Business Analytics and Data Analysis Assignments

Comm 414

Data Visualization

Group Assignment 3: Theatre Management

Team CHAMN

Amanda Bamford - 12074143

Monica Dhaliwal - 31689136

Nunu Ding - 30274147

Hayley Moeller - 24733140

Cailey Zadunayski - 46878138

For

Dr. Chunhua Wu

DUE: November 21st, 2016

QUESTION I: Understanding Revenue

1. How many possible combinations are there? (2 points)

For each of the 5 theatres, there are 4 possible states:

1. Doctor Strange
2. The Accountant
3. Arrival
4. Nothing/Closed

From this, we can calculate the total number of combinations as:

4x4x4x4x4 = 1024

However, not all of these are valid combinations because of the constraints.  The next step is determining how many of these combinations are not true options.

The first thing that we must remove is any situation where theatre C, D or E are playing Doctor Strange, but theatre A and/or B is not.

To calculate this we take the probability theatre A is not playing Doctor Strange, times the probability theatre B is not playing Doctor Strange, times the probability theatre C/D/E is playing Doctor Strange.

Probability C playing Doctor Strange when shouldn’t: (.75)(.75)(.25) (1024)

Probability D playing Doctor Strange when shouldn’t: (.75)(.75)(.25) (1024)

Probability E playing Doctor Strange when shouldn’t:  (.75)(.75)(.25) (1024)

Total = 432 invalid combinations

1025 - 432 = 592

Then, we must subtract the one combinations where all 5 theaters are closed since we know that this is not allowed.

592 - 1 = 591 combinations

2. Sarah has come up with one schedule as follows, please help her to understand: (1 point)

• What is the expected revenue from movie ticket sales?

The expected revenue is $5,885.

• Sarah has a target revenue of $6,000. What is the probability that she will meet her target with this schedule?

The probability that she will meet her target with this schedule is 36.26%.

3. Can you come up with another schedule that would improve the expected revenue? (2 points)

The change that we made makes theatre C and E play Arrival while theatre D plays The Accountant.  The reason we thought to make that change is that there is 40% interest in Arrival and 20% interest in The Accountant.  Therefore, we were thinking that the ratio between the two should be closer to 1:2.  In the old schedule, the ratio was 160:50 for seats. We are changing it to be 130:80.

• What is the expected revenue from your schedule? What is the percentage of improvement from your schedule?

Our change is able to increase expected revenue from $5,885 to $5,906.  When the simulation is expanded to an n of 1,000,000 we get this improvement consistently. The percentage increase in expected revenue is 0.35%. However, the probability barely changed.  In both situations it stayed at approximately 35%.

• How likely is Sarah to meet her target of $6,000 based on your schedule?

The likelihood is 33.26%.

QUESTION II: Schedule Optimization

1. Please formulate the decision problem as a mathematical programming problem. (1 point)

• Write specific mathematical programming problem the question belongs to?

Binary programming

• Write down the objective function.

        Revenue = (120)*(19.99) + (80)*(12.99) + (40)*(19.99)x1 + (40)*(12.99)x2 + (40)*(12.99)x3 + (80)*(12.99)x4 + (80)*(12.99)x5 + (50)*(12.99)x6 + (80)*(12.99)x7 + (80)*(12.99)x8 + (50)*(12.99)x9

= 3438 + (40)*(19.99)x1 + (40)*(12.99)x2 + (40)*(12.99)x3 + (80)*(12.99)x4 + (80)*(12.99)x5 + (50)*(12.99)x6 + (80)*(12.99)x7 + (80)*(12.99)x8 + (50)*(12.99)x9

• Write down the constraints.

xi = {0,1}

x4 + x5 + x6 <= 1

x7 +x8 + x9 = 1

x1 + x4 + x7 <= 1

x2 + x5 + x8 <= 1

x3 + x6 + x9 <= 1

2. Solve the mathematical programming problem using R. (2 points)

• Write out the R code.

        Please refer to section 2.1 in our R script.

• What is the solution? Put your solution into a schedule.

There are two solutions. Because the remaining demand for Arrival and The Accountant is the same (80 people), both theatres B and D can hold that demand, and the ticket price for both movies is the same ($12.99), there is no difference as to which theatre (B or D) plays which movie (Arrival or The Accountant.)

Solution 1:

OR

Solution 2:

• What is the total revenue from your optimized schedule?

Revenue = $3,438 + $2,598 = $6,036

3. Discuss what you would do if the demand is uncertain, as in Question I of this assignment. (1 point)

• Just outline your discussion, you do not need to use R to solve it

As a starting point, we would assume that they have similar demand.  For example, if there are four movies, we would estimate that 25% are interested in each movie.  This would be an Occam’s Razor approach as all forecasting is only an estimation.  However, we would keep close watch over the ticket sales so that we could quickly respond to variations between the shows and optimize our schedule.

We could also look into other variables that would potentially affect demand; for example, marketing, budget of a film, or the name recognition for their actors.  This would be similar to how the weather data was collected for Assignment 2.  Linear regression could be performed using these variables, and if the ticket sales seem to match this prediction, we can adjust our schedule accordingly.