Or Case Study - Assignment Ii

DEPARTMENT OF MANAGEMENT STUDIES INDIAN INSTITUTE OF SCIENCE, BANGALORE

APPLIED OPERATIONS RESEARCH

ASSIGNMENT – II CASE STUDY: LP FORMULATION “TELEVISION VIEWERSHIP AND EXPECTED PROFIT OPTIMISATION”

Submitted toDr. M. Mathirajan Department of Management Studies IISc Bangalore

Submitted by1. Sumeet Kumar Ambastha 2. Gaurish Agarwal Students, 1st Year, DOMS

1. Problem Description: The 2019 Cricket World Cup (officially ICC Cricket World Cup 2019) is the 12th edition of the Cricket World Cup, scheduled to be hosted by England and Wales from 30 May to 14 July 2019. The hosting rights were awarded in April 2006, after England and Wales withdrew from the bidding to host the 2015 ICC Cricket World Cup, which was held in Australia and New Zealand. There is optimism surrounding the Cricket World Cup 2019 as advertisers make a beeline to advertise during the tournament, hoping to see the country win the title this time around.

According to officials at ESPN (the official broadcaster), on-air advertising is expected to fetch revenues to the tune of Rs 750 crore with two billion viewers across the world watching the matches being played amongst the top 14 cricketing nations. The country's sizeable population is expected to account for the biggest chunk of eyeballs and sponsors and advertisers are expected to pay rates that could go up to Rs 6.5 lakh for a 10-second slot on channels such as Star Sports, Star Cricket and ESPN for the India-specific matches.

Location Australia

Television broadcaster(s)

Radio broadcaster(s)

Cable/satellite (pay): Fox Sports

Europe (except UK and Ireland)

Web streaming

Mobile

Foxsports.com.au

Foxtel Now

Hotstar.com

Hotstar

Hotstar.com

Hotstar

India Nepal Maldives

Cable/satellite: Star Sports, DD National (India matches, Semifinals and Final only)

All India Radio, (India matches, Semi-Finals and Final)

Bhutan Table 1: Broadcasters of Cricket World Cup 2019 in different countries across different channels.

A Company named Markex Marketing makes advertisement for a beverage company named PepsiCo. They have signed contract to display advertisement during World Cup Cricket 2019. The team at Markex Marketing has been given a task to develop a television advertisement strategy for PepsiCo. One airing space is for 10 seconds and the pricing is done on the number of airing spaces an advertising agency buys from the broadcasting agency. An Analyst at Markex Marketing has come up with a rough estimate of the expected expense on the television advertisement during the World Cup match season on the channel airing the World Cup. One slot in advertisement means a span of 6 hours and a day consists of 4 such slots namely Morning, Afternoon, Evening and Night. The expected viewership in each slot is given in Table 2:

Sr. No.

Day of Advertisement

Advertising

Expected viewership per air of advertisement (in Thousands)

1

Friday

Morning

490

2

Saturday

Morning

540

3

Sunday

Morning

625

4

Friday

Afternoon

500

5

Saturday

Afternoon

550

6

Sunday

Afternoon

570

7

Friday

Evening

756

8

Saturday

Evening

880

9

Sunday

Evening

840

10

Friday

Night

750

11

Saturday

Night

820

12

Sunday

Night

800

Table 2: Expected Viewership of Advertisement in all Slots

Another consultant at PepsiCo. has come up with some of the findings about the advertisement schedule and has instructed the Markex Marketing Company to stick to some of the fundamental of advertisement schedule. Markex Marketing will have to take care of the requirements set forth by PepsiCo. The total amount to be spent during the campaign has been set to INR 90,00,000. The maximum amount to be spent on Friday is INR 44,00,000 in all the four available slots. The maximum amount to be spent is INR 57,60,000 on Saturday and INR 65,00,000 on Sunday in all the four available slots. There should be at least 72 displays of the advertisement on any Friday, 78 displays of advertisement on Saturday. There can be only 42 air space of the advertisements that can be bought from the broadcaster for Friday daytime (morning and afternoon) advertisement, 46 for Saturday daytime and 58 for Sunday daytime while there can be only 62 air spaces for the advertisements that can be bought from the broadcaster for Friday nighttime (evening and night) advertisement, 73 nighttime air spaces on Saturdays and 92 nighttime airspaces on Sunday . Total view in night is expected to be more than 50% of the total viewership.

