Optimal Factory Scheduling using Stochastic Dominance A*

We examine a standard factory scheduling problem with stochastic processing and setup times, minimizing the expectation of the weighted number of tardy jobs. Because the costs of operators in the schedule are stochastic and sequence dependent, standard dynamic programming algorithms such as A* may fail to find the optimal schedule. The SDA * (Stochastic Dominance A*) algo­ rithm remedies this difficulty by relaxing the pruning condition. We present an improved state-space search formulation for these prob­ lems and discuss the conditions under which stochastic scheduling problems can be solved optimally using SDA *. In empirical testing on randomly generated problems, we found that in 70%, the expected cost of the opti­ mal stochastic solution is lower than that of the solution derived using a deterministic ap­ proximation, with comparable search effort. 1 INTRODUCTION Generating production schedules for manufacturing fa­ cilities is a problem of great theoretical and practical importance. The Operations Research and Artificial Intelligence communities have studied various versions of this problem. During the last decade, an effort has been made to understand the relationships between the techniques developed by these two fields. The work described here aims to continue in this vein by showing how a class of well-defined scheduling problems can be mapped into a general search procedure. In particular, we are concerned with generating static schedules over a limited horizon in a multi-product fac­ tory with a single, bottleneck machine whose perfor­ mance is specified by stochastic processing times and sequence-independent, stochastic setup times. We re­ fer to this model as the stochastic lot-sizing problem. The demand on the factory is specified by a set of or­ ders for products with deadlines and tardy penalties. The challenging scheduling problems occur when de­ mand is greater than capacity. Although uncertainty in processing times is widely ac­ knowledged, few approaches produce strictly optimal F-�hedules in stochastic lot-sizing problems. We present a genera] approach based on SDA * (Stochastic Domi­ nance A*), a state-space search algorithm designed for uncertain, path-dependent costs (Wellman, Ford, and Larson 1995). To apply SDA *to scheduling problems, we must extend the algorithm to handle multidimen­ sional cost structures. In the next section we provide motivation for the prob­ lem. Section 3 reviews SDA *, and Section 4 describes the formulation of the factory scheduling problem in detail, including the multidimensional extensions to SDA *. In Section 5 we discuss the details of our im­ …