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 max i 1,..., 4 22 1 22 v j   xij v 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 • d ij distance from office of SR i to brick j • a ij 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 4 22  x d min i 1 j 1 s.t. ij    xij 1  aij v j   4 ij 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