The broadcaster has put forward the rates of airing an advertisement on television. One airing space is for 10 seconds and the pricing is done on the number of airing spaces a company buys from the broadcasting agency.

Sr. No.

Day of Advertisement

Advertising

Cost of one airing of advertisement (in Thousand INR)

1

Friday

Morning

37.5

2

Saturday

Morning

42.5

3

Sunday

Morning

47.5

4

Friday

Afternoon

40

5

Saturday

Afternoon

45

6

Sunday

Afternoon

50

7

Friday

Evening

52.5

8

Saturday

Evening

57.5

9

Sunday

Evening

65

10

Friday

Night

50

11

Saturday

Night

55

12

Sunday

Night

57

Table 3: Cost of airing advertisement in different slots

The Competition Commission of India in order to prevent misuse of this platform by large companies and big political parties. The Competition Commission of India has decided to limit the number of airs by an individual company. One company cannot put advertisement in three consecutive slots (one slot if of 6 hours). Out of any three consecutive slots, there can be advertisement for a company in only two of them. Due to large demand and shortage of air time, the broad caster has come up with some limitations wherein if a company has put forward an advertisement bid for Friday morning slot, then it cannot bid for Friday evening slot and vice versa. Similarly, if a company has bid for Saturday morning slot then it cannot bid for Saturday evening slot. If company has placed a bid for Sunday afternoon, company cannot bid for Sunday evening bid and vice versa. Table 4 illustrates the condition put forth by the broadcaster.

Table 4: Conditions on Slots by television broadcasters

Any consumer who buys the advertised product within 7 days is labelled as a conversion. PepsiCo has observed a pattern of conversation rate of 1% in the recent past. Assuming the conversation rate to be the same, devise a Marketing Strategy. The revenue from every purchase by a customeris Rs 10.

2. Problem Statement: You are working with Markex Marketing, devise a Marketing Strategy for PepsiCo and provide alternatives based on the revenue model (Topline and Bottomline) of the company PepsiCo (Topline Model means Maximize Revenue, Bottomline Model means Maximize Profit). Answer the following questions: 1. PepsiCo is considering hiring a celebrity for its television advertisements. What is the maximum amount that can be paid to the celebrity so that the allocations do not change? 2. 2. If PepsiCo considers reallocating budgets from advertisement to upgrade its supply chain, if possible what can be the maximum amount that can be withdrawn from the advertisement budget without affecting the current revenue generated. 3. Advertisement in which slot is maximum profitable for PepsiCo?

