考虑顾客耐心的呼叫中心人力资源配置模型

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,
s
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β β β
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s
,
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S
p . β
S
s
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2
cb = 1, ,
cr ,
1, 2
3.
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p
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2
3
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.
β (cb = 1, cr = 3) Table 3 Staffing and performance measures for different β with cb = 1, cr = 3 β 10% 30% 50% 70% 90% pB 0.024 0 0.039 7 0.070 8 0.138 9 0.242 2 pR 0.086 6 0.068 5 0.059 7 0.047 2 0.014 9 pS 0.889 3 0.891 9 0.869 5 0.813 8 0.742 9 E [W |S ] 0.006 0 0.007 8 0.013 2 0.026 4 0.041 6 s 21 21 20 18 16 3
p ,
B
p ,
∞
R
λ ,
R
L, (13)– (17)
. (13) (14) (15) (16) (17)
L=
i=1 ∞
ip(s + i), (α + (1 − α)pb (n))p(n + s),
n=0 ′
pB = pR =
θL , λ pS = 1 − pR − pB ,
∞
λR =
n=0
λα′ p(s + n)rn (ϕ).
28 2013
5 10 JOURNAL OF SYSTEMS ENGINEERING
Vol.28 No.5 Oct. 2013
,
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1
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,
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=
n=0 ∞
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L(i) =
(8)
(1)
(8)
∞ wn
rn (ϕ) = P {ϕT + (1 − ϕ)wn < Wn |T > wn )} = 1 − β − eθ(wn /ϕ)
,
n
gn (t)e−θt/ϕ dt.
(9)
rn (ϕ) = 1 − β −
i=0
sµ + jθ ′ (j − i)θ ′ j =0,j =i
n n
n
′ sµ + iθ ′ e−(sµ+iθ )wn , ′ sµ + θ/ϕ + iθ
,
. (20)
Min s cb pB
, cr
pR
s.t. cb pB + cr pR
, cb
γ,
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cr
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3
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θ,
′
λ = θ ′ L.
(13), (17) (21),
∞
θ′ =
, L, p(s + n), rn (ϕ)
110819)
Staffing model for call center with customer patience variation
Yu Miao, Gong Jun, Luo Xinggang, Zhu Huabo
(Department of Systems Engineering, Key Lab of Integrated Automation of Process Industry of MOE, Northeastern University, Shenyang 110819, China)
(10)
ϕ
U (a, b) 1 rn (ϕ) = b−a
b a b a
1−β −
i=0 n n
sµ + jθ ′ (j − i)θ ′ j =0,j =i
′ sµ + iθ ′ e−(sµ+iθ )wn ′ sµ + θ/ϕ + iθ
dϕ
=1−β −
i=0
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s
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gn (t)
Wn
n
, Gn (t)
n
Wn
′
, E[Wn ]
′
Wn 0,
(5)
gn (t) =
i=0
sµ + jθ (j − i)θ ′ j =0,j =i
′ sµ + iθ ′ e−(sµ+iθ )wn × ′ sµ + θ/ϕ + iθ
1−
2.2
θ ln (b − a)(sµ + iθ ′ )
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i=0 n
sµ + jθ ′ −(sµ+iθ′ )t e ,t ′ ( j − i ) θ j =0,j =i
(6) (7) ,
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i=1
1 . sµ + iθ ′
3
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1 β (cb = 1, cr = 1) Table 1 Staffing and performance measures for different β with cb = 1, cr = 1 β 10% 30% 50% 70% 90% pB 0.057 0 0.093 9 0.158 1 0.216 0 0.277 2 pR 0.208 0 0.168 8 0.137 9 0.074 7 0.017 2 pS 0.735 0 0.737 3 0.704 0 0.709 3 0.705 7 E [W |S ] 0.019 4 0.024 0 0.041 4 0.052 6 0.052 5 s 16 16 15 15 15
i=1
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λ L
α′ p(s + n)rn (ϕ).
n=0
(22)
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s
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−1
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1 Fig. 1 Schematic representation of call center with delay information
Abstract: The impact of impatience psychology on customer behaviors plays an important role in the human resources staffing of call centers. The paper formulates a model of staffing optimization of call centers considering stochastic customer patience variation on staffing, based on M/M/N+M queue with delay information announced. Firstly, the queuing model with delay information is given based on queuing theory, and customer patience variation and the probability of customers’ behavior of abandonment including balking and reneging are formulated as a function of the delay information. Secondly, we derive some related performances by analyzing the queuing process for steady state probability. Lastly, the optimal staffing level is calculated through a bisection algorithm and the fixed point algorithm. The numerical example illustrates that how the reliability probability of delay information, penalty coefficient of customer behavior, and patience variation affect staffing. The conclusion drawn has guiding implications for human resource management in call centers. Key words: call center; customer patience; delay information; human resources staffing; balking and reneging
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n+1
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n+1
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i=1
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θ , sµ + iθ ′
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(18)