Abstract
When watching plays, concerts, or some shows, the distance and the angle of the sight line from the audience to performers on the stage are major factors affecting the utility of the audience. The audience prefer to watch performers as close as possible and from the front as much as possible. We describe a two-dimensional region (theater hall) consisting of congruent square cells, and assign each cell to the facility (stage) or demand (audience seat). We construct a model that determines desirable location and shape of a facility for audience. We develop a heuristic method for the proposed problem and apply it to several shapes including the square, the trapezoidal, and the circular region. By analyzing the obtained local optimal solutions, when we place a large emphasis on the angle of the sight line, a facility with an elongated shape is placed at the edge of the region. Contrarily, when we emphasize the distance utility more strongly, a facility with a rounded shape is arranged in the center of the region.
