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Customer Demand PowerPoint PPT Presentation


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Customer Demand. Customer demand varies in both timing and quantity:. Individual Customer Order. Quantity. Time. Customer Demand.

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Customer Demand

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Customer demand l.jpg

Customer Demand

  • Customer demand varies in both timing and quantity:

Individual Customer Order

Quantity

Time


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Customer Demand

  • If demand for a product comes from many, independent customers, then we don’t need to be concerned about individual customer orders, but rather cumulative demand over a period of time.


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Customer Demand

Cumulative Demand for Period

Individual Customer Demand

Day 3

Day 4

Day 5

Day 6

Day 7

Day 8

Day 9

Day 1

Day 2

Demand


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Customer Demand

  • In statistics, when there is reason to suspect the presence of a large number of small effects acting additively and independently, it is reasonable to assume that the observations will be normally distributed.

  • Therefore, if demand for a product comes from many, independent customers, we can assume that the variability in cumulative demand over a period of time can be described by the normal distribution.


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Q

ROP

LT

LT

EOQ and Reorder Point Systems

  • Using the EOQ model, we developed a reorder point (ROP) inventory management system:

  • In the EOQ model, demand is assumed to be constant


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Q

Q

Q

ROP with Variable Demand

  • When demand is not constant, the reorder point calculation should consider demand variability. If the reorder point is only based on average demand, stockouts will occur:

ROP

DDLT*

LT

LT

*(average) Demand During Lead Time


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Q

Safety Stock

  • To avoid stockouts, the reorder point should include additional inventory, safety stock, to reduce the probability of a stockout.

ROP

DDLT*

Safety Stock

LT

LT

*(average) Demand During Lead Time


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DDLT

Safety Stock

Using the standard deviation of

the DDLT, we can set an

a safety stock level based on

the probability of a stockout

Probability of a

Stockout


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Cumulative

Probability

Z

Safety Stock

For a given service level (cumulative probability),

the safety stock is calculated as:


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If the lead time is one week,

then we have:

If we want a 95% service level,

then the safety stock should be:

So the reorder point should be:

So a ROP of 120 should be used

DDLT = 97.5

SS = (1.6449)(13.9) = 22.86

ROP = 97.5 + 22.86 = 120.36

Safety Stock Example

  • Suppose we have the following weekly demand (consumption) data for a product:


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Safety Stock using MAD

  • Many times, Safety Stock levels are calculated using the Mean Absolute Deviation as a measure of variability rather than the Standard Deviation. There are two reasons for this:

    • Historical: Before calculators, the calculation of a standard deviation was not a trivial task, while the calculation of the Mean Absolute Deviation is fairly simple to perform by hand

    • Robustness: The Mean Absolute Deviation measure is not as easily affected by outlier points as it is using the absolute value of the deviation rather than the squared deviation


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MAD Calculation

WeekDemand


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Standard Deviation Calculation

WeekDemand


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Safety Stock using MAD

  • The standard deviation can be estimated from the MAD using:

  • As a result, we can define a safety factor R which can be used to determine the safety stock based on the MAD and the desired service level:

SD = 1.25 MAD

SS = (R)(MAD)


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Safety Stock Example Revisited

  • The following weekly demand (consumption) data for the product was:

The Demand During Lead Time is:

For a 95% service level,

the safety stock should be:

So the reorder point should be:

So a ROP of 119 should be used

(vs. 120 calculated using the SD)

DDLT = 97.5

SS = (2.0561)(10.4) = 21.38

ROP = 97.5 + 21.38 = 118.88


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Demand Period vs. Lead Time Period

  • In the previous example, the demand period (the period of time used to accumulate customer demand) was one week, which was the same as the lead time.

  • Suppose the lead time was two weeks. Then the variability of the demand for a two week period would be greater than the MAD calculated from demand data aggregated weekly.

