*** Ch 5 ***

Earliest start time for a project activity:

ES = latest EF for all immediate predecessors

Earliest finish time for a project activity:

EF = ES + activity’s duration

Latest finish time for a project activity:

LF = earliest LS for all immediate successors

Latest start time for a project activity:

LS = LF – activity’s duration

Slack time for a project activity:

Slack time = LS – ES

*** Ch 7 ***

Takt time:

Takt time = available production time

Required output rate

Theoretical minimum number of workstations:

I∑i=1 Ti

Wmin = -----------------

Takt time

Where:

Ti = time required for the ith task

I∑i=1 Ti = total time for all I tasks

Cycle time for a production line:

CT = maximum amount of time spent in any one workstation

Idle time:

IT = Wactual CT – I∑i=1 Ti

Where:

WActual= actual number of workstations

Percent Idle time:

PI = 100% * IT / (WActual CT)

Efficiency delay:

ED = 100% - PI

*** Ch 8 ***

Total cost of a capacity alternative:

TC = FC + VC x X

Where:

TC = Total cost

FC = Fixed cost

VC = Variable cost per unit of business activity

X= Amount of business activity (number of customers served, number of units produced, etc.)

Expected value of a capacity alternative:

EVj = I∑i=1 Pi Ci

Where:

EVj= Expected value of capacity alternative j

Pi= Probability of demand level i

Ci= Financial result (cost, revenue, or profit at demand level i)

Break Even point

BEP = FC / (R-VC)

Where:

BEP= Break Even Point

FC= Fixed Cost

VC= Variable Cost

R= Revenue per unit of business activity

Probability of n arrivals in T time periods:

Pn = (λT)n e-λT

n!

Where:

Pn= Probability of n arrivals in T time periods

λ= arrival rate

T= Number of time periods

Average utilization of a waiting line system:

ρ=λ/μ

Where:

λ= Arrival rate

μ= Service rate

Average number of customers waiting in a waiting line:

CW = λ2 / μ(μ-λ)

Average number of customers in the waiting line system:

CS = λ / (μ-λ)

Average time spent waiting in a waiting line:

TW = λ / μ(μ-λ)

Average time spent in the waiting line system:

Ts = 1 / (μ-λ)

Productivity:

Productivity = outputs / inputs

Resources (usually labor) required to comlete the nth unit:

Tn = T1 nb

where:

Tn = resources (usually labor) required for the nth unit T1 = resources required for the 1st unit

b = ln (learning percentage) / ln2

*** Ch 2 ***

Value Index:

V = [pic]

Where: In = Importance of dimension n

Pn= Performance with regard to dimension n

*** Ch 3 ***

Productivity

Productivity = Outputs / Inputs

Efficiency

Efficiency = 100% (actual outputs / standard outputs)

Percent value-added time:

Percent value-added time = 100% (value-added time) / (total cycle time)

*** Ch 4 ***

Process capability ratio

[pic]

whereUTL= upper tolerance limit

LTL= lower tolerance limit

σ= process standard deviation for the variable of interest

Process capability index

[pic]

whereμ= process mean

UTL= upper tolerance limit

LTL= lower tolerance limit

σ= standard deviation

Sample average for a continuous variable

[pic]

wheren= number of observations in the sample

Xi= value of the ith observation

Sample range (R) for a continuous variable

R = (highest value in the sample) – (lowest value in the sample)

Sample proportion

[pic]

wheren= number of observations in the sample

ai= 0 if the attribute...