3. Lingo LP Formulation: Title = Revenue and Profit from Television Advertisement Optimization; !MAX = TOTAL_EXPECTED_PROFIT; ! Switch this comment to maximize expected profit; MAX = TOTAL_EXPECTED_REVENUE; ! Switch this comment to maximize expected revenue; ! Decision Variables FRI_AFT = Television Viewership on Friday Afternoon (Number of People) SAT_AFT = Television Viewership on Saturday Afternoon (Number of People) SUN_AFT = Television Viewership on Sunday Afternoon (Number of People) FRI_NI8 = Television Viewership on Friday Night (Number of People) SAT_NI8 = Television Viewership on Saturday Night (Number of People) SUN_NI8 = Television Viewership on Sunday Night (Number of People) FRI_MOR = Television Viewership on Friday Morning (Number of People) SAT_MOR = Television Viewership on Saturday Morning (Number of People) SUN_MOR = Television Viewership on Sunday Morning (Number of People) FRI_EVE = Television Viewership on Friday Evening (Number of People) SAT_EVE = Television Viewership on Saturday Evening (Number of People) SUN_EVE = Television Viewership on Friday Evening (Number of People) TOT_FRI_VIEW = Television Viewership on Fridays (Number of People) TOT_SAT_VIEW = Television Viewership on Fridays (Number of People) TOT_SUN_VIEW = Television Viewership on Sundays (Number of People) TOT_FRI_AD_AIR = Total advertisement aired on Fridays (Number of advertisements aired) TOT_SAT_AD_AIR = Total advertisement aired on Fridays (Number of advertisements aired) TOT_SUN_AD_AIR = Total advertisement aired on Sundays (Number of advertisements aired) BIN_FRI_AFT = If advertisement aired on Friday Afternoon (Binary variable) BIN_SAT_AFT = If advertisement aired on Saturday Afternoon (Binary variable) BIN_SUN_AFT = If advertisement aired on Sunday Afternoon (Binary variable) BIN_FRI_NI8 = If advertisement aired on Friday Night (Binary variable) BIN_SAT_NI8 = If advertisement aired on Saturday Night (Binary variable) BIN_SUN_NI8 = If advertisement aired on Sunday Night (Binary variable) BIN_FRI_MOR = If advertisement aired on Friday Morning (Binary variable) BIN_SAT_MOR = If advertisement aired on Saturday Morning (Binary variable) BIN_SUN_MOR = If advertisement aired on Sunday Morning (Binary variable) BIN_FRI_EVE = If advertisement aired on Friday Evening (Binary variable) BIN_SAT_EVE = If advertisement aired on Saturday Evening (Binary variable) BIN_SUN_EVE = If advertisement aired on Friday Evening (Binary variable) TOTAL_EXPECTED_REVENUE = Total Expected Revenue the advertisement in the Weekend (in 10 Lakhs Indian Rupees) TOTAL_EXPECTED_PROFIT = Total Expected Profit from the advertisement in the weekend (in 10 Lakhs Indian Rupees); ! Constraints; ! Slots Availability Constraints; BIN_FRI_AFT*FRI_AFT + BIN_FRI_MOR*FRI_MOR BIN_SAT_AFT*SAT_AFT + BIN_SAT_MOR*SAT_MOR BIN_SUN_AFT*SUN_AFT + BIN_SUN_MOR*SUN_MOR BIN_FRI_NI8*FRI_NI8 + BIN_FRI_EVE*FRI_EVE BIN_SAT_NI8*SAT_NI8 + BIN_SAT_EVE*SAT_EVE BIN_SUN_NI8*SUN_NI8 + BIN_SUN_EVE*SUN_EVE

<= <= <= <= <= <=

42; 46; 58; 62; 73; 92;

! Number of advertisements aired Constraints; BIN_FRI_AFT*FRI_AFT+BIN_FRI_NI8*FRI_NI8+ BIN_FRI_MOR*FRI_MOR + BIN_FRI_EVE*FRI_EVE >= 52; BIN_SAT_AFT*SAT_AFT+BIN_SAT_NI8*SAT_NI8+ BIN_SAT_MOR*SAT_MOR + BIN_SAT_EVE*SAT_EVE >= 64;

! Night Viewership consists of more than 50% of the Total Viewership; BIN_FRI_NI8*FRI_NI8 + BIN_SAT_NI8*SAT_NI8 + BIN_SUN_NI8*SUN_NI8 >= 0.5*( BIN_FRI_AFT*FRI_AFT + BIN_SAT_AFT*SAT_AFT + BIN_SUN_AFT*SUN_AFT + BIN_FRI_NI8*FRI_NI8 + BIN_SAT_NI8*SAT_NI8 + BIN_SUN_NI8*SUN_NI8 + BIN_FRI_MOR*FRI_MOR + BIN_SAT_MOR*SAT_MOR + BIN_SUN_MOR*SUN_MOR + BIN_FRI_EVE*FRI_EVE + BIN_SAT_EVE*SAT_EVE + BIN_SUN_EVE*SUN_EVE ); ! Daily Budget Constraints; 40*BIN_FRI_AFT*FRI_AFT + 50*BIN_FRI_NI8*FRI_NI8 + 37.5*BIN_FRI_MOR*FRI_MOR + 52.5*BIN_FRI_EVE*FRI_EVE <= 4400; ! In Thousands; 45*BIN_SAT_AFT*SAT_AFT + 55*BIN_SAT_NI8*SAT_NI8 + 42.5*BIN_SAT_MOR*SAT_MOR + 57.5*BIN_SAT_EVE*SAT_EVE <= 5760; ! IN Thousands; 50*BIN_SUN_AFT*SUN_AFT + 57*BIN_SUN_NI8*SUN_NI8 + 47.5*BIN_SUN_MOR*SUN_MOR + 65.0*BIN_SUN_EVE*SUN_EVE <= 6500; ! IN Thousands; ! ( + + +

