# Bp Cheatsheet Essay

1447 Words Jan 14th, 2016 6 Pages
Waiting Time Formula, Multi Parallel Resources (Servers)
Utilization, u = (1/a)/(m x 1/p) = p/am
Tq = (p/m) x (u^[√(2(m+1)-1)-1]/(1-u) x (CVa2+CVp2)/2
Iq = (1/a)*Tq
Ip = u*m = (1/a)*p
I = Iq + Ip
Flow Time = Tq + p

Waiting Time Formula, Multi Parallel Resources (Servers)
Utilization, u = (1/a)/(m x 1/p) = p/am
Tq = (p/m) x (u^[√(2(m+1)-1)-1]/(1-u) x (CVa2+CVp2)/2
Iq = (1/a)*Tq
Ip = u*m = (1/a)*p
I = Iq + Ip
Flow Time = Tq + p

Waiting Time Formula, Single Server
Utilization, u = Flow Rate/Capacity = (1/a)/(1/p) = p/a
Inventory Related Measures
Iq = (1/a) x Tq
Ip = u
I = Iq + Ip
Time in queue, Tq = Activity Time (p) x (u)/(1-u) x (CVa2+CVp2)/2
Flow Time = Tq + p

Waiting Time Formula, Single Server
Utilization, u
rivals on any sub interval depends only on length of interval, not on when interval starts a = average inter-arrival time (IAi+1 – IAi)
Sa = standard deviation (absolute measure of variability)
CVa = Standard deviation/average inter-arrival time (Sa/a) – relative variability
CVp = Standard deviation/Average activity time (Sp/p)

Abnormal peaks of processing time Would be more efficient to automate it
Variability leads to waiting time (even if p/a < 100%)
To predict waiting time even if u<100%
Waiting Time Formula, Single Server
Utilization, u = Flow Rate/Capacity = (1/a)/(1/p) = p/a
Inventory Related Measures
Iq = (1/a) x Tq
Ip = u
I = Iq + Ip
Time in queue, Tq = Activity Time (p) x (u)/(1-u) x (CVa2+CVp2)/2
Flow Time = Tq + p

Inventory Related Cost: C = (Q/2)(Ch) + (D/Q)(Co)
Total Cost Per Year: C = (Q/2)(Ch) + (D/Q)(Co) + DC
Where Ch = Cost of Product x Cost of Capital, C x r
Minimum Cost: Holding cost = Ordering Cost, (Q/2)(Ch) = (D/Q)(Co)
EOQ, Q* = (2DCo/Ch)^1/2
Where R = D, K = Co, h = Ch

Average Level of Inventory = Q*/2
Cycle Time, Order cycle: T* = Q*/D

Finite Production Rate
Production Time: Q/p
Order Cycle: Q/D
Maximum Level of Stock = Q(1-D/p)
Production Rate = (p-D)
Inventory Related Cost: C= (Q/2)(1-D/p)(Ch) + (D/Q)(Co)
EOQ, Q* = 2DCo/[Ch(1-D/p)]^1/2
Inventory Related Cost: C = (Q/2)(Ch) + (D/Q)(Co)
Total Cost Per Year: C = (Q/2)(Ch) + (D/Q)(Co) + DC
Where Ch = Cost of Product x Cost of Capital, C x r
Minimum

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