Unformatted text preview: needed in month t • zt # to hire as trainees in month t Long Term Planning
0 zt = max @0, ⌘t+⌧ t+⌧ 1
X yj (1 r) j =t ⌧ (j t) A at time t, plan for time t+τ
sometimes, what you
have is more than
what you need time length from j to t+τ1 applicable in a wider range! 1 Square Root Law
• In M/M/∞ queue, the number of servers is Poisson
with parameter R=λ/µ. • Poisson(R) can be approximated by Normal(R,R) ⇡1 ✓ NR
p
R ◆ Standard normal(0,1) distribution function Square Root Law
• Now if delays are not prevalent, the number of busy
servers in a ﬁnite server queue can be
approximated by the number of inﬁnite server
queue. • So P(wait) = P(# busy serves >N ) ﬁnite inﬁnite
⇡ P(# busy serves >N )
✓
◆
NR
computable
p
⇡1
R Square Root Law
• To decide the number of servers N
✓ NR
p
R ◆ =1 NR
p
=
R
P(wait) N =R+ = P(wait) P(wait)
1 (1 P(wait) P(wait)) p R Part 8: Process Flow Analysis Process ﬂow diagram
I Processing times
Capacity
Capacity per hour III 37
Resource II 46 37 I II III 37 46 37 [sec/cust] 0.02703 0.02174 0.02703 [cust/sec] 97.29730 78.26087 97.29730 [cust/hour] Process capacity
Demand 78.26087 [cust/hour]
60 60 60 60 [cust/hour] Utilization 0.617 0.767 0.617 Cycle time 60 60 60 [sec] Idle time 23 14 23 [sec] Total idle time 60 [sec] Labor content 120 [sec] Labor utilization 0.667 Basic deﬁnitions
• Processing times: how long does the worker spend on the task? • Capacity = 1/processing time:
• how many units can the worker make per unit of time • If there are m workers at the activity: Capacity = m/activity time • Bottleneck: process step with the lowest capacity • Process capacity: capacity of the bottleneck • Flow rate = Minimum{Demand rate, Process Capacity) • Utilization = Flow Rate / Capacity • Flow Time: The amount of...
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 Fall '14
 huff location model, Square Root Law

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