Call center resource allocation
View Patent ↗A method for determining call center resource allocation can include modeling call center performance over an operations time period using a computer. A number of replicas of the modeled call center performance are simulated, using the computer, over a planning time period, each replica having random contact arrivals and contact service times following a stochastic arrival and service process according to a probability distributions of inter-arrival time and service time. Multiple iterations of each simulation are run on the computer to optimize call center resource allocation. A particular simulation iteration is tested against a criterion of convergence, and call center resource is allocated based on the particular simulation iteration with a successful criterion of convergence.
1. A method for determining call center resource allocation, comprising:
modeling call center performance over an operations time period using a computer;
simulating, using the computer, a number of replicas of the modeled call center performance over a planning time period, each replica having random contact arrivals and contact service times following a stochastic arrival and service process according to probability distributions of inter-arrival time and service time;
running, on the computer, multiple iterations of each simulation to optimize call center resource allocation;
testing a particular simulation iteration against a criterion of convergence; and
allocating call center resource based on the particular simulation iteration with a successful criterion of convergence.
2. The method as set forth in claim 1 , wherein the call center performance includes: contact arrivals, contact classification corresponding to at least one of multiple skill pools, queuing order; queuing time, contact routing to a queue associated with one of multiple skill pools based on contact classification, staffing of the multiple skill pools with servers, contact assignment from the queue to a particular server associated with one of multiple skill pools, contact service time, and abandoned contacts.
3. The method as set forth in claim 1 , wherein events included in a simulation of the modeled call center performance for every server skill i, and skill pool k, include: contact arrival by i; contact service start time by i, k; contact service completion time by i, k; customers abandonment by i; and server shift beginning and end times by k; server (k).
4. The method as set forth in claim 1 , further comprising:
constraining the model to satisfy a service level agreement (SLA), the SLA including at least a percentage of contacts (α) be addressed in a specified queuing time; and
constraining the model to satisfy the SLA for each one of multiple skill pools.
5. The method as set forth in claim 4 , further comprising, for each of the multiple skill pools, determining a minimum pool size to at least meet a delay probability to satisfy the SLA, the minimum pool size z kt being:
Z kt =arg min{ bεN:P ( Z kt ≧b )≦α}, ∀k;∀t
wherein a distribution of contacts in the call center model allocated to each pool at time t for iteration n is Z t =(Z 1 , . . . , Z r ) t (n) , and
Z
kt
(
n
)
=
∑
i
∈
ϕ
k
N
ikt
(
n
)
+
∑
i
∈
ϕ
k
Q
it
(
n
)
(
s
kt
(
n
)
μ
ik
∑
j
∈
k
(
i
)
(
s
jt
(
n
)
μ
ij
)
)
∀
k
;
∀
t
and
Q
it
(
n
)
s
kt
(
n
)
∑
j
∈
k
(
i
)
s
jt
(
n
)
,
i
=
1
,
…
,
m
for server k, i possible server skills, and j skill pools.
6. The method as set forth in claim 4 , further comprising determining a minimum number of servers for each contact classification to satisfy the SLA, the minimum number of servers y it for each contact classification being:
y it =arg min{ bεN:P ( x it (n) ≧b)≦α i },∀i;∀t
wherein a distribution of servers allocated to each of m contact classifications at time t for iteration n is X t =(X 1 , . . . , X m ) t (n) , and
x
it
=
∑
k
∈
k
(
i
)
N
ikt
(
n
)
+
Q
it
(
n
)
,
i
=
1
,
…
,
m
.
for server k, and i possible server skills.
7. The method as set forth in claim 6 , further comprising determining a minimum number of servers to assign to each of j skill pools
x
kt
=
∑
i
∈
ϕ
k
(
y
it
s
kt
(
n
)
μ
ik
∑
j
∈
k
(
i
)
s
jt
(
n
)
μ
ij
)
,
∀
k
;
∀
t
where
k
(
i
)
=
{
k
:
i
∈
ϕ
k
}
for server k, and wherein p is a respective weighted proportionality allocation constant.
8. The method as set forth in claim 1 , further comprising determining, for a loose bound, an initial staffing value s kt at a first iteration of a simulation replica for skill pool k at time t as
s
kt
(
0
)
=
M
*
∑
i
∈
ϕ
(
k
)
k
_
(
i
)
λ
it
μ
ik
,
∀
k
,
t
where
M
>
10
,
k
_
(
i
)
=
M
*
1
k
(
i
)
and |k(i)| is the number of servers that can serve the class i, and where t is obtained by forecasting an interval to obtain an infinite server approximation solution for staffing levels after a first iteration.
