self insured
100,000
10,000
0 .03(100000) + .07(10000) + .9(0) = $3700
17,126 cheapest but most variable
Sampledeviation = √ [(3(102103.3)^2) +(8(103103.3)^2) +(9(103
103.3)^2) / 20 1]
Xbar = (3(102)+8(103) +9(104)/ 20)
Efficiency = total value of output/total value of inputs  CP = (USL –
LSL)/ 6s

Mean Control chart
:
UCL = xbarbar + 3 σ xbar aka mean of
sample means + 3σ of
σ of sample means: σ/ √ N where N is the #
samples per day  Range control: day 1: largest: 20.4, smallest: 20.2,
20.420.2=
.2
range. Find R
= avg range:
.2+.2+.3 + .1 / 4 = .2 (the
middle line)
UCL and LCL are from a chart.
multiplicative
model where: trend = new mean/ old mean
seasonal = [(spring 06/mean06) +(spring 07/mean 07)] / 2 = .7083 
now to forecast: spring 08 : x
07 x trend component x seasonal
component for spring.  Additive forecast
: Trend = NEW
mean – OLD
mean Seasonal = (spring06  xbar06) + (spring 07  xbar 07)/ 2  Now
to forecast = (most recent actual mean) + (trend) + (seasonal)  actual –
forecast = error
∑/n to find MFE (bias, + means forecast too low, if
all +, there is an upward trend,  means forecast too high, if all , there
is a downward trend.)  actual – forecast^2 = e^2
∑/n to find MSE
(punish big errors)  abs value of actual – forecast = e
∑/n to find
MAD (proportional errors)  Data Smoothing
: 3 month moving avg,
weighted, exponential
period
forecast
actual
1
F1 (last year’s mean)
A1
2
F2= α(A1) + (1α)F1
A2
so (% of actual) + (%
of previous forecast)
Small α if data is random, big α if data is consistent  Plant size/# OR
Choose machines:
TC = a+bq +cq^2, ATC = a/q + b +cq, Datc/dq = a/
q^2 + c = 0, C = a/q^2,
Q= √a/c
(optimal q per facility), solve for q,
and plug into ATC to find $cost/unit to compare machine models. OR
find q* per plant and divide into desired total output  Expected Profit:
= traffic count X yield X (income – cost per customer)
 lease – fixed
cost, 90,000 cars pass by. Can be by foot traffic in a mall, different
alleys have different traffic.
Yield factor: how many of the people enter from the traffic: .005,
Monthly lease: $5,000,Expected cost per customer: $22, Upfront costs
to setup the site (starbucks design): financed as monthly payment of
25,000/ 3 years = $694  Facility Layout
: Max Cycle time =
(total time
in workshift) /(total # of units per shift required)
this is the max
station time. Then pick task from slowest to fastest that will fit.
Efficiency: “eyeball” N *actual cycle time – 1to n∑ ti
= 3*56 –
(56+53+48) = 11 minutes. This is the idle time per cycle, aka time
wasted per cycle. Line Efficiency: Formula: e = 1 to n ∑ times needed /
divided by # of minutes if everyone was busy
= (56+53+48)/ (3*56)
x 100% = 93.45% busy  Dominated flow patterns: when different
products use the same standard order. Variable flow patterns: when
different products don’t follow a standard path ex. hospital.  mass of
movement = Mass of movement = # of trips X Weight of avg load X
distance (V*W*D), we’ll minimize distance based on weight and usage
 Job Design
: efficiency school: (GILBRETH each motion is called a
therblig), Behavioral school: Emphasizes worker motivation,
Henry Towne wrote an article called “the Engineer as an Economist”
argued that we’ve been focusing on all the automated machines and
how productive they are but we should look at the economics of WHEN
and HOW MANY units we should run the machines.