more relevant. For example, if a store normally obtains an item directly from the supplier, then the most appropriate method of obtaining the item in an emergency might be to obtain it from another store.
Inventory management improvement should be tackled on many fronts. That will usually produce much better results than concentrating on just a few improvements. An exception is if those improvements have been identified as the ones which will have the greatest effects.
It should now be apparent that good inventory management is far from being simple and that there are many inter-related things to be considered.
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]]>Click here to obtain a copy in Open Document Format. That is a standard format which can be read using almost all modern spreadsheet software. If you are using a pre-2013 version of Microsoft Office then click here instead to obtain an Excel 97 version of the spreadsheet. That version has not been tested as thoroughly as the Open Document Format version.
You cannot use the spreadsheet online so you will need to download a copy. To do so, click on the icon with three dots near top right hand corner of the browser window and then click “Download”.
If you encounter any problems then please contact me and let me know what spreadsheet software you are using. You are least likely to encounter problems if you use Libre Office which is a free download.
The yellow cells are the cells in which you can enter data.
Cell E4 should contain the number of the forecasting algorithm which is to be used. At present it should contain 1 which is exponential smoothing. The Croston, Croston Median and Holt-Winters algorithms are to be added later.
In Cell E5, enter the desired smoothing constant for exponential smoothing. The smoothing constant is the weighting to be given to the most recent period’s demand and should be between 0 and 1.
In Cell E6, enter the lead time in periods starting from when the order is sent to the supplier. It must be 1 or 2 or 3 or 4 or 5 because of the limitations of spreadsheets. The length of a period can be anything you like (e.g. month or week or day). At the beginning of each period, if the inventory position is strictly less than the reorder point then an order is sent to the supplier to increase the inventory position to the “maximum” level. The inventory position is the quantity on hand minus the quantity on customer back order plus the quantity on supplier order. The lead time is treated as being deterministic (fixed). If you want to use stochastic (varying) lead times then you will need to use the online simulator.
In Cell E7, enter the reorder point expressed as a number of periods supply,
In Cell E8, enter the “maximum” level expressed as a number of periods supply. It should not be less than the entry in cell E7.
In Cell E9, enter the mean demand per period to be used when the spreadsheet is used to carry out Monte Carlo simulations.
If no entries are made in Column C, Monte Carlo simulations will be carried out. Changing the contents of a yellow cell or re-entering what is already there will result in a new Monte Carlo simulation. If you want simulations to be carried out using your own demand history, enter that history in the yellow cells in Column C, starting from the oldest period. Deleting Cell C12 will result in a return to Monte Carlo simulation. The Monte Carlo simulation of demands is carried out in the same manner as in the online simulator.
In Cell D12, enter the assumed initial estimate of the mean demand per period.
In Cell E12, enter the assumed starting inventory level (stock on hand minus the quantity on customer back order).
Columns E to J show the situation at the beginning of each period.
The estimated mean demand per period is updated, using exponential smoothing, at the end of each period
The results of the simulation are shown in the two graphs and in cells L5 to P6.
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]]>The simulations are carried out on a daily basis and continue until there have been at least 1000 customer demands.
In the event of a shortage, customer backordering takes place. I intend to allow for lost sales at a later date.
The daily customer demands are assumed to be independent and identically distributed negative binomial random variates. That type of distribution is a realistic one for modeling daily demands. It is a type of stuttering Poisson distribution. In other words, the daily number of customer requests is treated as having a Poisson distribution and the quantity requested by each customer can vary. The Poisson distribution is a special case. For items which move fairly fast, the negative binomial distribution can be approximated by a gamma distribution. For very fast moving items, it can be approximated by a normal distribution.
The figure below shows the probability function of a negative distribution with a mean of 1 and a standard deviation (a measure of spread) of 1.8. It is typical of the probability function of the single period demand of an item for which the mean demand per period is 1.
The figure below shows the probability function of a negative distribution with a mean of 1 and a standard deviation of 5.3. It is typical of the probability function of the single period demand of an item for which the mean demand per period is 6.
From the above two graphs, it can be seen that the normal distribution is not suitable as a model of demands for slow moving items. Customer demands distributions are skewed and negative demands would not normally occur.
