Method and system for minimizing risk in contact center management contracts
View Patent ↗A method (and system) for contact center management contract evaluation including determining a potential profitability/risk for contact center management based upon a proposed contract term between one of a client and a service provider, and a service provider and a vendor.
1. A method of contact center management contract evaluation, said method comprising:
determining, using a processor in a computer, a potential profitability/risk for contact center management based upon a proposed contract term between at least one of:
a client and a service provider; and
a service provider and a vendor,
wherein said profitability/risk comprises a profitability risk associated with such contract terms as payment structures and not meeting profitability targets of contracts for said contact center management,
wherein said determining of said potential profitability/risk comprises modeling a contact center environment and satisfying an objective function for said model, wherein said objective function comprises one of maximizing revenue to a service provider, minimizing cost to a client, maximizing revenue to a vendor, and minimizing variability in staff utilization, using a mixed-integer optimization of said objective function, and
wherein said objective function comprises a service provider's objective function having a format as follows for said mixed-integer optimization and selectively subject to one or more of the identified constraints:
Model Formulation:
Objective
Function
max
.
Z
=
∑
snopt
r
s
x
snopt
(
1
)
-
∑
snopt
:
v
n
∈
V
R
f
v
n
no
x
snopt
(
2
)
-
∑
vnot
:
v
∈
V
T
[
y
^
vnot
b
vno
+
λ
vnot
(
UB
vn
vol
-
LB
vn
vol
)
f
vno
]
(
3
)
-
∑
p
t
d
p
t
(
c
+
FCR
q
+
FCR
-
c
-
FCR
q
-
FCR
)
(
4
)
-
∑
p
t
d
p
t
/
A
H
_
T
t
(
c
+
AHT
q
-
AHT
-
c
-
AHT
q
+
AHT
)
(
5
)
-
∑
t
c
-
CSAT
z
t
(
6
)
Forecast
Satisfaction
Constraint
∑
sno
x
snopt
=
d
p
t
∀
p
∈
P
,
t
=
1
,
…
,
T
(
7
)
Vendor
Capacity
Constraint
∑
nop
x
snopt
≤
∑
p
c
spt
∀
s
∈
S
,
t
=
1
,
…
,
T
(
8
)
Occupancy
-
Based
Vendor
Rate
‘
Selection
’
Constraints
∑
p
x
snopt
≤
y
snot
UB
v
s
o
occ
∑
p
c
spt
∀
s
∈
S
,
n
=
1
,
…
,
N
v
s
,
o
=
1
,
…
,
O
v
s
,
t
=
1
,
…
,
T
(
9
)
∑
p
x
snopt
≥
y
snot
LB
v
s
o
occ
∑
p
c
spt
∀
s
∈
S
,
n
=
1
,
…
,
N
v
s
,
o
=
1
,
…
,
O
v
s
,
t
=
1
,
…
,
T
(
10
)
∑
ps
:
s
ε
S
v
x
snopt
≤
y
^
vnot
UB
vo
occ
∑
ps
:
s
ε
S
v
c
spt
∀
v
∈
V
T
,
n
=
1
,
…
,
N
v
,
o
=
1
,
…
,
O
v
,
t