Total Budget Constraint; 37.5*BIN_FRI_MOR*FRI_MOR 40.0*BIN_FRI_AFT*FRI_AFT 52.5*BIN_FRI_EVE*FRI_EVE 50.0*BIN_FRI_NI8*FRI_NI8

+ + + +

42.5*BIN_SAT_MOR*SAT_MOR 45.0*BIN_SAT_AFT*SAT_AFT 57.5*BIN_SAT_EVE*SAT_EVE 55.0*BIN_SAT_NI8*SAT_NI8

+ + + +

47.5*BIN_SUN_MOR*SUN_MOR 50.0*BIN_SUN_AFT*SUN_AFT 65.0*BIN_SUN_EVE*SUN_EVE 57.0*BIN_SUN_NI8*SUN_NI8)<= 9000;

! Total viewership on Each Day; TOT_FRI_VIEW - ((490*BIN_FRI_MOR*FRI_MOR) + (500*BIN_FRI_AFT*FRI_AFT) + (756*BIN_FRI_EVE*FRI_EVE) + (750*BIN_FRI_NI8*FRI_NI8)) = 0; TOT_SAT_VIEW - ((540*BIN_SAT_MOR*SAT_MOR) + (550*BIN_SAT_AFT*SAT_AFT) + (880*BIN_SAT_EVE*SAT_EVE) + (820*BIN_SAT_NI8*SAT_NI8)) = 0; TOT_SUN_VIEW - ((625*BIN_SUN_MOR*SUN_MOR) + (570*BIN_SUN_AFT*SUN_AFT) + (840*BIN_SUN_EVE*SUN_EVE) + (800*BIN_SUN_NI8*SUN_NI8)) = 0; ! Total advertisement on each day; TOT_FRI_AD_AIR - (BIN_FRI_MOR*FRI_MOR + BIN_FRI_AFT*FRI_AFT + BIN_FRI_EVE*FRI_EVE + BIN_FRI_NI8*FRI_NI8) = 0; TOT_SAT_AD_AIR - (BIN_SAT_MOR*SAT_MOR + BIN_SAT_AFT*SAT_AFT + BIN_SAT_EVE*SAT_EVE + BIN_SAT_NI8*SAT_NI8) = 0; TOT_SUN_AD_AIR - (BIN_SUN_MOR*SUN_MOR + BIN_SUN_AFT*SUN_AFT + BIN_SUN_EVE*SUN_EVE + BIN_SUN_NI8*SUN_NI8) = 0; ! Maximum of 2 advertisement in 3 consecutive Slots; BIN_FRI_MOR + BIN_FRI_AFT + BIN_FRI_EVE <= 2; BIN_FRI_AFT + BIN_FRI_EVE + BIN_FRI_NI8 <= 2; BIN_FRI_EVE + BIN_FRI_NI8 + BIN_SAT_MOR <= 2; BIN_FRI_NI8 + BIN_SAT_MOR + BIN_SAT_AFT <= 2; BIN_SAT_MOR + BIN_SAT_AFT + BIN_SAT_EVE <= 2; BIN_SAT_AFT + BIN_SAT_EVE + BIN_SAT_NI8 <= 2; BIN_SAT_EVE + BIN_SAT_NI8 + BIN_SUN_MOR <= 2; BIN_SAT_NI8 + BIN_SUN_MOR + BIN_SUN_AFT <= 2; BIN_SUN_MOR + BIN_SUN_AFT + BIN_SUN_EVE <= 2; BIN_SUN_AFT + BIN_SUN_EVE + BIN_SUN_NI8 <= 2; ! Broadcaster BIN_FRI_EVE + BIN_SAT_MOR + BIN_SUN_AFT +

