Case Study 3-3
Reallocating Bricks to Sales
Representatives of Pfizer Turkey
Charles Delort
Markus Hartikainen
Dorothy Miller
Jouni Pousi
Lisa Scholten
Jun Zheng
Problem Structuring
Increase the work satisfaction and travel efficiency of sales representatives (SR)
Develop a general method for reallocating
bricks to SR within a territory
Decrease SR
workload (WL) complaints
Increase SR
travel efficiency
Avoid breaking
SR-client relationships
Increase the work satisfaction and travel efficiency of sales representatives
Decrease SR
WL complaints
Minimize SR
WL imbalance
Minimize maximal difference
from average workload
measured with
brick index values
Increase SR
travel efficiency
Avoid breaking
SR-client relationships
Increase the work satisfaction and travel efficiency of sales representatives
Decrease SR
WL complaints
Minimize SR
WL imbalance
Minimize maximal difference
from average workload
measured with
brick index values
Increase SR
travel efficiency
Avoid breaking
SR-client relationships
Modeling assumptions
1. Brick index is constant within model
2. Brick index updated periodically
-> problem solved again
3. WL does not depend on travel
distance
Increase the work satisfaction and travel efficiency of sales representatives
Decrease SR
WL complaints
Increase SR
travel efficiency
Minimize SR
total travel distance
Minimize sum of
distances from office
to bricks allocated to SR
Avoid breaking
SR-client relationships
Increase the work satisfaction and travel efficiency of sales representatives
Decrease SR
WL complaints
Increase SR
travel efficiency
Minimize SR
total travel distance
Minimize sum of
distances from office
to bricks allocated to SR
Avoid breaking
SR-client relationships
Modeling assumptions
1.All travel originates
and returns to the SR
home office
2.Only one brick visited
per trip
3.Each brick is visited by
only one SR
Increase the work satisfaction and travel efficiency of sales representatives
Decrease SR
WL complaints
Increase SR
travel efficiency
Avoid breaking
SR-client relationships
Minimize overall
disruptions due to
brick reassignment
Minimize sum of
index-weighted
disruptions
Increase the work satisfaction and travel efficiency of sales representatives
Decrease SR
WL complaints
Increase SR
travel efficiency
Modeling assumptions
1.Total number of SR, bricks and territories is constant
2.Home office location does not change
3.Size/shape of brick/territory does not change
Avoid breaking
SR-client relationships
Minimize overall
disruptions due to
brick reassignment
Minimize sum of
index-weighted
disruptions
Multi-Objective Optimization Problem
• No preference information  obtain Pareto set
• Multi-objective integer linear program
SR in
– 3 objectives
columns
– 88 binary decision variables
0 0 0 1
0 0 0 1
– 22 constraints

X 
    
22
13
– 4  1.7610 feasible solutions 0 0 0 1


Bricks 1,2 and 22
assigned to SR 4
Bricks in
rows
Multi-Objective Integer Program
Total travel
distance

 4 22
" min" xij d ij ,

 i 1 j 1
4
s.t.
x
i 1
ij
Imbalance
Disruption
 x 1  a v ,
4
22
i 1 j 1
ij
ij
j
maxi 1,...,4
22

1 22

v

x
v
 j 
ij j 
4 j 1

j 1

 1 for all j  1, , 22
Can be formulated
• Decision variables
• xij 1 if SR i allocated brick j, else 0 as a linear program!
• Parameters
• dij distance from office of SR i to brick j
• aij 1 if SR i allocated brick j in initial allocation, else 0
• v j index value of brick j
Augmented Epsilon Constraint Method
• Mixed Integer Linear Program
• Epsilon variations schemes for computing the
whole Pareto set are hard for more than two
objectives [e.g., Laumanns et al, 2006]
– For this reason we compute Pareto optimal
solutions only for some meaningful values of
maximum difference of workloads from mean
 A subset of the Pareto set
Results
• Implementation
– Octave with GLPK
– C++ interface to CPLEX using Concert technology
• Initial allocation of bricks can be improved
• Obtained Pareto set consisting of 191
solutions
– MCDA methods applicable
– Interactive Decision Maps used to obtain
interesting solutions [Lotov et al., 2010]
Pareto Set
Imbalance
http://www.rgdb.org/idm/start2.jsp
[Lotov et al., 2010]
Candidate SolutionsImbalance
Initial Solution
Index
value
+
Compromise Solution 1
(187.4100)
(0.0000)
(0.3377)
Index
value
+
Compromise Solution 2
(187.4100)
(0.0000)
(0.3377)
Index
value
+
Compromise Solution 3
(187.4100)
(0.0000)
(0.3377)
Index
value
+
Engage Decision Maker
• Present candidate solutions to Merih Caner
(Decision Maker)
• Explore different goals with feasibility set
visualizations
• Narrow preferred alternative set with decision
support software
– E.g., MAVT using Spatial Decision Support
Software (SDSS) [Yatsalo et al. 2010]
MAVT – Equal Weights
MAVT – Travel Distance Less Important
References
• Laumanns M., Thiele L., Zitzler E., ”An efficient, adaptive parameter
variation scheme for metaheuristics based on the epsilon-constraint
method”, European Journal of Operational Research, 169(3), 2006
• Lotov A., Efremov R., Kistanov A., Zaitsev A., Visualization of Large
Databases, Prototype WEB Application Server RGDB © 2007-2010.
http://www.ccas.ru/mmes/mmeda/rgdb/index.htm. Accesssed July
7, 2010
• Yatsalo B., Didenko V., Gritsyuk S., Mirzeabasov O., Tkachuk A.,
Slipenkaya V., Babucki A., Vasilevskaya M., Shipilov D., Okhrimenko
I., Pichugina I., Gobuzova O., Tolokolnikova N., Okhrimenko D.,
DECERNS SDSS © 2006-2009, http://www.decerns.com/. Accessed
July 8, 2010
Additional Slides
Mathematical Formulation of The
Augmented Epsilon Constraint Method
min  xij dij    xij 1  aij v j  
4
22
4
i 1 j 1
s.t.
22
i 1 j 1
22
1 22
v j   xij v j  

4 j 1
j 1
22
1 22
xij v j   v j  

4 j 1
j 1
4
x
 x 1  a v
4
i 1
22
i 1 j 1
ij
ij
ij
1
j
 1
  2
for all i  1, ..., 4
for all i  1, ..., 4
for all j  1, , 22
With varying  1 and  2 ,
 small positive constant
 decision variable
Extreme Solution 1
(187.4100)
(0.0000)
(0.3377)
Index
value
Extreme Solution 2
(187.4100)
(0.0000)
(0.3377)
Index
value
Extreme Solution 3 (Initial)
Index
value
Further Considerations
•
•
•
•
•
•
•
Simultaneously minimize time and distance
Optimize travel routes
Include regional growth projections
Better understand brick index values
Initiate SR preferences/assignment satisfaction (survey)
Track SR complaint reduction filed with management
Allow flexibility in the number of SR per brick, bricks per
territories, and/or territories per country
• Allow SR home office location to change