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Unformatted text preview: rs, we calculate the
probability that customers from area i will visit
a particular store j Huff Location Model
• Annual customer expenditures for item k at store j can
now be calculated.
• Pij = Probability customers from area i travel to store j • Ci = Number of customers in area i (e.g. census track) • Bik = Annual budget for product k for customers in
area i • m = Number of customer areas in the market region Huff Location Model
• Market share of product k purchased at
store j can now be calculated Part 6: Queueing System Simplest Possible System
• M/M/1 Queue
• inter arrival time ~ exp(λ), iid • service time ~ exp(µ), iid • buffer has inﬁnite capacity • every customer get served (FIFO)
Formulas More General Systems • G/G/1 Queue !
! E(Wq ) ⇥ 1 • G/G/N Queue
E(Wq ) ⇡ c2 + c2
a
s
E(S )
2 ⇢ p 2(N +1) 1 1 ⇢ c2 + c2 E(S )
a
s
2
N Calculation of coefﬁcient of
variation, formulas Formulae for M/M/n queues
⇢=
P0 = /µ (0 < ⇢ < n)
1
⇣P
⌘
n 1 ⇢i
⇢n
+ n!(1 ⇢/n)
i=0 i!
n+1 ⇢
Lq =
(n 1)!(n
L = Lq + ⇢
W = L/ Wq = Lq / P0
⇢)2 Nominal load/expected
# of busy servers Kill me! Intuitive
Little’s law Little’s Law
• Formulae
!
! •
• Lq = Wq L= W Conditions and Caveats
Steady state, ......
(I) Inventory = (R)Flow Rate × (T)Flow Time Part 7: Call Center Management Long Term Planning
• # of CSRs to hire and train
• r monthly turnover rate • τ time to train an employee (month) • yt # of employees on hand at time t • yj # of employees who ﬁnish training at the beginning
of month t • ηt # of employees...
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 Fall '14

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