Constraints; BIN_FRI_NI8 <= 1; BIN_SAT_EVE <= 1; BIN_SUN_EVE <= 1;

! Nature of Decision Variable; @BIN(BIN_FRI_AFT); @BIN(BIN_SAT_AFT); @BIN(BIN_SUN_AFT); @BIN(BIN_FRI_NI8); @BIN(BIN_SAT_NI8); @BIN(BIN_SUN_NI8);

@BIN(BIN_FRI_MOR); @BIN(BIN_SAT_MOR); @BIN(BIN_SUN_MOR); @BIN(BIN_FRI_EVE); @BIN(BIN_SAT_EVE); @BIN(BIN_SUN_EVE); @GIN(FRI_AFT); @GIN(SAT_AFT); @GIN(SUN_AFT); @GIN(FRI_NI8); @GIN(SAT_NI8); @GIN(SUN_NI8); @GIN(FRI_MOR); @GIN(SAT_MOR); @GIN(SUN_MOR); @GIN(FRI_EVE); @GIN(SAT_EVE); @GIN(SUN_EVE); @GIN(TOT_FRI_VIEW); @GIN(TOT_SAT_VIEW); @GIN(TOT_SUN_VIEW); @GIN(TOT_FRI_AD_AIR); @GIN(TOT_SAT_AD_AIR); @GIN(TOT_SUN_AD_AIR); ! Non-Negativity Constraints; FRI_AFT >=0; SAT_AFT >=0; SUN_AFT >=0; FRI_NI8 >=0; SAT_NI8 >=0; SUN_NI8 >=0; FRI_MOR >=0; SAT_MOR >=0; SUN_MOR >=0; FRI_EVE >=0; SAT_EVE >=0; SUN_EVE >=0; TOT_FRI_VIEW >=0; TOT_SAT_VIEW >=0; TOT_SUN_VIEW >=0; TOT_FRI_AD_AIR >=0; TOT_SAT_AD_AIR >=0; TOT_SUN_AD_AIR >=0; ! Optimization Function Variable(z1) for Maximizing Expected ! Expected Conversion Rate is 1%; TOTAL_EXPECTED_REVENUE = (0.01 * 10.0) * ( (490*BIN_FRI_MOR*FRI_MOR) + (540*BIN_SAT_MOR*SAT_MOR) + + (500*BIN_FRI_AFT*FRI_AFT) + (550*BIN_SAT_AFT*SAT_AFT) + + (756*BIN_FRI_EVE*FRI_EVE) + (880*BIN_SAT_EVE*SAT_EVE) + + (750*BIN_FRI_NI8*FRI_NI8) + (820*BIN_SAT_NI8*SAT_NI8) +

Revenue; (625*BIN_SUN_MOR*SUN_MOR) (570*BIN_SUN_AFT*SUN_AFT) (840*BIN_SUN_EVE*SUN_EVE) (800*BIN_SUN_NI8*SUN_NI8) );

! Optimization Function Variable(z2) for Maximizing Expected Profit; TOTAL_EXPECTED_PROFIT = (TOTAL_EXPECTED_REVENUE) - (40*BIN_FRI_AFT*FRI_AFT + 50.0*BIN_FRI_NI8*FRI_NI8 + 37.5*BIN_FRI_MOR*FRI_MOR + 52.5*BIN_FRI_EVE*FRI_EVE) - (45*BIN_SAT_AFT*SAT_AFT + 55.0*BIN_SAT_NI8*SAT_NI8 + 42.5*BIN_SAT_MOR*SAT_MOR + 57.5*BIN_SAT_EVE*SAT_EVE) - (50*BIN_SUN_AFT*SUN_AFT + 57.0*BIN_SUN_NI8*SUN_NI8 + 47.5*BIN_SUN_MOR*SUN_MOR + 65.0*BIN_SUN_EVE*SUN_EVE);