=
1
,
…
,
T
(
11
)
∑
ps
:
sε
S
v
x
snopt
≥
y
^
vnot
LB
vo
occ
∑
ps
:
s
ε
S
v
c
spt
∀
v
∈
V
T
,
n
=
1
,
…
,
N
v
,
o
=
1
,
…
,
O
v
,
t
=
1
,
…
,
T
Volume
-
Based
Vendor
Rate
‘
Selection
’
Constraints
(
12
)
∑
p
x
snopt
≤
y
snot
UB
v
s
n
vol
∀
s
∈
S
,
n
=
1
,
…
,
N
v
s
,
o
=
1
,
…
,
O
v
s
,
t
=
1
,
…
,
T
(
13
)
∑
p
x
snopt
≥
y
snot
LB
v
s
n
vol
∀
s
∈
S
,
n
=
1
,
…
,
N
v
s
,
o
=
1
,
…
,
O
v
s
,
t
=
1
,
…
,
T
(
14
)
∑
ps
:
s
ε
S
v
x
snopt
≤
y
^
vnot
UB
vn
vol
∀
v
∈
V
T
,
n
=
1
,
…
,
N
v
,
o
=
1
,
…
,
O
v
s
,
t
=
1
,
…
,
T
(
15
)
∑
ps
:
s
ε
S
v
x
snopt
≥
y
^
vnot
LB
vn
vol
∀
v
∈
V
T
,
n
=
1
,
…
,
N
v
,
o
=
1
,
…
,
O
v
s
,
t
=
1
,
…
,
T
(
16
)
∑
ps
:
s
ε
S
v
x
snopt
=
y
^
vnot
LB
vn
vol
+
λ
vnot
(
UB
vn
vol
-
LB
vn
vol
)
∀
v
∈
V
T
,
n
=
1
,
…
,
N
v
,
o
=
1
,
…
,
O
v
,
t
=
1
,
…
,
T
(
17
)
Special
Ordered
Constraints
∑
no
y
snot
≤
1
∀
s
:
v
s
∈
V
R
,
t
=
1
,
…
,
T
(
18
)
∑
no
y
^
vnot
≤
1
∀
v
∈
V
T
,
t
=
1
,
…
,
T
(
19
)
Service
Level
Agreement
Constraints
(
∑
snop
x
snopt
AHT
s
/
∑
p
d
p
t
)
-
A
H
_
T
t
=
q
+
,
t
AHT
-
q
-
,
t
AHT
∀
t
=
1
,
…
,
T
(
20
)
(
∑
snop
x
snopt
FCR
s
/
∑
p
d
p
t
)
-
F
C
_
R
t
=
q
+
,
t
FCR
-
q
-
,
t
FCR
∀
t
=
1
,
…
,
T
(
21
)
(
∑
snop
x
snopt
CSAT
s
/
∑
p
d
p
t
)
-
C
S
_
AT
t
=
q
+
,
t
CSAT
-
q
-
,
t
CSAT
∀
t
=
1
,
…
,
T
(
22
)
Linearizing
Constraints
q
-
t
CSAT
≤
w
t
CSAT
∀
t
=
1
,
…
,
T
(
23
)
z
t
≤
z
_
t
w
t
CSAT
∀
t
=
1
,
…
,
T
(
24
)
z
t
≥
∑
snop
x
snopt
r
s
-
z
_
t
(
1
-
w
t
CSAT
)
∀
t
=
1
,
…
,
T
(
25
)
where z t is given, and is an upper bound on z* t
Decision
Variables
:
x
snopt
=
Minutes
of
LOB
p
allocated
to
site
s
in
month
t
at
vendor
cost
rate
f
v
s
no
where
p
∈
P
,
s
∈
S
,
t
=
1
,
…
,
T
y
snot
=
{
1
,
if
site
s
experiences
call
volume
in
threshold
range
n
and
occupancy
in
threshold
range
o
in
month
t
,
0
,
otherwise
,
for
all
s
:
v
s
∈
V
R
,
n
=
1
,
2
,
…
,
N
v
,
o
=
1
,
2
,
…
,
O
v
,
t
=
1
,
…
,
T
y
^
vnot
=
{
1
,
if
vendor
v
experiences
call
volume
in
threshold
range
n
and
occupancy
in
threshold
range
o
in
month
t
0
,
otherwise
,
for
all
v
∈
V
T
,
n
=
1
,
2
,
…
,
N
v
,
o
=
1
,
2
,
…
,
O
v
,
t
=
1
,
…
,
T
q
+
,
t
AHT
(
q
-
,
t
AHT
)
=
Positive
(
negative
)
deviation
of
actual
AHT
from
targeted
AHT
,
t
=
1
,
…
,
T
q
+
,
t
FCR
(
q
-
,
t
FCR
)
=
Positive
(
negative
)
deviation
of
actual
FCR
from
targeted
FCR
,
t
=
1
,
…
,
T
q
+
,
t
CSAT
(
q
-
,
t
CSAT
)
=
Positive
(
negative
)
deviation
of
actual
CSAT
from
targeted
CSAT
,
t
=
1
,
…
,
T
w
t
=
{
1
,
if
CSAT
target
is
met
in
month
t
0
,
otherwise
.
