Dimensioning methods for reducing
capital in safety stock
Evaluation of dimensioning methods and improvement of practical use
Erik Björling Emil Pålsson
Faculty of Engineering at Lund University The Department of Industrial Management and Logistics
Division of Production Management
By taking a holistic view of the entire inventory, and let articles differentiate in achieved order line service to reach a total shared service level towards costumers, there is a huge potential to reduce the capital tied up in safety stock. By using average cost per order line instead of dimensioning with Serv2 the study shows that for real company cases there are possibilities to reduce the capital tied up in safety stock with up to 45 percentages, for an order line service of 97 percentages. Even when using a general safety time, which is very easy to use and understand, there is a huge potential to reduce tied up capital compared to Serv2. When comparing the methods with respect to parameter values and achieved order line service the results differ. The statistical dimensioning method Serv2 is the best method to estimate achieved order line service compare to other dimensioning methods. By using Serv2-methodology, the accuracy in beforehand estimation in achieved order line service for the other dimensioning methods will increase.
Background
Lack of space, obsolescence and capital tied up in stock are all issues related to today's warehouse complexity of problems to store products. The main problem for companies is to minimize the capital tied up in stock to fulfill a specified service to its
customers.
In a research paper published in autumn 2011 (Mattsson, 2011a) the author claimed that by using time as a parameter for the design of safety stock instead of statistical service methods, the capital could be reduced while maintaining the same service levels towards customers.
PipeChain is a company that develops and distributes software for supply chain management, integration and communication. PipeChain uses the dimension parameter unit time to set stock levels and to control their system. Today there are no rules for initially set the safety stock levels in their new software
PipeChain View. Instead the experience and understanding about the industries are applied.
Objective
The objective of the study is to evaluate different methods for dimensioning safety stock with respect
to capital tied in safety stock and develop methods for improving practical usability.
Method for evaluating various methods
for dimensioning safety stock
As the study is based on real historical order data collected from different companies and industries in Sweden, the main part is to develop a simulation program that reflect those transactions.
Simulation and calculation has been processed in the calculation program Matlab.
All data that is included in the study is
processed with the same procedure, shown in figure to the right. All data is processed and filtered before simulated and evaluated.
Data is processed and filtered to minimize the impact of errors and orders that should not be supported from stock. The filtration methods are both manual and statistical. The manual method will remove obvious errors at item and order basis. The statistical method removes orders that deviates a certain bases at item level. In the statistical method the average and multiple of standard deviation at day and order basis for each item is used.
The five dimensioning methods that have been
evaluated in the study are safety time, two versions of shortage cost and the two most common statistical methods used in the industry, Serv1 and Serv2. The shortage costs are based on shortage of a unit and a complete order line.
All dimensioning methods except safety time is the lead time demand assumed to be normal distributed, based on the article (Mattsson, 2011b) and are dimensioned through Axsäters equations in his publication Inventory control (Axsäter, 2006). Safety time is set as a general time for a complete system in fraction of days.
The simulation results are evaluated according to the figure below, where all dimensioning methods have to obtain the same order line service (OLS) level at 97 percentages.
The simulated system needs to be stable and not influenced by the initial inventory levels that must be added to the system at start up. Therefore it is required to simulate over a period which contains sufficient storage cycles to give reliable results with respect to levels of service.
Result and analysis
The results from the simulations for company case 1-5 shows that shortage cost per order line outperforms all other methods when comparing capital for 97% order line service, see below. The table shows the percentage above min cost from each simulation.
Sim Serv1 Serv2 Safety Time Shortage cost (unit) Shortage cost (order line) 1 8% 14% 6% 20% 0% 2 34% 74% 34% 48% 0% 3 62% 81% 43% 0% 0% 4 5% 8% 6% 9% 0% 5 4% 5% 38% 0% 7%
Among the other dimensioning methods safety time perform better than the statistical methods in three out of five cases.
The difference in tied up capital between the methods depends on differentiation of service levels between products. For some products achieving 97% service level is quite expensive because of high volatility and high product value.