4. Topline Model (Maximizing Revenue): Local optimal solution found. Objective value: Objective bound: Infeasibilities: Extended solver steps: Total solver iterations: Elapsed runtime seconds:

13456.50 13456.50 0.000000 391 2424 1.59

Model Class:

MIQP

Total variables: Nonlinear variables: Integer variables:

32 24 30

Total constraints: Nonlinear constraints:

53 21

Total nonzeros: Nonlinear nonzeros:

272 104

Model Title: = Revenue from Television Advertisement Optimisation Variable TOTAL_EXPECTED_REVENUE BIN_FRI_AFT FRI_AFT BIN_FRI_MOR FRI_MOR BIN_SAT_AFT SAT_AFT BIN_SAT_MOR SAT_MOR BIN_SUN_AFT SUN_AFT BIN_SUN_MOR SUN_MOR BIN_FRI_NI8 FRI_NI8 BIN_FRI_EVE FRI_EVE BIN_SAT_NI8 SAT_NI8 BIN_SAT_EVE SAT_EVE BIN_SUN_NI8 SUN_NI8 BIN_SUN_EVE SUN_EVE TOT_FRI_VIEW TOT_SAT_VIEW TOT_SUN_VIEW TOT_FRI_AD_AIR TOT_SAT_AD_AIR TOT_SUN_AD_AIR TOTAL_EXPECTED_PROFIT

Value 13456.50 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 0.000000 0.000000 1.000000 0.000000 1.000000 1.000000 1.000000 62.00000 0.000000 0.000000 0.000000 0.000000 1.000000 73.00000 1.000000 29.00000 0.000000 0.000000 46500.00 64240.00 23825.00 62.00000 73.00000 30.00000 4458.500

Reduced Cost 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.1000000 -0.1000000 -0.1000000 0.000000 0.000000 0.000000 0.000000

Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

Slack or Surplus 13456.50 42.00000 46.00000 57.00000 0.000000 0.000000 63.00000 10.00000 9.000000 8.500000 1300.000 1562.500 4799.500 2.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 62.00000 0.000000 29.00000 0.000000 0.000000 1.000000 0.000000 73.00000 0.000000 46500.00 64240.00 23825.00 62.00000 73.00000 30.00000 0.000000 0.000000

Dual Price 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.1000000 -0.1000000 -0.1000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000

4. Reports for Topline Model (Maximizing Revenue): Table 5: Number of airs in different slots

Table 6: If aired in any time slot

Friday

Saturday

Sunday

Total Airs

Slot / Day

Friday

Saturday

Sunday

Morning

0

0

1

1

Morning

0

0

1

Afternoon

0

0

0

0

Afternoon

1

1

1

Evening

0

73

0

73

Evening

0

1

0

Night

62

0

29

91

Night

1

0

1

Total

62

73

30

165

Slot / Day

Table 7: Number of airs in different halves of the day Number of Airs

Maximum Number of Airs allowed

Unused Slots

Daytime

0

42

42

Nighttime

62

62

0

Daytime

0

46

46

Nighttime

73

73

0

Daytime

1

58

57

Nighttime

29

93

64

Day

Time of Day

Friday Saturday Sunday

Table 8: Daily Budget Usage Day

Friday

Time of Day

Number of Airs

Cost of each Air (in Thousands)

Total Cost (Thousands)

Morning

0

37.5

0

Afternoon

0

40

0

Evening

0

52.5

0

Night

62 0

50 42.5

3100

0 73

0 4198 0

Morning

0 1

45 57.5 55 47.5

48

Afternoon

0

50

0

Evening

0

65

0

Night

29

57

1653

Morning Saturday

Sunday

Total

Afternoon Evening Night

Maximum Spending Limit (Thousands)

Remaining Budget (Thousands)

