Supply Chain Formulas

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Mid Term KEY FORMULAE

*** 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...
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