On a stochastic sequencing and scheduling problem

Abstract

We present a framework for solving multistage pure 0–1 programs for a widely used sequencing and scheduling problem with uncertainty in the objective function coefficients, the constraint matrix and the right-hand side. The problem has the following form: given a set of operations to be executed along a time horizon, find a schedule to minimize a function included by the expected operations cost over the scenarios under consideration, subject to a set of constraints. Typical elements are: limited availability of the resources, multiperiod operations, subsets of operations with exclusivity and implicative constraints, precedence relationships in the execution of the operations, etc. The stochasticity is in the resources’ consumption by the operations, their availability and the operations cost along the time horizon. A multistage scenario analysis with complete recourse is used. Given the high dimensions of the problem and its combinatorial nature, it is not realistic to obtain the optimal solution for the problem. Instead, we present the so-called Fix-and-Relax Coordination algorithmic framework to exploit the characteristics of the non-anticipativity constraints for each scenario group in the stochastic model. This exploitation basically consists of selectively exploring the nodes of the branching trees in which the branch-and-bound tree is decomposed while the non-anticipativity constraints are relaxed. The algorithm is specifically designed for coordinating and reinforcing the node pruning, and the branching node and variable selection at each branching tree, such that the non-anticipativity constraints are satisfied. Some computational experience is reported.