A system called CineSelect uses a binary integer programming model to help theat

Question

A system called CineSelect uses a binary integer programming model to help theatre managers decide which movies to show on a weekly basis at a movie theatre with multiple screens. Managers at a local theatre in Ottawa would like to investigate the potential of using a similar scheduling system and have selected their downtown two-screen location for a pilot test of the system. They would like to develop an integer binary programming model to help schedule movies for the next four weeks. Six movies are available and arc listed in the table below. Also, in this table are shown: the first week each movie is available, the last week each movie can be shown, and the maximum number of weeks that each movie can run. The overall viewing schedule for the theatre is composed of the individual schedules for each of the six movies. For each movie, a schedule must be developed that specifies the week the movie starts and the number of consecutive weeks it will run. For instance, one possible schedule for movie B is for it to start in week 1 and run for two weeks. Theatre policy requires that once a movie starts, if must be shown in consecutive weeks. It cannot be stopped and restarted again To represent the schedule possibilities for each movie, the following decision variables were developed. A_ij = {1 if movie A is scheduled to start in week i and run f or i weeks 0 otherwise B_ij = {1 if movie B is scheduled to state in week i and run f or j weeks 0 otherwise F_ij = {1 if movie F is scheduled to state in week i and run f or j weeks 0 otherwise For example, E_32 = 1 means that the schedule selected for movie E is to begin in week 3 and run for 2 weeks. For each movie, a separate variable is given for each possible schedule. a) Three possible schedules are associated with movie A (i.e. movie 1), list the decision variables that represent these schedules. b) Write a constraint requiring at most one schedule to be selected for movie 1. c) Write a constraint requiring that one schedule and only one must be selected for movie 5. d) What restricts the number of movies that can be shown in week 1? Write a constraint that restricts the number of movies selected for viewing in week 1. e) Write a constraint that restricts the number of movies selected for viewing in week 3.

Explanation / Answer

Answers:

a) The three schedules available for movie A are:

start in week 1 and run for 1 week, start in week 1 and run for 2 weeks and start in week 2 and run for 1 week.

Hence the decision variables are A11, A12 and A21 .

b) The constraint is A11 + A12 + A21 <= 1.

c) The first week availability of movie E is week 3 and it can be run for 3 weeks. Hence the constraint is

   E31 + E32 + E33 + E41 + E42 + E43 + E51 + E52 + E61 <= 1

d) Only 2 screens are available in week 1.

The movies available on week 1 are A,B and C.

Hence the constraint is    A11 + A12 + B11+ B12 + B13 +C11 <= 2

e) B13 + B22 + B31 + D22 + D31 + E 31 + E32 + E33 + F31 + F32 + F33 <=2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.