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US 7,734,498 B2Granted
Method and system for minimizing risk in contact center management contracts
AssigneeInternational Business Machines Corporation
InventorsChing-Hua Chen-Ritzo, Daniel Connors, Laura Wynter
Life of this patent
Estimating the term…
Abstract
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.
Claims1
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 zt 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
- VR is the set of regular Vendors
- VT is the set of through Vendors
- S is the set of all Sites
- Sv⊂S is the subset of sites that belong to vendor vεVR∪VT
- vs is the vendor of site sεS
- T=Number of months in planning horizon
- Nv=Number of call volume threshold ranges for vendor vεVR∪VT
- Ov=Number of occupancy threshold ranges for vendor vεVR∪VT
- cspt=Capacity (in minutes) at site s for LOB p in month t,
- where sεS, pεP, t=1, 2, . . . , T
- dpt=Call Volume Forecast (in minutes) for LOB p in month t, where pεP, t=1, 2, . . . , T
- Objective Function Parameters:
- rs=Revenue earned from client per minute allocated to site sεS
- fvno=Payment rate to vendor vεVR∪VT per minute allocated at call volume threshold range n=1, . . . , Nv and occupancy threshold range o=1, . . . , Ov
- bvno=Cumulative payment to vendor vεVT up to call volume threshold range n=1, . . . , Nv for occupancy threshold range o=1, . . . , Ov
- 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:
- fvno=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, . . . , Nv and o=1, 2, . . . , Ov
- bvno=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, . . . , Nv and o=1, 2, . . . , Ov
- LBvnvol=Lower limit on call volume in threshold range n=1, 2, . . . , Nv for vendor vεVR∪VT
- UBvnvol=Upper limit on call volume in threshold range n=1, 2, . . . , Nv for vendor vεVR∪VT
- LBvoocc=Lower limit on occupancy level in threshold range o=1, 2, . . . , Ov for vendor vεVR∪VT
- UBvoocc=Upper limit on occupancy level in threshold range o=1, 2, . . . , Ov for vendor vεVR∪VT
- Client Service Level Related Contract Parameters:
- AHTs=Historical average handling time (sec. per call) at site sεS
- FCRs=Historical average fraction of calls handled within first response at site sεS
- CSATs=Historical average customer satisfaction rating at site sεS
- A HTt=Targeted AHT in month t=1, 2, . . . , T
- F CRt=Targeted FCR in month t=1, 2, . . . , T
- C SATt=Targeted CSAT in month t=1, 2, . . . , T.
1,928 more elements
Dependencies are inferred from the claim text.