Movie Shoot Scheduling Problem
Problem specification
for the project of the course
Advanced Scheduling Systems (2015-16)
version 1.1 (Feb 3, 2016)
We consider a simplified version of the Movie Shoot Scheduling Problem defined by Bomsdorf and Derigs [1],
which is an extension of the Talent Scheduling problem proposed by Cheng et al [2]. Instances are artificial and
created by the generator developed by Morgante Piano [3].
A movie is composed by a set of scenes. The shooting of the movie is obtained by the sequential shooting of
every scene. The order of shooting is not influenced by the order in the final version of the movie, but by economic
reasons related to costs of actors and locations. Finding the optimal sequence of shooting is the subject of the
Movie Shoot Scheduling Problem.
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Problem formulation
The main features of the problem are:
Locations: venues where scenes take place; each location has a fixed cost for shooting a sequence of scenes in the
location.
Actors: set of talents playing in the movie; each actor has an associated daily cost.
Scenes: atomic elements of shooting, that take place in a location and involves a set of actors; each scene has a
duration in terms of number of working days.
Precedences: between two scenes there might be a precedence relation, stating that a scene must be shot before
the other one.
The problem consists in finding the sequence of scenes that satisfies the precedence constraints and minimizes
the following costs.
LocationCost: For any sequence of consecutive scenes in one single location, the cost of the location is added,
independently of the length of the sequence. Actually, given that any location must be visited at least one,
we consider only the cost of the sequences excluding the first one to that location.
ActorCost: The cost of the actor is the length (in number of days) of the sequence of scene going from the first one
in which the actor appears to his/her last one (extremes included). The cost is paid also if the actor is not
taking part to the scene, because it is assumed that the actor remains in the set between scenes that he/she
has to play. Similarly to LocationCost, we actually consider only the extra cost, which is the cost of the scenes
in which the actor does not play.
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File formats
The input files are provided in MiniZinc data format, with the structure that can be deduces from the following
example.
NumActors = 4;
NumScenes = 10;
NumLocations = 5;
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NumPreferences = 2;
ActorCost = [14, 4, 10, 6];
LocationCost = [0, 32, 26, 33, 25];
SceneDuration = [5, 3, 3, 5, 3, 3, 2, 5, 3, 1];
SceneLocation = [1, 2, 4, 0, 2, 4, 2, 3, 4, 1];
Presence = [|1, 0, 0, 0, 1, 1, 0, 1, 0, 1
|1, 1, 1, 0, 0, 1, 0, 1, 1, 1
|1, 0, 0, 1, 0, 1, 0, 1, 0, 0
|1, 1, 1, 0, 1, 0, 1, 1, 1, 0|];
Precedences = [|8, 5
|3, 2|];
The Presence matrix states if an actor plays (value 1) or not (value 0) in a scene.
The output file format is in the form of a MiniZinc array, containing a permutation. For example, the array [3,
1, 2, 8, 5, 7, 9, 0, 4, 6] represents a solution (notice that indexes of both input and output files start from
0).
The given solution does not violate any precedence constraint and has a total cost of 150, divided into 26 location
cost and 124 actors cost.
The costs are highlighted by Table 1 that shows the location of the scenes in the sequence and the participants.
We see that the sequence returns to location 2, for scenes 4 and 6 after having been there earlier for scene 1. In
addition, actor 2 is unnecessarily on stage for scenes 1, 2, 8, and 9, and actor 3 is unnecessarily on stage for scenes
5 and 9.
The solution [3, 2, 8, 5, 7, 0, 9, 4, 1, 6], shown in Table 2, also does not violate constraints, it has a
cost equal to 116, and is optimal. It has no location costs and 6 scenes with an unnecessary actor on stage.
Scene
Location
Actor 0
Actor 1
Actor 2
Actor 3
3
0
X
-
1
2
X
X
2
4
X
X
8
4
X
X
5
4
X
X
X
-
7
3
X
X
X
X
9
1
X
X
-
0
1
X
X
X
4
2
X
X
6
2
X
Table 1: Graphical representation of the solution [3, 1, 2, 8, 5, 7, 9, 0, 4, 6]
Scene
Location
Actor 0
Actor 1
Actor 2
Actor 3
3
0
X
-
2
4
X
X
8
4
X
X
5
4
X
X
X
-
7
3
X
X
X
X
0
1
X
X
X
9
1
X
X
-
4
2
X
X
1
2
X
X
6
2
X
Table 2: Graphical representation of the (optimal) solution [3, 2, 8, 5, 7, 0, 9, 4, 1, 6]
References
[1] Felix Bomsdorf and Ulrich Derigs. A model, heuristic procedure and decision support system for solving the
movie shoot scheduling problem. r Spectrum, 30(4):751–772, 2008.
[2] T. Cheng, J. Diamond, and B. Lin. Optimal scheduling in film production to minimize talent hold cost. Journal
of Optimization Theory and Applications, 79(3):479–492, 1993.
[3] Sara Morgante Piano. Un generatore pseudocasuale di istanze per il talent scheduling problem. Bachelor thesis,
University of Udine. In preparation, in Italian, 2015.
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