Pfizer Turkey, one of the leading pharmaceutical companies in Turkey, introduces$/$markets its products to medical doctors $($MDs$)$ via the visits of sales representatives $($SRs$).$ Each SR has a working territory that includes the doctors to be visited. A territory is composed of several small geographic units called "bricks". Due to the dynamic structure of the market, the existing structure of the sales territories has to be renewed in order to maintain the workload balance among SRs$.$ The main problem considered in this case study is to pursue multiple objectives of minimizing the travel distance of SRs and minimizing the percent of change from the current structure $("$disruption$")$ while reconstructing the sales territories, i$.$e$.,$ assigning each brick to an SR$,$ such that the feasibility with respect to workload balance criterion is ensured. This criterion forces the total workload of each SR to be in an allowable interval of $[1-$ a$,1+$ a$].$ As the two objectives may be conflicting, i$.$e$.,$ the solution minimizing the travel distance does not necessarily maintain the existing structure, it is unlikely for a single solution optimizing both objectives. Therefore, obtaining a set of solutions demonstrating the trade$-$off between the two objectives is useful to help the decision$-$maker.

A$)$ Required part: $[80$ points $+20$ points for the quality of your report for part A$]$

Q$1)$ Formulate a mathematical model for the problem of Pfizer Turkey. Clearly state your sets, parameters, decision variables, objective functions, and constraints.

Q$2)$ Code your mathematical model in Python and use Pyomo to solve it$.$ Describe your approach in obtaining all efficient solutions that capture both objectives with a $=0\mathrm{.}2.$ Plot your Efficient Frontier chart.

Q$3)$ Discuss the properties of the current solution in comparison with the new efficient solutions you obtained. For this, compare the travel distances, disruption level, and workload balance of the current system and your efficient solutions, and explain your observations.

Q$4)$ We can see different sets of efficient solutions and tradeoffs by tightening up and relaxing the workload constraint. Try at two different ranges $($you may use a $=0\mathrm{.}15$ and a $=0\mathrm{.}1)?$ Compare the Efficient Frontiers of all ranges and discuss your results.