1. Case Study 3-3 Reallocating Bricks to Sales Representatives of Pfizer Turkey
Charles Delort
Markus Hartikainen
Dorothy Miller
Jouni Pousi
Lisa Scholten
Jun Zheng

2. 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

3. Decrease SR WL complaints Increase SR travel efficiency
Increase the work satisfaction and travel efficiency of sales representatives
Decrease SR WL complaints
Increase SR travel efficiency
Avoid breaking SR-client relationships
Minimize SR WL imbalance
Minimize maximal difference
from average workload
measured with
brick index values

4. Decrease SR WL complaints Increase SR travel efficiency
Increase the work satisfaction and travel efficiency of sales representatives
Decrease SR WL complaints
Increase SR travel efficiency
Avoid breaking SR-client relationships
Minimize SR WL imbalance
Modeling assumptions
Brick index is constant within model
Brick index updated periodically -> problem solved again
WL does not depend on travel distance
Minimize maximal difference
from average workload
measured with
brick index values

5. Decrease SR WL complaints Increase SR travel efficiency
Increase the work satisfaction and travel efficiency of sales representatives
Decrease SR WL complaints
Increase SR travel efficiency
Avoid breaking SR-client relationships
Minimize SR total travel distance
Minimize sum of
distances from office to bricks allocated to SR

6. Decrease SR WL complaints Increase SR travel efficiency
Increase the work satisfaction and travel efficiency of sales representatives
Decrease SR WL complaints
Increase SR travel efficiency
Avoid breaking SR-client relationships
Modeling assumptions
All travel originates and returns to the SR home office
Only one brick visited per trip
Each brick is visited by only one SR
Minimize SR total travel distance
Minimize sum of
distances from office to bricks allocated to SR

7. Decrease SR WL complaints Increase SR travel efficiency
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

8. Decrease SR WL complaints Increase SR travel efficiency
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
Modeling assumptions
Total number of SR, bricks and territories is constant
Home office location does not change
Size/shape of brick/territory does not change
Minimize sum of index-weighted disruptions

9. Multi-Objective Optimization Problem
No preference information ð obtain Pareto set
Multi-objective integer linear program
3 objectives
88 binary decision variables
22 constraints
feasible solutions
SR in columns
Bricks in rows
Bricks 1,2 and 22 assigned to SR 4

10. Multi-Objective Integer Program
Total travel distance
Imbalance
Disruption
Can be formulated as a linear program!
Decision variables
1 if SR i allocated brick j, else 0
Parameters
distance from office of SR i to brick j
1 if SR i allocated brick j in initial allocation, else 0
index value of brick j

11. 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

12. Results Implementation Initial allocation of bricks can be improved
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]

13. Pareto Set
Imbalance

14.
[Lotov et al., 2010]

15. Candidate Solutions
Imbalance

16. Initial Solution
Index value +

17. Compromise Solution 1
Index value
( )
(0.0000)
(0.3377) +

18. Compromise Solution 2
Index value
( )
(0.0000)
(0.3377) +

19. Compromise Solution 3
Index value
( )
(0.0000)
(0.3377) +

20. 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]

21. MAVT – Equal Weights

22. MAVT – Travel Distance Less Important

23. 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 © 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 © , Accessed July 8, 2010

24. Additional Slides

25. Mathematical Formulation of The Augmented Epsilon Constraint Method
With varying and , small positive constant
decision variable

26. Extreme Solution 1
Index value
( )
(0.0000)
(0.3377)

27. Extreme Solution 2
Index value
( )
(0.0000)
(0.3377)

28. Extreme Solution 3 (Initial)
Index value

29. 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