The standard deviation of daily demands is modeled using the equation
\[\sigma=a\mu^b\]
where is the mean daily demand and a and b are constants. This model performs remarkably well in practice. That is, perhaps, not too surprising considering that the standard deviation of a Poisson distribution is the square root of the mean and that daily customer demands tend to have higher standard deviations than for a Poisson distribution. The reasons for being higher are that some customers might request quantities of greater than one and sometimes customers might arrive in groups.
Supplier lead times in days are also assumed to be independent and identically distributed negative binomial random variates.
Reordering takes place at any reorder review at which the inventory position is less than the reorder point. The quantity ordered is then that which is required to increase the inventory position to the “maximum”.
Measurement of the service level and the mean stock on hand in days supply takes place after the simulation has had time to settle down.
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]]>Each simulation is carried out for each day until there have been at least 1000 customer demands. Consequently, if an item is only sold about once per year then the simulation is for about 1000 years. I tried such a simulation using an eight year old laptop and it took a few milliseconds.
I developed the simulator because inventory management theory which is in widespread use involves theoretical assumptions which have limited applicability to the real world. The three main problems in that regard which are overcome by the simulator are as follows:
Part 2 gives detailed information concerning how the simulator works.
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]]>The post Inventory Management Simulation appeared first on Inventory Management Advice.
]]>If you want to use a particular algorithm for demand forecasting or reordering then it is desirable to simulate the effects first in order to avoid unpleasant surprises.
A useful starting point is to use a spreadsheet to gain a qualitative insight into the behaviour of the algorithms to be used. I intend to provide a spreadsheet for this purpose when I write articles on specific forecasting and reordering techniques. You can enter the demand history for an item into the spreadsheet to see the effects of an algorithm in relation to that item. It is helpful for the spreadsheet to contain graphs showing demand forecasts and inventory levels. I suggest that the spreadsheet be used for a number of items including both fast and infrequently moving ones. You might also like to try hypothetical demand histories to see how the algorithm would behave with particular types of demand patterns. A variety of different values of the algorithm parameters should be tried. What I have described so far is reasonably easy to do in a spreadsheet. However, taking variability of lead times into account in a spreadsheet is relatively difficult.
Ideally, the algorithm should be tested on your entire inventory. The computer program to be used for this purpose should provide the average overall inventory value and the overall service level for the new algorithm. It should also be used to ascertain the effects of continuing to use the current algorithm. The necessary programming is quite involved and would require a substantial amount of work. Also, the program would need to be modified for every algorithm to be tested. I might do such programming for some algorithms when time permits. After running the program, you should compare
the computer predicted overall average service level and average total inventory value if the new algorithm and its proposed parameters are used,
ditto for the current algorithm and its parameters and
the current actual overall service level and total inventory value.
The need for the above-mentioned programming can be avoided by means of stratified sampling. I suggest that the stratified samples consist of the items at the top of Category A (the items with the highest annual sales values) and a random sample of each of the following:
the remaining Category A items.
Category B and
Category C.
Extrapolation from the stratified sample will give an indication of the overall effects. If you would like me to produce an online calculator to carry out the extrapolation, please leave a comment to that effect. The stratified sample can be analysed using either the above-mentiored spreadsheet or Monte Carlo simulation (described below). If the spreadsheet is used then it will need to show the service level and final or average inventory level for the item concerned. Using a spreadsheet for these purposes will produce highly inaccurate service level predictions for individual items. However, application to the stratified sample will, to a large extent, smooth out the effects of those inaccuracies. If the spreadsheet is used then there would still probably be the problem of variation in lead times not being taken into account.
Monte Carlo simulation of inventory management involves
development of a statistical model for customer demands,
development of a statistical model for lead times,
random sampling from the statistical distributions and
use of those random samples by the computer to estimate the effects of forecasting and reordering algorithms and their parameters.
Monte Carlo simulation is particularly useful in relation to inventory management scenarios which are not adequately catered for by existing inventory management theory. That includes most real life inventory management! For example, lead time demand is usually assumed to have a normal distribution. That is highly inappropriate for infrequently moving items. If the reorder review period is not small in comparison with the lead time then inventory management theory becomes complicated. Also, setting of safety stocks is usually done on the basis of a target probability of not encountering a shortage during a particular order cycle. This often differs greatly from what most people consider “service level” to mean, i.e. the percentage of customer demand which is satisfied immediately. As a result of these problems, highly inaccurate approximations tend to be used in practice.
