Post on 11-Apr-2017
Background
McMartin Catalog Distributors sells its products by way of phone orders from customers calling a toll-free number
ABC Ltd
(3rd party call centre)
Product distribution
forwards
to McMartin
customer
places order
Background
Having established a successful business, McMartin is now looking to open its own inbound telemarketing centre(s)
Direct orders
ABC Ltd
(3rd party call centre)
Product distribution
Background
Preliminary analysis has identified 10 possible sites
Sites differ in respect to theirFixed Operating CostsWage CostsCall Costs (vary by originating region)
Objective
Determine the number of call centres to open and their locations
McMartin has no preference for any location over any other and is simply looking for the most economical outcome
Assumptions
Call times – Mean 6 minutes (independent of origin)
Processing times – Mean 1 minute/call (independent of origin and processing centre)
Employee Utilisation – Mean 87% (independent of processing centre)
(*) Call Centre Capacities
Methods
Use ILP (Integer-Linear Programming)2 types of choices -which call centres to open (binary decisions) -how many calls to direct from a calling region to a
particular call centre (inequality constraints)
SoftwareXpress-IVE (MP)MS Excel
Formulation
Decision Variables
For i = 1,2,...,10 and j = 1,2,...,17,
Let x(i) = 1 if call centre i is openedLet x(i) = 0 if call centre i is not opened
Let y(ji) be the number of calls from region jprocessed at call centre i
Formulation
Costs - Fixed Costs
Let f(i) be the annual fixed cost at site i.
Then the total fixed cost is
€
x(i) f (i)i
∑
Formulation
Costs - Call Costs
Let c(ji) be the hourly call rate for calls from region j processed at call centre i.
Then the total call cost is given by
The factor represents the average call time (in hours)
€
j
∑i
∑ c jiy ji
Formulation
Costs - Wage costs
Let w(i) be the hourly wage rate at call centre i
Then the total wage cost is given by
The factor incorporates fringe benefit loadingscall connection times & post-processing timesemployee utilisation
€
w(i)y( ji)j
∑i
∑
Formulation
Constraints
(1) Sites are either open or not
(2) Expected demand must be met
(3) (*) Capacity cannot be exceeded€
x(i) ∈ 0,1{ }
€
y( ji) ≥ D j( )i
∑
€
y( ji) ≤ Cj
∑ (i)x(i)
Formulation
Objective Function
subject to
€
min x(i) f (i) +i
∑ α + βw(i)( )y( ji)j
∑i
∑ ⎧ ⎨ ⎩
⎫ ⎬ ⎭
€
x(i) ∈ 0,1{ }
€
y( ji) ≥ D j( )i
∑
€
y( ji) ≤ Cj
∑ (i)x(i)
Analysis
(1) Assume slack capacity constraints at the sites
Optimal solution is to open a single call centreAny of the 10 prospective call centres is a cheaper option than
opening more than 1 call centre
Rankings#1 (8) Shawinigan, PQ $5.443M#2 (9) Drummondville, PQ $5.474M (+0.58%)#3 (10) Sydney, NS $5.507M (+1.18%)... ...#10 (2) Brandon, MB $5.775M (+6.11%)
AnalysisTotal Costs by Site
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8 9 10
($m)
Fixed Cost Wage Cost Call Cost
Analysis
(2) Tighten capacity constraint to force opening of additional call centresShawinigan All $5.443M 100%Brandon $5.775M 100% Shawinigan $5.842M 96.1%Brandon 204Shawinigan $5.854M 92.6%Brandon 204, 306Shawinigan $5.857M 91.7%Brandon 204, 306, 817Shawinigan $5.862M 88.1%St. Jerome 514
Analysis
(2) Tighten capacity constraint to force opening of additional call centres (continued)
...ShawiniganSt. Jerome 514 + Others
...Drummondville 11 Regions $5.897M 62.8%Cornwall 6 Regions
...Drummondville $5.912M 50.0%Cornwall
Sensitivities
Fixed costs small in proportion to total cost but large compared to reduction in variable costs that can be achieved from opening additional sites.
Key unknown is site capacities - completely determines optimal site location(s).
Trade off is between lowering variable costs by opening more sites and increasing fixed costs.
Shawinigan stable solution for single-site problem - demand would have to decrease by 22% or increase by 133% to change the solution.
Issues
Reliability of supplied dataMarginal choices between sitesSolution depends critically on the accuracy of
the dataCalling demandsCost estimates
Cost structureWhat does the fixed cost cover?What happens to calls not answered?Wage structure (F/T, P/T, casual)
Recommendations
Tentative conclusion is to open single call centre at Shawinigan if capacity sufficient
Otherwise open centres at Drummondville & Cornwall to balance demand
Follow-up
Further information requiredSite capacitiesUnanswered calls (busy tone vs hold costs)Cost saving vs outsourcing
Cost differences between sites may be minor compared to savings/extra costs from outsourcing
Expansion goal - new regions/old regions?Qualitative factors
Staff quality, location of other premises