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A live interactive narrative (LIN) is an experience where multiple players take on fictional roles and interact with real-world objects and actors to participate in a pre-authored narrative. Temporal properties of LINs are important to its viability and aesthetic quality and hence deserve special design consideration. In this paper, we tackle the largely overlooked problem of scheduling a multiplayer interactive narrative and propose the Live Interactive Narrative Scheduling Problem (LINSP), which handles reasoning under temporal uncertainty, resource scheduling, and non-linear plot choices. We present a mixed-integer linear programming formulation of the problem and empirically evaluates its scalability over large narrative instances.

In this paper, we consider an assembly scheduling problem (ASP) with tree-structured precedence constraints. In our problem, there are a number of work centers. Each work center contains a number of machines of the same functionality. The job to be processed via this system is a job with tree-structure precedence constraints. Each operation in the job has a designated work center. We propose a mixed integer linear programming formulation and solve the problem with a Lagrangian relaxation (LR) approach. We solve the subproblems of the LR problem via a heuristic method and generate feasible solutions via a randomized list scheduling algorithm. Near-optimal results are obtained and the computational time is within a few seconds for problems with size up to 20 machines and 300 operations.Note to Practitioners-Most industrial products are complex assemblies made up of multiple manufactured products-organized as Bills-Of-Materials (BOMs)-that are produced in a shared manufacturing facility with possibly multiple functionally identical machines. There are a few rigorous approaches to deal with these kinds of problems in the literature. The job-shop scheduling problem has been extensively addressed, but these problems do not provide for any relationship between the multiple manufactured parts. In an assembly scheduling problem, the completion time of a child component becomes the release time of the parent part; hence, the multiple jobs become connected in a tree structure defined by the BOM. The second aspect that has been less considered in the scheduling literature is multiple, functionally identical machines-a common occurrence in industry. This paper takes on these two challenges and solves this problem using a LR approach and associated heuristics. Industrial strength problems of about 300 operations and 10 work centers are solved in a few seconds using this approach to near-optimality, while commercial strength mixed integer programming solvers are unable to find useful solutions in an hour.Index Terms-Assembly scheduling, Lagrangian relaxation (LR), makespan, parallel machine scheduling, randomized algorithm, subgradient search.