考虑顾客耐心的呼叫中心人力资源配置模型

, pB
, ,
, pR
,
s
,
β β β
,s .
s
,
p E [W |S ]
S
p . β
S
s
,
4.2
λ = 20, a = 0, b = 1 ,
, 1
2
cb = 1, ,
cr ,
1, 2
3.
cb /cr
, .
γ
p
R
2
3
, ,
.
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
,
(
: M/M/N+M . , . . : ; : N945; O2 24 ; ; :A , , ,
,
,
,
. . ( , . ; : 1000−5781(2013)05−0686−08 , ) ,
θ′
(4)
,
T ′ = ϕT + (1 − ϕ)wn ,
688
28
T
. (4) , [9] ,
, θ′
“ ,
”
[12]
,ϕ ;
ϕ=1
.
T
,
wn
ϕ < 0. ϕ
,
ϕ=0 , ,
U (a, b). Wn
, ,
s+n+1 s , ′ ′ ′ sµ + θ , sµ + 2θ , . . . , sµ + nθ n
Wn wn
1
,
:
β wn
,
,
Wn
(1) ; ( , ), (2)
β = P {Wn < wn } .
, , , , “
s, α;
”,
pb (n) = P {T < wn } = 1 − e−θwn ,
,
α′ α′ = (1 − α)(1 − pb (n)).
, (3)
[9]
T T′
,
, . T′
.
2
θ ′(0) ← θ, i ← 0, ε; θ
′(i)
−θ θ ′(i−1)
′(i−1)
>ε λ
R(i)
,
∞
θ ′ = f (θ ′ )
,
=
n=0 ∞
λα′ (θ ′(i−1) ))p(s + n)(θ ′(i−1) )rn (θ ′(i−1) ), ip(s + i)(θ ′(i−1) );
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,
,
cr
690
28
, , , cb < cr . γ , , “
. ”
, .
3
s,
, “ ”
R
.
, (21)
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
sµ + jθ ′ (j − i)θ ′ j =0,j =i
s
sP
Wn s+n+1 s
,
Ă
s+n
s P +nT '
, “
2 ”. .
. , Wn
Wn
s+1
s+n+1
2 Fig. 2 The diagram of the pure-death process
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 ′ )
3 , ,
(b − a)(sµ + iθ ′ ) +1 θ
, ,
(11)
5
:
689
.
[13]
L(t)
,
3
O
0 1 ĂS-1t (t , NhomakorabeaO
S
0)
,
O(1D)(1 pb (1))
n n
(sµ + iθ ′ ) e−(sµ+iθ )t , t 0,
Gn (t) = 1 −
i=0 n
sµ + jθ ′ −(sµ+iθ′ )t e ,t ′ ( j − i ) θ j =0,j =i
(6) (7) ,
E[Wn ] =
i=1
1 . sµ + iθ ′
3
rn (ϕ)
n+1 rn (ϕ) = P {T ′ < Wn |T > wn )} .
1
, . ,
: 2013−07−05; : : 2013−09−05. (71271052; 71021061).
[1,2]
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687
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[7]
.
, , , , . , Armony
[10]
. Jouini (balking) ; , . , M/M/N+M, (reneging)
,
5
:
691
. 1 ,β . , .
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
3 4
θ ′(i) , +1,
θ ′(i) = λR(i) /L(i) ;
2.
4
, . 2GB ,λ