Branch and price for nonlinear production-maintenance scheduling in complex machinery

TL;DR

The paper tackles integrated production-maintenance scheduling for complex machinery where each machine is a structure of interacting components whose maintenance and degradation influence production. It presents a general mixed-integer nonlinear programming model with nonlinear degradation functions and maintenance implications, and develops a Dantzig-Wolfe reformulation solved by Branch-and-Price, augmented with aggregation of identical subproblems and acceleration techniques. Computational experiments compare the extended DW approach to solving the compact formulation directly, showing decomposition improves performance on larger instances, especially for infeasibility detection and solution times, while the compact model can excel on easy cases. The work contributes a scalable exact method for MINLP production-maintenance problems and discusses practical implementation aspects and directions for future research, including more refined extended formulations and diversified maintenance action types.

Abstract

This paper proposes a mixed-integer nonlinear programming approach for joint scheduling of long-term maintenance decisions and short-term production for groups of complex machines with multiple interacting components. We introduce an abstract model where the production and the condition of machines are described by convex functions, allowing the model to be employed for various application areas fitting the scheme. We develop a branch-and-price algorithm to solve this problem, enhanced with acceleration techniques to find primal solutions and reduce the number of pricing rounds. An experimental comparison of this approach to solving the compact formulation directly demonstrates the benefit of the decomposition approach, in particular in larger instances.