Optimal Factory Scheduling using Stm

Generating optimal production schedules for manufacturing facilities is an area of great theoretical and practical importance. During the last decade, an effort has been made to reconcile the techniques developed by the AI and OR communities. The work described here aims to continue in this vein by showing how a class of well-defined stochastic scheduling problems can be mapped into a general search procedure. This approach improves upon other methods by handling the general case of multidimensional stochastic costs We consider scheduling in a multi-product, single machine factory with sequence independent setup times. The machine processing and setup times are random variables. The factory is faced with a set of jobs that incur a late penalty if not completed by their deadlines, The optimization problem is to generate a static schedule that minimizes the expected penalty. Given that factory performance is stochastic, it is easy to show that an optimal solution to a deterministic model using the expected run times will lead to sub-optimal schedules. Instead, we tackle the stochastic problem directly using an algorithm called Stochastic Dominance A* (Wellman, Ford, & Larson 1995). SDA* is designed for problems with path-dependent, stochastic operator costs. In SDA”, paths can be pruned only if their path cost is stochastically dominated by an already discovered path to the same state. For heuristics to be admissibile, the actual remaining cost must be stochastically dominated by the heuristic estimate. In addition, we impose a benign consistency condition to retain validity. Our work extends SDA* to the scheduling problem. We formulate the problem as a state space search where the state is defined by the current inventory, the current machine setup, and the orders that have been filled. Three classes of operators are allowed. Make operators increment the inventory of the state. Ship operators decrement the inventory and change orders from unfilled to filled. Setup operators change the current product that can be built.