A stochastic programming approach to scheduling in TAC SCM

Abstract

In this paper, we combine two approaches to handling uncertainty: we use techniques for finding optimal solutions in the expected sense to solve combinatorial optimization problems in an online setting. The problem we address is the scheduling component of the Trading Agent Competition in Supply Chain Management (TAC SCM) problem, a combinatorial optimization problem with inherent uncertainty (see www.sics.se/tac/). This problem is formulated as a stochastic program, and is solved using the sample average approximation (SAA) method in an online setting to find today's optimal schedule, given probabilistic models of the future. This optimization procedure forms the heart of Botticelli, one of the finalists in the TAC SCM 2003 competition. Two sets of experiments are described, using one and two days' worth of information about the future. In the two day experiments (using one day's worth of information about the future), it is shown that SAA outperforms the expected value method, which solves a deterministic variant of the problem assuming all stochastic inputs have deterministic values equal to their expected values. In the three day experiments (using two days' worth of information about the future), it is shown that SAA with look ahead outperforms greedy SAA. This approach generalizes to N days of lookahead, and since the problem setting is one of online optimization, the benefits of two day lookahead accrue rapidly.