Use of Monte Carlo simulation rather than a spreadsheet with the above-mentioned stratified sample avoids the need to enter demand histories. Also, it is easier to cater for variable lead times than would be the case with a spreadsheet.
I am currently developing an online Monte Carlo inventory management simulator and I expect it to be available for use fairly soon.
Parts of this article will be dealt with in greater detail in subsequent articles.
If you need help with application of the techniques mentioned in this article, please feel free to contact me.
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]]>The lead time for an item starts when the item should be ordered, not when the order is sent to the supplier. To find out the effect on the required investment in inventory of that time difference, see the table in the article entitled “Reducing Lead Times”.
If a periodic review replenishment system is used then the reorder review period should be reduced as much as possible because ordering will be delayed until the next reorder review. See the article entitled “Reducing Reorder Review Periods” in that regard.
If reordering decisions are based on out of date information then the age of that information forms part of the lead time. If periodic, rather than continuous, review is used for reordering then the computer’s reordering recommendations should be produced immediately before the purchasing officer is ready to review those recommendations.
The purchasing officer should review those recommendations as quickly as is possible while exercising due care. If it is found necessary to examine demand history for that purpose then consideration should be given to replacement of the algorithm used to forecast demands. It should not be necessary to review the appropriateness of the computer’s reordering recommendations on the basis of data held in the computer. If it is then the appropriateness of the reordering algorithms should be looked at. It should only be necessary to examine the computer’s recommendations on the basis of information which is not held in the computer (e.g. market knowledge). Time spent examining data held in the computer forms part of the lead time and, consequently, adversely affects the overall service level and/or investment in stock.
Approval of the resulting proposed order should be carried out as soon as possible after the purchasing officer has finalised it. That approval must not be delayed. There must always be someone available to attend to the task promptly. For that reason, there should be more than one person who can approve orders. Approval should never be delayed by absences, workload or other commitments. The approval process contributes to the lead time and, consequently, to the investment in inventory required to provide the desired overall service level. The longest approval time, rather than the average, is what has the greatest effect on the overall service level and/or investment in inventory. People responsible for approving orders should be made aware of the effects of delays. See the table in the article entitled “Reducing Lead Times” in that regard.
One simple method of facilitating rapid approval of orders is for the computer’s reordering recommendations to show the value of the recommended order quantity for each item for which reordering is recommended. It is also helpful for the total cost of the recommended order to be shown. If the review of the computer’s reordering recommendations is carried out using a spreadsheet then a column could be added showing the cost, for each item, of the order quantity proposed by the purchasing officer. The total of the costs in that column should also be shown.
Ideally, people responsible for approving orders should approve the maximum level for each item rather than approving individual orders. Under those circumstances, the approval process does not form part of the lead time. This could be done progressively. After an order has been approved, the new inventory position of an item could be regarded as the approved maximum level for that item. Such approval could be for a specified period of time or until there is a substantial change in the demand rate. Appropriate exception reporting (including reporting of substantial demand rate changes) by the computer would be helpful.
Consideration should be given to not requiring approval for items for which the value of the quantity to be ordered is small.
If management has sufficient confidence in the decisions of a purchasing officer then, instead of approving each order, spot checking of the purchasing officer’s decisions could be carried out retrospectively. That does not delay ordering and, consequently, the time taken for the spot checking would not form part of the lead time.
This should be done as soon as possible after the order has been approved. In order to facilitate this, it is desirable for the computer’s reordering recommendations to be held in the computer as a tentative order. Then only the changes to the tentative order need to be entered into the computer. Also, any subsequent computer recommended orders can take into account the tentative order. If a decision is made not to proceed with a tentative order then it must be deleted immediately. Failure to do so will probably result in serious shortages.
In order to provide a high overall service level and minimise the investment in inventory required to achieve it, it is important to send orders to suppliers as soon as possible after the inventory positions of the items concerned fall below their reorder points. All delays in the process should be minimised. The data used for reordering purposes should be up to date.
