SchedulingTian HeFrank Zhi

TV Commercial

TV Commercial SchedulingBackground

• Commercials traditionally scheduled by hand– Human error

• Case study: NBC network– Automated scheduling

heuristics– Increased profit

• Number of commercials bought by a company

• First and last slots in a commercial break highly coveted

• Evenly spaced commercials of same type

• Juxtaposition of competitor commercials in same break

SchedulingHeuristic considerations

• General MIP Model– Considers commercial types, number bought, commercial and break lengths, client goals– Enormous runtime!

• ISCI model (integer program)– Evenly spaced commercials of same type– Intuitive but has problems

• Network Flow model– Improves runtime greatly for smaller problems– Less intuitive

Heuristics

General MIP- variables

Takes into account client goals

General MIP –model

• Client goals– Product conflict constraints– Position percentage

constraints

ISCI model - variables

ISCI model: IP

The method is simple and intuitive, but for larger problems becomes overwhelming.

ISCI model: Colored Balls

• We coded the ISCI model.– example uses I=3, with i1=3, i2=2, i3=4

• IP solves schedule optimally as follows:

• I eyeball schedule as follows:

Conclusion of ISCI problem

• VERY small spacing problems can be done by hand

• Larger scale problems are infeasible by hand and require heuristics like the ISCI model

Network FlowFormulation - variables

Network FlowFormulation

• Each commercial type has above networkNodes: slot spacesArcs: f(c,j,k) indicates that a commercial of type “c” is consecutively scheduled

in slots “j” and “k”

Conclusion

• Scheduling heuristics much more efficient than scheduling by hand “on-the-fly”

• Important to find heuristics that will solve large problems in an acceptable timeframe

References• Bussieck, Michael R. Bollapragada, Srinivas. Mallik,

Suman. "Scheduling Commercial Videotapes in Broadcast Television." Operations Research 52 (2004): 679-89

• Garbiras, Marc. Bollapragada, Srinivas. "Scheduling commercials on Broadcast Television." Operations Research 52 (2004): 337-45.