Dynamic location of modular manufacturing facilities with relocation of individual modules

Meeting highly variable product demands in a cost-efficient manner is an essential task for the chemical industry. Small-scale, modular, and mobile production units allow for a more agile response to spacial and temporal changes in demand while reducing the need of building new units. In this work, we present a generic mixed-integer linear programming (MILP) framework for determining optimal location and relocation of mobile production modules given time-varying demands. We introduce a new metric, the value of module mobility, to quantify the economic benefits of mobile production modules, and we demonstrate how it changes as a function of various economic parameters. Moreover, multiple different solution methods are developed to solve large instances of this dynamic modular and mobile facility location problem. First, we reformulate the original MILP by adding auxiliary variables which track the numbers of modules active at each site at any given time. This augmented formulation can be solved either directly using an off-the-shelf MILP solver, using the same solver but with priority branching on the auxiliary variables, or applying a branch-and-price algorithm. In the proposed branch-and-price algorithm, pricing subproblems for different time periods are solved separately and in parallel to generate new columns for the restricted master problem. Results from an extensive computational study show that solving the full-space augmented formulation is best when the number of time periods is small; however, the branch-and-price algorithm becomes superior for instances with a large number of time periods.