If you need help with implementation of anything suggested in this article, feel free to contact me.
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]]>The post What is Optimal Replenishment? appeared first on Inventory Management Advice.
]]>Claims that particular software packages provide optimal inventory management are commonplace. Such claims, by themselves, are meaningless. They only become meaningful if there is a full description of the theoretical assumptions involved and of the objective function (whatever is to be minimised or maximised).
Total cost is the objective function which is used most often. It can be used in relation to a single item or the overall inventory. It should be the total of all relevant costs which includes, at least
How close reordering is to optimal is probably limited by the least accurate of the types of costs involved. The main exceptions are that if neither deterioration nor obsolescence are major problems then inaccuracies in the costs related to them might not matter much.
Let’s look at those costs individually:
This is often expressed as a percentage, per annum, of the cost price. One of components is the opportunity cost of capital. This is often more that the interest rate minus the inflation rate, especially if there are difficulties raising more capital or if money is needed for other purposes or if there is a desire to reduce debt.
Each item needs storage space and, hence, contributes to the warehouse rental cost or the opportunity cost of the warehouse space involved which could, perhaps, be used for other purposes. Some items are more bulky than others and, consequently, treating the holding cost as a percentage, per annum, of the cost price is not always appropriate.
There is the cost of insurance of the inventory and of the warehouse. It might be appropriate to treat the insurance of the inventory as a percentage, per annum, of the cost of the inventory. The same does not apply to the insurance of the warehouse because bulky items have more effect on the required warehouse size than is the case for less bulky items. If there are dangerous goods then the insurance cost is affected simply by the fact that there are dangerous goods in the warehouse. The resulting effect on insurance premiums should be attributed to the dangerous items alone.
The fact that every item stocked needs to be counted from time to time is a cost which can probably, reasonably, be looked upon as a cost per item per annum.
The holding costs mentioned above are, perhaps, the main ones but not the only ones.
Holding costs are commonly treated as a percentage of cost price per annum in spite of the fact that doing so is not completely appropriate.
This is often treated as being the same for each order placed regardless of whether or not it is the same for all items at all times. If an order is being prepared to send to a supplier for a number of items then the ordering cost per item ordered might be lower than if an order is to be placed for only one item.
If there is a quantity discount then first find the optimal order quantity without the discount being taken into account. If the resulting order quantity is less than that required for the discount, re-optimise with the order quantity set equal to that required for the discount and with the ordering cost reduced by the discount for that quantity. Compare the value of the objective function with the value obtained previously to ascertain whether or not the quantity discount should be taken advantage of.
You might be thinking that you can’t ascertain accurately what the shortage costs are and that is likely to be correct to some extent. If the shortage cost is the least accurate then that is the cost which should have the most attention. Whenever you aim for a particular service level for a particular item, that indicates that you have some idea of the cost of shortages.
Most of the theoretical work in relation to inventory management which I have seen assumes that the shortage cost is a cost per unit short per day and that quantities which cannot be supplied to customers immediately are backordered. Under these circumstances, if the holding cost per unit per day is h then the shortage cost per unit per day (s) and service level (l) are connected using the following two formulae which are equivalent to each other:
\[l=\frac{s}{s+h}\]
\[s=\frac{hl}{1-l}\]
For example, suppose that the cost of an item is $300, and the holding cost is 18% per annum.
\[h=\frac{0.18\times300}{365}=$0.148\text{ per unit per day}\]
The shortage cost per unit per day which corresponds to a service level of 90% is given by
\[s=\frac{0.148\times0.9}{1-0.9}=$1.33\text{ per unit per day}\]
The service level which corresponds to a shortage cost of $1.33 per unit per day is given by
\[l=\frac{1.33}{1.33+0.148}=0.9=90\text{%}\]
Treating the shortage cost as a cost per unit short per day that the customer has to wait might be reasonably appropriate for a distributor. It is certainly not appropriate for a retailer because shortages usually result in lost sales. In the case of a retailer, the profit margin is a better indication of the shortage cost. That will vary from item to item. Treating it as a percentage of the cost price might be appropriate in some cases. However, inexpensive items are likely to have a higher percentage mark up than expensive items. Shortages affect the reputation of a company. Unfortunately, it is difficult to quantify the financial value of reputation.