for
all
t
=
1
,
…
,
T
z
t
=
{
∑
snopt
r
s
x
snopt
,
if
CSAT
target
is
not
met
in
month
t
,
where
t
=
1
,
…
,
T
0
,
otherwise
.
for
all
t
=
1
,
…
,
T
λ
vnot
=
{
Fration
of
interval
[
LB
vn
vol
,
UB
vn
vol
]
covered
by
allocation
of
calls
to
vendor
in
month
t
,
if
y
^
vnot
=
1
0
,
otherwise
for
all
v
∈
V
T
,
n
=
1
,
2
,
…
,
N
v
,
o
=
1
,
2
,
…
,
O
v
,
t
=
1
,
…
,
T
Sets and Parameters:
P is the set of all LOBs
V R is the set of regular Vendors
V T is the set of through Vendors
S is the set of all Sites
S v ⊂S is the subset of sites that belong to vendor vεV R ∪V T
v s is the vendor of site sεS
T=Number of months in planning horizon
N v =Number of call volume threshold ranges for vendor vεV R ∪V T
O v =Number of occupancy threshold ranges for vendor vεV R ∪V T
c spt =Capacity (in minutes) at site s for LOB p in month t,
where sεS, pεP, t=1, 2, . . . , T
d pt =Call Volume Forecast (in minutes) for LOB p in month t, where pεP, t=1, 2, . . . , T
Objective Function Parameters:
r s =Revenue earned from client per minute allocated to site sεS
f vno =Payment rate to vendor vεV R ∪V T per minute allocated at call volume threshold range n=1, . . . , N v and occupancy threshold range o=1, . . . , O v
b vno =Cumulative payment to vendor vεV T up to call volume threshold range n=1, . . . , N v for occupancy threshold range o=1, . . . , O v
c + AHT =Per minute bonus for undershooting AHT target
c − AHT =Per minute penalty for overshooting AHT target, c + AHT <c − AHT
c + FCR =Per minute bonus for overshooting FCR target
c − FCR =Per minute penalty for undershooting FCR target, c + FCR <c − FCR
c − CSAT =Per minute penalty for undershooting CSAT target
Vendor Cost Related Parameters:
f vno =Rate (in dollars per minute) charged by vendor v for in call volume threshold range n and occupancy threshold range o,
where n=1, 2, . . . , N v and o=1, 2, . . . , O v
b vno =Amount that would be charged by vendor v if the vendor's total call volume exactly fills threshold range n and occupancy threshold range o,
where n=1, 2, . . . , N v and o=1, 2, . . . , O v
LB vn vol =Lower limit on call volume in threshold range n=1, 2, . . . , N v for vendor vεV R ∪V T
UB vn vol =Upper limit on call volume in threshold range n=1, 2, . . . , N v for vendor vεV R ∪V T
LB vo occ =Lower limit on occupancy level in threshold range o=1, 2, . . . , O v for vendor vεV R ∪V T
UB vo occ =Upper limit on occupancy level in threshold range o=1, 2, . . . , O v for vendor vεV R ∪V T
Client Service Level Related Contract Parameters:
AHT s =Historical average handling time (sec. per call) at site sεS
FCR s =Historical average fraction of calls handled within first response at site sεS
CSAT s =Historical average customer satisfaction rating at site sεS
A H T t =Targeted AHT in month t=1, 2, . . . , T
F C R t =Targeted FCR in month t=1, 2, . . . , T
C S AT t =Targeted CSAT in month t=1, 2, . . . , T.