case study 3-3 reallocating bricks to sales representatives of pfizer turkey charles delort markus...
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Case Study 3-3Reallocating Bricks to Sales
Representatives of Pfizer Turkey
Charles DelortMarkus Hartikainen
Dorothy MillerJouni Pousi
Lisa ScholtenJun Zheng
Develop a general method for reallocatingbricks to SR within a territory
Avoid breakingSR-client relationships
Decrease SRworkload (WL) complaints
Increase SRtravel efficiency
Increase the work satisfaction and travel efficiency of sales representatives (SR)
Problem Structuring
Increase the work satisfaction and travel efficiency of sales representatives
Avoid breakingSR-client relationships
Decrease SRWL complaints
Increase SRtravel efficiency
Minimize SRWL imbalance
Minimize maximal differencefrom average workload
measured with brick index values
Increase the work satisfaction and travel efficiency of sales representatives
Avoid breakingSR-client relationships
Decrease SRWL complaints
Increase SRtravel efficiency
Minimize SRWL imbalance
Minimize maximal differencefrom average workload
measured with brick index values
Modeling assumptions
1.Brick index is constant within model2.Brick index updated periodically -> problem solved again3.WL does not depend on travel distance
Modeling assumptions
1.Brick index is constant within model2.Brick index updated periodically -> problem solved again3.WL does not depend on travel distance
Increase the work satisfaction and travel efficiency of sales representatives
Avoid breakingSR-client relationships
Decrease SRWL complaints
Increase SRtravel efficiency
Minimize SRtotal travel distance
Minimize sum ofdistances from office
to bricks allocated to SR
Increase the work satisfaction and travel efficiency of sales representatives
Avoid breakingSR-client relationships
Decrease SRWL complaints
Increase SRtravel efficiency
Minimize SRtotal travel distance
Minimize sum ofdistances from office
to bricks allocated to SR
Modeling assumptions
1.All travel originates and returns to the SR home office2.Only one brick visited per trip3.Each brick is visited by only one SR
Modeling assumptions
1.All travel originates and returns to the SR home office2.Only one brick visited per trip3.Each brick is visited by only one SR
Increase the work satisfaction and travel efficiency of sales representatives
Avoid breakingSR-client relationships
Decrease SRWL complaints
Increase SRtravel efficiency
Minimize overalldisruptions due tobrick reassignment
Minimize sum ofindex-weighted
disruptions
Increase the work satisfaction and travel efficiency of sales representatives
Avoid breakingSR-client relationships
Decrease SRWL complaints
Increase SRtravel efficiency
Minimize overalldisruptions due tobrick reassignment
Minimize sum ofindex-weighted
disruptions
Modeling assumptions
1.Total number of SR, bricks and territories is constant2.Home office location does not change3.Size/shape of brick/territory does not change
Modeling assumptions
1.Total number of SR, bricks and territories is constant2.Home office location does not change3.Size/shape of brick/territory does not change
Multi-Objective Optimization Problem
• No preference information obtain Pareto set• Multi-objective integer linear program– 3 objectives– 88 binary decision variables– 22 constraints– feasible solutions
1000
1000
1000
X
Bricks 1,2 and 22assigned to SR 4
Bricks 1,2 and 22assigned to SR 4
Bricks inrows
SR incolumns
1322 1076.14
Multi-Objective Integer Program
22
1
22
14,...,1
4
1
22
1
4
1
22
1 4
1max,1,min""
j jjijjijij
i jijij
i jij vxvvaxdx
Imbalance
• 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
ijd
jv
ijx
ija
4
1
22,,1 allfor 1i
ij jx s.t.
Total traveldistance Disruption
Can be formulatedas a linear program!Can be formulated
as a linear program!
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 SetImbalance
Candidate SolutionsImbalance
Indexvalue
Initial Solution+
Indexvalue
Compromise Solution 1+
(187.4100) (0.0000) (0.3377)
Indexvalue
Compromise Solution 2+
(187.4100) (0.0000) (0.3377)
Indexvalue
Compromise Solution 3+
(187.4100) (0.0000) (0.3377)
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
jiji j
ijiji j
ij vaxdx 1min4
1
22
1
4
1
22
1
4
1
22,,1 allfor 1i
ij jx
s.t.
22
1
22
1
4...,,1 allfor 4
1
j jjjij ivvx
22
1
22
1
4...,,1 allfor 4
1
jjij
jj ivxv
1
4
1
22
1
1
jiji j
ij vax With varying and , small positive constant decision variable
1 22
Indexvalue
Extreme Solution 1(187.4100) (0.0000) (0.3377)
Indexvalue
Extreme Solution 2(187.4100) (0.0000) (0.3377)
Indexvalue
Extreme Solution 3 (Initial)
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