ptg6843605
shortage report – simulated annealing
The Encyclopedia of Operations Management Page 328
shortage report – A list of items not available to meet requirements for customer orders or production orders; also
called a shortage list.
See Over/Short/Damaged Report.
shrinkage – (1) In an inventory context: Inventory lost due to deterioration or shoplifting (theft from “customers”),
breakage, employee theft, and counting discrepancies. (2) In a call center context: The non-revenue generating
time as a percentage of the total paid time; also called staff shrinkage.
In the inventory context, shrinkage is usually discovered during a cycle count. In the call center context,
shrinkage is the percentage of paid working time that is unproductive. Unproductive time includes breaks,
meetings, training, benefit time (sick, vacation, etc.), and other off-phone member service activities.
See call center, carrying charge, carrying cost, cycle counting, obsolete inventory.
SIOP – See Sales & Operations Planning (S&OP).
sigma level – A metric that measures the defect rate for a process in terms of the standard normal distribution with
an assumed shift in the mean of 1.5 standard deviations.
The sigma level metric is often taught in lean sigma programs as a measure of effectiveness for a process.
The estimation process usually assumes that the control limit is set based on a standard normal random variable
with mean 0 and standard deviation 1, but that the true process has a standard deviation of 1 and mean of 1.5
(instead of 0). The sigma level metric uses this model to estimate the number of defects per million opportunities
(DPMO). The table below shows the DPMO for a range of sigma level and assumed mean shift values.
The well-known “3.4 defects per million
opportunities” can be found in the top right
cell of the table. For a sigma level of SL = 6
and mean shift MS = 1.5, the probability of a
defect in the right tail is 0.000003398, the
probability of a defect in the left tail is
practically 0, and the overall probability of a
defect is 0.000003398. Therefore, the total
expected DPMO is 3.3977 ≈ 3.4.
Four-sigma represents an average
performance level across many industry
sectors. If the entire world operated on a
four-sigma standard, the world would have
some serious problems:
20,000 lost articles of mail per hour
Unsafe drinking water 15 minutes per day
5,000 surgical errors per week Two bad
aircraft landings per day
200,000 wrong prescriptions each year
No electricity 7 hours each month
The Excel formula for converting a
“sigma level” (SL) with a mean shift (MS)
into a defect rate (per million opportunities) is = (NORMDIST(-SL, MS, 1, TRUE) + 1 - NORMDIST(SL, MS, 1,
TRUE))*1000000. As noted above, it is commonly assumed that the mean is shifted by MS = 1.5 sigma.
Contrary to the hyperbole found in many popular practitioner publications, six sigma may not be the optimal
sigma level. The optimal sigma level may be lower or higher than six sigma and should be based on the cost of a
defect relative to the cost of preventing a defect.
See defect, Defective Parts per Million (DPPM), Defects per Million Opportunities (DPMO), DMAIC, lean
sigma, operations performance metrics, process capability and performance, specification limits.
simple exponential smoothing – See exponential smoothing.
simulated annealing – A heuristic search method used for combinatorial (discrete) optimization problems.
Simulated annealing is analogous to how the molecular structure of metals is disordered at high temperatures
but ordered (crystalline) at low temperatures. In simulated annealing, the “temperature” starts out high, and the
DPMO by sigma level and assumed mean shift
Assumed shift in the mean (MS)
MS = 0.0 MS = 0.5 MS = 1.0 MS = 1.5
Sigma level (SL)
6.0
0.0 0.0 0.3 3.4
5.6 0.0 0.2 2.1 20.7
5.2
0.2 1.3 13.3 108
4.8
1.6 8.6 72.4 483
4.4
10.8 48.6 337 1,866
4.0
63.3 236 1,350 6,210
3.6
318 988 4,663 17,865
3.2 1,374 3,575 13,917 44,567
2.8
5,110 11,208 36,003 96,809
2.4
16,395 30,582 81,094 184,108
2.0
45,500 73,017 160,005 308,770
1.6
109,599 153,530 278,914 461,140
1.2
230,139 286,529 434,644 621,378
0.8 423,711 478,889 615,190 768,760
0.4
689,157 723,888 806,504 893,050
Source: Professor Arthur V. Hill