9. The method as set forth in claim 1 , further comprising:
determining, for a tight bound, an initial staffing value s kt at a first iteration of a simulation replica for skill pool k at time t as
s
kt
(
0
)
=
⌈
L
kt
+
β
(
α
_
k
)
L
ky
⌉
,
∀
k
,
t
where
L
kt
=
1
k
(
i
)
∑
i
∈
ϕ
(
k
)
λ
it
μ
ik
,
∀k,t and |k(i)| is the number of servers that can serve the class i, and where t is obtained by forecasting an interval, with α k estimated as the average of the SLA served by the group;
fixing S t (n) ={( s 1 ,s 2 , . . . ,s r ) t ,1 ≦t≦T};
evaluating probability distributions of stochastic processes X 1 , i=1, . . . , m from paths N ikt (n) and Q it (n) according to
X
it
=
∑
k
∈
k
(
i
)
N
ikt
(
n
)
+
Q
it
(
n
)
,
i
=
1
,
…
,
m
;
letting, for each t; 1≦t≦T, S k n+1 be a least number of servers that meet delay-probabilities that satisfy customer class service level calculated by
x
kt
=
∑
i
∈
ϕ
k
(
y
it
s
kt
(
n
)
μ
ik
∑
j
∈
k
(
i
)
s
jt
(
n
)
μ
ij
)
,
stopping if Max{|S t (n+1) −S t n |:1 ≦t≦T}≦ε, with S n+1 being the particular simulation iteration with the successful criterion of convergence.
10. The method as set forth in claim 1 , further comprising determining a minimum cost of staffing the multiple skill pools with servers over time T as
min
∑
t
=
1
T
∑
k
=
1
r
c
kt
∑
i
∈
ϕ
k
x
ikt
where
∑
t
∑
k
∈
k
(
i
)
x
ikt
≥
y
it
,
∀
i
and
s
kt
(
n
+
1
)
=
∑
i
∈
ϕ
k
x
ikt
*
,
∀k and
wherein x ikt is an allocation of servers from skill pool k to satisfy a service level agreement in period t and is a positive integer, and the cost per skill pool k in period t is c kt .
11. The method as set forth in claim 1 , further comprising further comprising determining a minimum cost of scheduling the multiple skill pools with servers as
min
∑
j
=
1
NS
∑
k
=
1
r
c
jk
b
jk
where
∑
j
=
1
NS
a
jt
b
jk
≥
∑
i
∈
ϕ
k
x
ikt
,
∀
k
,
t
and
∑
k
=
1
r
x
ikt
≥
y
it
,
∀
i
,
t
and wherein the cost per skill pool k in period t is c kt and X ikt is an allocation of servers from skill pool k to satisfy a service level agreement in period t and is a positive integer that satisfies 0≦x ikt ≦M.
12. A non-transitory computer-readable medium having computer-readable instructions stored thereon that, if executed by one or more processors, cause the one or more processors to:
model call center performance over an operations time period, call center performance including:
staffing of multiple skill pools with servers, some servers having skills corresponding to more than one of the multiple skill pools, and
contact assignment from the queue to a particular server associated with one of multiple skill pools;
simulate a number of replicas of the modeled call center performance over a planning time period, each replica having random contact arrivals and contact service times following a stochastic arrival process according to a Poisson probability distribution;
run on the computer multiple iterations of each simulation to optimize call center resource allocation;
test a particular simulation iteration against a criterion of convergence; and
allocate call center resource based on the particular simulation iteration with a successful criterion of convergence.
13. The non-transitory computer-readable medium of claim 12 , further having computer-readable instructions stored thereon that, if executed by one or more processors, cause the one or more processors to assign a contact to a particular server associated with one of multiple skill pools based on first-in, first-out (FIFO) rules, wherein a particular contact is assigned to a first available server associated with the one of multiple skill pools, and a contact routed earliest to a queue associated with one of multiple skill pools is assigned to a longest idle server.
14. The non-transitory computer-readable medium of claim 12 , further having computer-readable instructions stored thereon that, if executed by one or more processors, cause the one or more processors to assign a contact to a particular server associated with one of multiple skill pools based on primary/secondary roles rules, wherein the FIFO rules are applied first to servers associated with the one of multiple skill pools as a primary role, and if a server associated with the one of multiple skill pools as a primary role is not available then the FIFO rules are applied second to servers associated with the one of multiple skill pools as a secondary role.
15. A system for assigning support in a customer support system comprising: processor executing computer readable instructions to model call center performance over an operations time period, call center performance including: contact arrivals, contact classification corresponding to at least one of multiple skill pools, queuing order, queuing time, contact routing to a queue associated with one of multiple skill pools based on contact classification, staffing of the multiple skill pools with servers, contact assignment from the queue to a particular server associated with one of multiple skill pools, contact service time, and abandoned contacts; processor executing computer readable instructions to simulate a number of replicas of the modeled call center performance over a planning time period, each replica having random contact arrivals and contact service times following a stochastic arrival process according to a Poisson probability distribution; processor executing computer readable instructions to run multiple iterations of each simulation to optimize call center resource allocation; processor executing computer readable instructions to test a particular simulation iteration against a criterion of convergence; and processor executing computer readable instructions to allocate call center resource based on the particular simulation iteration with a successful criterion of convergence.