4400

1300

5760

1563

6500

4800

9000

2

0

8998

5. Bottomline Model (Maximizing Profit): Local optimal solution found. Objective value: Objective bound: Infeasibilities: Extended solver steps: Total solver iterations: Elapsed runtime seconds:

4458.500 4458.500 0.000000 522 2850 2.03

Model Class:

MIQP

Total variables: Nonlinear variables: Integer variables:

32 24 30

Total constraints: Nonlinear constraints:

53 21

Total nonzeros: Nonlinear nonzeros:

272 104

Model Title: = Revenue from Television Advertisement Optimization Variable TOTAL_EXPECTED_PROFIT BIN_FRI_AFT FRI_AFT BIN_FRI_MOR FRI_MOR BIN_SAT_AFT SAT_AFT BIN_SAT_MOR SAT_MOR BIN_SUN_AFT SUN_AFT BIN_SUN_MOR SUN_MOR BIN_FRI_NI8 FRI_NI8 BIN_FRI_EVE FRI_EVE BIN_SAT_NI8 SAT_NI8 BIN_SAT_EVE SAT_EVE BIN_SUN_NI8 SUN_NI8 BIN_SUN_EVE SUN_EVE TOT_FRI_VIEW TOT_SAT_VIEW TOT_SUN_VIEW TOT_FRI_AD_AIR TOT_SAT_AD_AIR TOT_SUN_AD_AIR TOTAL_EXPECTED_REVENUE

Value 4458.500 0.000000 0.000000 1.000000 1.000000 1.000000 1.000000 0.000000 0.000000 1.000000 0.000000 1.000000 1.000000 1.000000 62.00000 0.000000 0.000000 0.000000 0.000000 1.000000 73.00000 1.000000 29.00000 0.000000 0.000000 46500.00 64240.00 23825.00 62.00000 73.00000 30.00000 13456.50

Reduced Cost 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 5.485714 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.2346939E-01 -0.1818182E-01 -0.4571429E-01 0.000000 0.000000 13.57143 0.000000

Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

Slack or Surplus 4458.500 42.00000 46.00000 57.00000 0.000000 0.000000 63.00000 10.00000 9.000000 8.500000 1300.000 1562.500 4799.500 2.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 2.000000 1.000000 1.000000 1.000000 1.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000 0.000000 62.00000 0.000000 29.00000 1.000000 0.000000 1.000000 0.000000 73.00000 0.000000 46500.00 64240.00 23825.00 62.00000 73.00000 30.00000 0.000000 0.000000

Dual Price 1.000000 0.000000 0.000000 0.000000 7.397959 14.50000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.2346939E-01 -0.1818182E-01 -0.4571429E-01 0.000000 0.000000 13.57143 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 1.000000 1.000000

6. Reports for Bottomline Model (Maximizing Profit): Table 9: Number of airs in different slots

Table 10: If aired in any time slot

Slot / Day

Friday

Saturday

Sunday

Total Airs

Morning

1

0

1

2

Afternoon

0

1

0

1

Evening

0

73

0

73

Night

62

0

29

91

Total

63

74

30

167

Table 11: Number of airs in different halves of the day

Daytime

1

Maximum Number of Airs allowed 42

Nighttime

62

62

0

Daytime

1

46

45

Nighttime

73

73

0

Daytime

1

58

57

Nighttime

29

93

64

Day

Time of Day

Friday Saturday Sunday

Number of Airs

Unused Slots 41

Table 12: Daily Budget Usage Day

Friday

Time of Day

Number of Airs

Cost of each Air (in Thousands)

Total Cost (Thousands)

Morning

1

37.5

38

Afternoon

0

40

0

Evening

0

52.5

0

Night

62 0

50 42.5

3100

1 73

45 57.5 55

45 4198 0

47.5

48

Morning Saturday

Sunday

Total

Afternoon Evening Night

Maximum Spending Limit (Thousands)

Remaining Budget (Thousands)

4400

1263

5760

1518

6500

4800

9000

-81

0

Morning

0 1

Afternoon

0

50

0

Evening

0

65

0

Night

29

57

1653 9081

6. Conclusion and Observations