  • We have assumed that customer demand is independent, i.e. that the demand for the product comes from a number of unrelated customers. In that case, then we can use a theorem from statistics to determine the appropriate variability of demand during lead time when the demand period is different from the lead time period


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Demand Period vs. Lead Time Period

  • Suppose we have two independent, normally distributed random variables:

    • X: mean X, standard deviation X

    • Y: mean Y, standard deviation Y

  • Then the sum of these variables, Z = X + Y has mean:

    • Z = X + Y

      and standard deviation


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DP=1 week

LT=2 weeks

Demand Period vs. Lead Time Period

  • Suppose that the demand period is 1 week (customer demand is measured on a weekly basis) and the lead time is two weeks. Then the standard deviation for the lead time can be calculated as:


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Demand Period vs. Lead Time Period

  • Suppose that the demand period is 2 weeks (customer demand is accumulated in 2 week intervals) and the lead time is one week. Then the standard deviation for the lead time can be calculated as:

DP=2 weeks

LT=1 weeks


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Safety Stock

In general terms, the standard deviation of the demand

for the lead time is:

where the lead time and demand period are measured in

the same time units (typically days). The demand period is

level of aggregation used for determining demand.


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Safety Stock

So the safety stock level can be calculated as:

using the standard deviation of demand and:

using the MAD, where:


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DDLT

Note that if the Demand Period does not equal the Lead

Time, then the DDLT is calculated as:


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Safety Stock: Example 1

Demand data for a material has been collected on a weekly

basis for 6 months. Demand appears level, with:

Mean: 270 units/week

Standard deviation: 40 units/week

The lead time is 10 days. Calculate the safety stock

required for a 99% customer service level.


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Safety Stock: Example 1

  • The formula for safety stock using the standard deviation is:

    so for this example we have:


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Safety Stock: Example 2

Demand data for product has been collected on a weekly

basis with the following results:

Mean:109 units/week

MAD:20 units/week

The lead time is 4 days. Calculate the safety stock

required for a 95% customer service level.


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Safety Stock: Example 2

  • The formula for safety stock using the standard deviation is:

    so for this example we have:


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Demand Period and Lead Time in SAP

Demand period is set by the Period Indicator on the Forecasting View

of the Material Master

The applicable periods are:

M – Monthly

W – Weekly

T – Daily


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Demand Period and Lead Time in SAP

In-house production is used for

Lead Time for products made in-house

Plnd delivery time + GR processing time +

Purchasing proc. time is used for

Lead Time for externally procured materials


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LT

LT

LT

Exposure to Stockout

  • Stockouts usually occur when stock gets low—for example, during the lead time period before a new order arrives:

Periods of maximum exposure to stockout


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LT

LT

LT

LT

LT

LT

LT

LT

LT

LT

Exposure to Stockout

  • The more frequently we order, the more chances there are of stocking out.

Twice as many

opportunities for

stockout


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Exposure to Stockout

  • To fully evaluate the customer service level, we should calculate the customer service level on an annual basis:

    where D is annual demand and Q is the order quantity.


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Exposure to Stockout

  • For example, if we used a service level of 95% in calculating the safety stock, the annual demand D is 12,000 units and the order quantity Q is 800 units, then we have:

  • So there is only a 46.3% chance of going a year without a stockout


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Regular Demand

Day 3

Day 4

Day 5

Day 6

Day 7

Day 8

Day 9

Day 1

Day 2

Week 2

Week 1

Day 3

Day 4

Day 5

Day 6

Day 7

Day 8

Day 9

Day 1

Day 2

Week 1

Week 2

Sparse Demand

Demand Patterns


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Demand Patterns

  • In developing the safety stock calculations, it was assumed that demand was generated from a “large” number of independent sources, and

  • The individual demands are aggregated over a time period sufficiently long so that there are a number of individual demands contributing to each period demand.

  • If these conditions are not met, then the safety stock values may not perform as expected.


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Demand Patterns

  • If demand is sparse, then a more detailed approach to inventory planning that considers the expected time between orders as well as the expected order quantity

Quantity

Expected

order

quantity

Expected time

between orders

Time


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