The statistical methods do not take those factors into account when dimensioning and aim for equal service levels for all products. When using safety time, it dimensions a higher service level for products with short lead time and low volatility.
Shortage cost methods work similar to the statistical methods, but also take the product value into account. The methods differentiate service levels between the products with respect to product value. When using shortage cost methods, products with low product value achieve a higher service level than products with higher value.
Sim Serv1 Serv2 Safety Time Shortage cost (unit) Shortage cost (order line) 1 97,0% 99,4% 5,70 32 000 180 000 2 50,0% 96,7% 0,20 900 2 000 3 61,0% 95,6% 1,00 17 000 16 000 4 82,0% 95,0% 1,25 14 000 6 600 5 98,3% 99,9% 5,70 76 000 600 000
When comparing the parameter values from the simulations with 97% order line service, there are tendencies that all methods except for Serv2 deviate heavily between the simulations. Serv1 which is equal to cycle service, generally overestimates its target level. Among the remaining dimensioning methods, there are no general tendencies for which parameter value that corresponds to a given service level.
Methods for improving practical usability
From the previous analysis, where different
dimensioning methods where compared with respect to capital, dimensioning with shortage cost and safety time outperformed the statistical methods. These methods are however quite hard to use when the main goal is to fulfill a specified service level, since the correlation between parameter value and service level is dependent on different characteristics that not could be captured by the method. Since Serv2 is the best method of meeting a specific target service level, the approach is to use it backwards to set a safety time or a shortage cost.
For safety time the Serv2 formula could be converted into a formula that is dependent on the safety time, ordering frequency and lead time demand volatility.
Where
(ordering frequency)
(lead time demand volatility divided by average demand)
With a fixed service level the equation could be transformed into a 3-dimensions and plotting level curves for ST. Using those level curves with average values for the system is the easiest way of finding a safety time that corresponds to a given service level, when starting up a PipeChain View without formal computation and analysis of data.
Safety time as a dimensioning method performs in some cases worse than the statistical methods, and always worse than shortage cost methods with respect of capital tied up in safety stock. Therefore shortage cost methods are to prefer. The approach to estimate the shortage cost is the same as in the case of safety time i.e. using Serv2 backwards. The shortage cost methods are however more sensitive than safety time methods and a graphical solution could not be used with sufficient accuracy. Instead of using average values for the system, each article needs to be computed separately. The method for practical usage is: Starting with a backorder cost sufficiently low, return reorder-points, compare them with a weighted Serv2 and then iterating the
backorder cost until given Serv2 is reached.
Results and analysis
The method of using Serv2 to estimate safety times and shortage costs works well for all simulation cases. The simulation cases are the same as from previous chapter of evaluation of dimensioning methods. The results for a desired order line service of 97 percentages could be seen in the table below.
Sim Service level with Safety time Service level with Shortage cost per unit
Service level with Shortage cost per order
line Service level with Serv2 1 95,4% 96,0 % 95,6 % 96,0% 2 97,0% 97,0 % 99,0 % 97,0% 3 98,8% 99,2 % 99,3 % 98,0% 4 96,3% 97,6 % 98,1 % 97,7% 5 92,4% 93,7 % 93,2 % 92,6%
All dimensioning methods are performing with similar order line service for each simulation case. In simulation cases where the Serv2 method does not performs well do not either the Serv2-based perform well.
Conclusion
Depending on the level of detailed analysis before booting a new system there are different approaches for dimensioning safety stock.
With limited opportunities of data analysis, the graphical method to set a general safety time could be
used. The method performs quite well in achieving the same service level as if dimensioning with Serv2 and is also easy to use. This is mainly the strength of a general safety time even though there is no warranty that the tied up capital is particularly low in relation to other dimensioning methods. In most of the simulation cases the capital tied up in safety stock is however lower than for pure statistical Serv-methods given the same service level.
With a possibility to make a more detailed analysis and some more calculations the shortage cost method is preferable to reduce the capital tied up in safety stock. However, the shortage cost is very difficult to estimate when the goal is to achieve a certain service level. By using a Serv2-based methodology the method works reasonably well with respect to this, especially if Serv2 performs well.
