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Broadcast Programming - PowerPoint Presentation

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Broadcast Programming - PPT Presentation

Paul Parker Donald McKinnon Production Scheduling Spring 13 Agenda Problem Overview Our Solution Analysis Conclusion Extensions 2 Problem Overview 1 Description Schedule shows of equal duration such that the sum of the viewers over all periods is greatest ID: 178696

objective viewers shows schedule viewers objective schedule shows period show number valueaverage jobs periods trials time 000 heuristic sum

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Slide1

Broadcast Programming

Paul Parker

Donald McKinnon

Production Scheduling Spring ‘13Slide2

Agenda

Problem Overview

Our Solution Analysis Conclusion Extensions

2Slide3

Problem Overview (1)

Description

: Schedule shows of equal duration such that the sum of the viewers over all periods is greatest.

Given: The number of viewers a shows garners is dependent on

its time period and neighbors.

Example

: Schedule 48 different 30 minute shows in a 24 hour period. Maximize the sum of viewers over all periods, where number of viewers of the show in period 35 depends on the 35th period and the shows in periods 34 and 36.

3Slide4

Problem Overview (2)

Upper Bound

:

The sum of the maximum number of viewers any show can have over each time slot (typically infeasible to schedule).

NP Hard:

Broadcast

Programming reduces KnapsackAssumptionsAll jobs (shows) have the same duration.

Unscheduled jobs

gain no

viewers.Jobs can only occur in 1 period in a schedule (no reruns).

4Slide5

Our Solution: Ratio Based S

wapping

Objective

: Given n shows,

m

periods, and

function(ni-1,n

i

,n

i+1

,m

j

) = vi,j, viewers for show ni in period mj, max Σj (vi,j), where i=1…n, and j=1…m.Algorithm:Randomly schedule shows until all m time slots have a distinct show, or all shows are scheduled.Determine the show S with the smallest ratio of its viewers in its current period, P, to its average viewers in all periods of the current schedule: vS,P ÷ AVG(all vS,j) where j=1…m. If S can be swapped with another period such that the sum of the viewers over all periods increases, then swap S such that the greatest increase in viewers results and go to Step 2. Otherwise, STOP and output the objective value of the current schedule.

5Slide6

Analysis – Function 1

Method

Max Objective Value

Average Objective

Value

Average Number

of Swaps

Our

Heuristic

(5 trials)

8677832215Random Scheduling (1,000,000 trials)72974816-*Simulations done in MATLAB or JavaVi,j = 100 * [1 + sine(Si,j-1 * Si,j * Si,j+1)], where i=1…n, and j=1…mSlide7

Analysis – Function

2

Method

Max Objective Value

Average Objective

Value

Average Number

of Swaps

Our

Heuristic

(10,000 trials)10757293Random Scheduling (10,000 trials)978665-*Simulations done in MATLAB or JavaVi,j = Si,j-1 * Si,j * Si,j+1, where i=1…n, and j=1…mSlide8

Analysis – Function

3

Method

Max Objective Value

Average Objective

Value

Average Number

of Swaps

Our

Heuristic

(1,000 trials)338718393Random Scheduling (10,000 trials)30901557-*Simulations done in MATLAB or JavaVi,j = j * (Si,j-1 * Si,j * Si,j+1), where i=1…n, and j=1…mSlide9

Conclusion

Our Heuristic:

Consistency Average objective value is good (above average)

Efficiency

Good objective values result after few swaps Scalability

Yields high objective values given different viewership functionsSlide10

Algorithmic Extensions Considered

D

erive initial schedule as follows

Schedule the show and its neighbors that will garner the most viewers in the remaining time slot until there are no empty time slots remaining.Expanded search after finding local maximum

When a maximum objective value is achieved, swap the two jobs in the time slots having the least viewers and resolve this instance, disallowing the algorithm to re-swap these two jobs immediately.

Advertisements

Model advertisements for shows as shorter jobs and schedule them (not necessarily adjacent to the show they promote) to maximize viewership.

10Slide11

Heuristic for Initial S

chedule

C

onfigurationResultsInconclusivePossible Implication:

11

Objective Value

Initial

Final

Heuristic < Random

Heuristic >

Random

*Simulations done in MATLAB or JavaSlide12

Thank You