Creating wedge-shaped territories
Question - what data is available to use in dividing up the territories? Any chance you have point data showing each inspection?
Also, let me add in who probably has several ideas on how to solve your original proposal:
EDIT: Xander Bakker beat me to it. I need to learn how to type faster...... 
Chris Donohue, GISP
Several possibilities...
- If you have an origin point (office) and destination points (the other stuff), you can create points that radiate from the origin to the destination quite easily. BUT, your map may look like this which isn't too helpful but looks really cool in color.
2. You could artificially create a circle to overlay your area and divide into the desired number of sectors needed and sample your points within each sector
3. You could use the network analyst extension (aka the not free extension) and produce a service area AND shortest route to the destinations from the office and divide it up as in step 2. It might look like the above, but there might be fewer lines since the same road could be used to go from the different points (ie from point 59 to 99 to 26 might be the shortest, so you reduce 3 lines to 1, if they were connected by a road.)
4. other ideas pending... a nice screen grab would help fine-tune the above
Here is a quick screen grab. The star is our office and the dots are locations to be inspected.
Interesting what you can do with wedges...
Precision is off (not much intelligence in the definition of the cut-off angles), but I'm getting somewhere... Will try to post some code tomorrow.
Xander Bakker forgot about this one... only got so far... I am sure you are using numpy too 
and could use a distraction
import numpy as np
import pylab as plt
angle = [np.deg2rad(i) for i in range(-180,180,30)]
R= 100
Xs = R*np.cos(angle) # X values
Ys = R*np.sin(angle) # Y values
pnts = np.round(np.array(zip(Xs,Ys)), 3) # create the points
print("{}".format(pnts))
# center point and mean distance
XY_c = np.array([0.0,0.0]) # create a center point
Xc, Yc = XY_c.flatten() # pull out values separately
#
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
circ = plt.Circle((Xc, Yc), radius=R, color='w',lw=2,alpha=.5)
ax.add_patch(circ)
plt.axis('equal')
plt.scatter(Xs,Ys)
plt.show()Now just change the radius, give it a real center, connect the center to the points as triangles and you have a big circle for intersection or select by attributes (distractions... distractions... )
[[-100. -0. ] [ -86.603 -50. ] [ -50. -86.603] [ 0. -100. ] [ 50. -86.603] [ 86.603 -50. ] [ 100. 0. ] [ 86.603 50. ] [ 50. 86.603] [ 0. 100. ] [ -50. 86.603] [ -86.603 50. ]]
ADDENDUM
c =np.array([0,0]) p = np.array([[c,pnts[i-1],pnts,c] for i in range(1,len(pnts))]) >>> print(p) [[[ 0. 0. ] [-100. -0. ] [ -86.603 -50. ] [ 0. 0. ]] [[ 0. 0. ] [ -86.603 -50. ] [ -50. -86.603] [ 0. 0. ]] etc
should get you polys which can be "Arc'ed" into shape