This is the cost of an item multiplied by the probability that it will not be sold before its expiry date.
This is the expected cost resulting from an item not being sold before it becomes obsolete. This is usually difficult to model although history of items becoming obsolete provides an indication of the magnitude of this cost.
Profit can be used as an objective function. All of the costs mentioned above should be taken into account except that, instead of forfeiture of gross margin being treated as a component of shortage costs, the gross margin on sales should be treated as a profit.
Overall service level and total inventory value are often used as indicators of inventory management performance. However, the overall service level which can be achieved with a given investment in inventory or the investment in inventory required to achieve a given overall service level are not suitable for use as objective functions. Optimising on this basis would result in a small total inventory value in relation to the overall service level provided but the profitability could be adversely affected. To illustrate, on this basis, a car dealer would stock spark plugs but not cars. The reason for this not being appropriate is that the profit on the sale of a car is far greater than the profit on the sale of a spark plug.
The usefulness of the results of any optimisation depends of the validity of the theoretical assumptions involved.
The classical EOQ formula is
\[\text{EOQ}=\sqrt{\frac{2DK}{h}}\]
where
D = demand per annum,
K = cost of placing an order and
h = annual holding cost.
It is obtained by minimising the total of the ordering and holding costs in a continuous review system. Those are only two of the five costs mentioned above. It does not take into account
The demand rate is assumed to be constant forever.
As mentioned above, it is assumed that a continuous review system is used. If a periodic review system is used then the order quantity should depend on the quantities on hand, on supplier order and on customer backorder.
Do not be fooled by claims of optimality unless the assumptions involved and the objective function are stated. If they are stated then ascertain the applicability of the assumptions to your company and check to see that all of the relevant costs have been taken into account..
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]]>Reordering takes place when the net quantity falls strictly below a level known as the reorder point (ROP). Notice that reordering does not take place when the net quantity is equal to the reorder point. The reason for this is that it is desirable for a reorder point of zero to indicate that the item should not be stocked and should only be ordered when a customers wants it (i.e. when the net quantity is negative).
When an item is reordered, the amount ordered should be such as to increase the net quantity to a level which is referred to as the “maximum” (MAX) or, more descriptively, as the “order-up-to level”.
In Fig.1 below, the reorder point is 31 and the “maximum” level is 50. Items are looked at for possible ordering every day; in other words, the reorder review period is one day. The remainder of the lead time (the time from when the item should be reordered until replenishment) is 30 days. One unit is demanded by customers every day. The letters “H”, “S” and “B” stand for the quantities on hand, on supplier order and on customer back order respectively. Note that H-B+S (orange) is the “net quantity” and that the difference in height between the orange and blue is the quantity on supplier order.
“H”, “S” and “B” are all treated as being zero initially; hence the customer back orders prior to the arrival of the first shipment.
Note that the reorder point is set to the demand during the lead time which includes the remainder of the reorder review period. Careful examination of the graph will show that there is a shortage of one unit just before each replenishment arrives. This is because the item is not ordered until the next reorder review after the net quantity falls below the reorder point. In this case, the actual lead time can be as much as 31 days consisting of the supplier lead time (30 days) plus the reorder review period (1 day).
Notice that, because of the fact that reordering takes place when the net quantity is 30 (one less than the reorder point), each order quantity is the “maximum” (50) minus the net quantity (30) which gives 20.
There are two aspects of this simulation which are unrealistic. The main one is that demand patterns are rarely as stable as indicated above. In the following graph (Fig.2), everything, including the average daily demand, is the same as in the graph above except that the demand pattern is realistic.
Notice the shortages (when the blue curve is below the axis). For this reason, the reorder point needs to be greater than the forecast demand during the reorder review period plus the lead time. The extra amount is known as the “safety stock”. It is the amount of stock which would exist just before replenishment if the demand was perfectly stable.
In practice, there would also be variation in the lead time. This variation increases the amount of safety stock required.
The average order quantity is MAX – ROP + 1 plus the average demand during half the reorder review period.
Unless an item has frequent shortages, its average stock is approximately the safety stock plus half the average order quantity minus half the average demand during the reorder review period.
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