chicagosupermarkets =
  Join[
    Uncompress[BarcodeRecognize[Import["https://i.stack.imgur.com/kSqkM.png"]]],
    Uncompress[BarcodeRecognize[Import["https://i.stack.imgur.com/kWFxR.png"]]]]

spheremiles[{θ1_, ϕ1_}, {θ2_, ϕ2_}] :=
  3959
    InverseHaversine[
      Haversine[ϕ1 Degree - ϕ2 Degree] +
        Cos[ϕ1 Degree] Cos[ϕ2 Degree] Haversine[θ1 Degree - θ2 Degree]]

cells =
  And @@@
    Table[
      spheremiles[chicagosupermarkets[[i]], {x, y}] <=
        spheremiles[chicagosupermarkets[[j]], {x, y}],
      {i, Length[chicagosupermarkets]},
      {j, Complement[Range[Length[chicagosupermarkets]], {i}]}];

RegionPlot[cells[[1]], {x, -88, -87.5}, {y, 41.8, 42.2}]