Embed Size (px)
DESCRIPTION
Chapter3 Output Variability
Citation preview
2/19/2013
1
Manufacturing Output Variabilityand the Service Level Output variability occurs in manufacturing systems
due to: Manual labor performance variability Machines failure and repair mechanisms
Output Variability at Scania EngineProduction Line
25
50
75
100
125
150
175
200
0 10 20 30 40 50 60 70 80 90 100
Nu
mb
er
of p
arts
pro
du
ced
Day
2/19/2013
2
The main output variable of interest is the totalamount of parts produced by the system during thetime period [1,t]
This variable, denoted with Zt, is random withexpected value E[Zt] and variance var[Zt], which bothdepend on the time period of evaluation as they areincreasing functions in t.
The Service Level Zt approximately normally distributed
This enables calculating the Service Level (SL) whichis, the probability to meet a certain customer order(composed of x products) within a certain due time t.
t
Zv
tv
tRxxZPtxSL
t
t
pt
varlim
where,
1),(
2/19/2013
3
Example An industrial engineer collected and reported to you
the daily production quantities from a production lineover a period of two weeks. Estimate the SL of thesystem for orders 350, 940 and 1012 products to bedelivered within 8 days?
Day 1 2 3 4 5 6 7 8 9 10
Q(daily) 122 165 95 135 88 126 177 125 78 93
Example Daily Rp = avg [122, 165, … 93] = 120.4 product/day
v var[122,165 ,… 93] / 10 = 107.8 product2 /day
188.107
84.1203501)8,350(
SL
785.088.107
84.1209401)8,940(
SL
05.088.107
84.12010121)8,1012(
SL
2/19/2013
4
SL vs. order size (x) for due date = 8days
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
850 900 950 1000 1050 1100Order size
SL vs due date (t) for an order of900 products
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
5 5.5 6 6.5 7 7.5 8 8.5due date
2/19/2013
5
SL as a function of (x,t)
4
6
8
10
12
0
0.2
0.4
0.6
0.8
1
900
940
980
1020
1060
1100
1140
1180
1220
1260
1300
1340
1380
1420
1460
1500
1540
1580
1620
1660
1700
1740
1780
1820
1860
1900
1940
1980
2020
2060
2100
0.8-1
0.6-0.8
0.4-0.6
0.2-0.4
0-0.2
