Motion Picture Distribution

Unified Artistos Corporation (UAC) is a distributor and exhibitor of motion pictures. They not only distribute new films to independent movie houses, but own a circuit of theaters on which films are shown. The Southwest Division of UAC is a typical locally operated film distribution center. They are responsible for the acquisition of individual films for showing at the 11 UAC theaters in the Dallas-Ft. Worth metroplex. The metroplex is divided into a series of districts, each with different demographics and a district manager.

In each month, approximately 10 to 15 new movies are released by film makers and are assigned to the 50 screens at the districts' 12 theaters. The volume increases to around 25 films per month in the summer.

As new films are released, they are screened by the district managers and rated according to their perceived acceptance by the audiences of each theater. The ratings are used to compute an estimated box office gross for a given film at a given theater in a normal day, as follows: estimated daily box office gross = (rating)(seating capacity)(average ticket price).

Model Considerations

Movie houses, or theaters, typically have more than one screen, and each screen has a certain capacity reflecting the number of associated seats. Also, for each movie in upcoming release there will be a limited number of prints available, thereby restricting the number of screens which can show it simultaneously (since one print is needed for each screen on which the film is shown). The following information is available:

1. For each theater we know:
   1. The number of screens and the capacity of each.
   2. The average ticket price.
2. For each upcoming movie we know:
   1. The number of prints available.
   2. Any special visual/sound system requirements (Dolby/THX sound, 70mm projector, etc.) These will be used if available, but are not required for showing.  
   3. The average district-manager's rating for that movie at each theater.
   4. The week in which it will become available for showing.
   5. The percentage change in rating for each successive week that the film is shown at a particular theater (i.e., the rating decreases only at those theaters that showed the film in the previous week).  

Small Example

Consider a situation where there are three theaters, A, B, and C, with two screens apiece. Individual theater and screen information is as follows:

There are six new movies coming available in the first two weeks of May. Their ratings, and availabilities are as follows.

Assignment

1. Using the data from the small example, formulate a pure network model to maximize the total daily box-office gross for all theaters combined over a two-week period (ignore considerations 2b and 2e). Assume that each movie can be shown on only one screen in a given theater. Can each week's problem be solved as a separate model? Why or why not?
2. How could consideration 2b be incorporated into the model? Would your answer be different if Dolby/THX was required for showing a Dolby/THX film, as opposed to simply attracting more people if it was used?
3. Is it possible to include consideration 2e into your model? Explain your reasoning.