Scheduling Jobs on Unrelated Machines with Job Splitting and Setup Resource Constraints for Weaving in Textile Manufacturing

Abstract

This work considers the production scheduling of the weaving process in a real-life textile industry, where a set of jobs - linked to the production of a fabric type and accompanied by a quantity - arrive over time and have to be processed (woven) by a set of parallel unrelated machines (looms) with respect to their strict deadlines (delivery dates), under the goal of makespan minimization. A number of critical job and machine properties demonstrate the challenging nature of weaving scheduling, i.e., a) job splitting: each order’s quantity is allowed to be split and processed on multiple machines simultaneously, b) sequence-dependent setup times: the setup time between any two orders j and k is different than setup time between jobs k and j on the same machine and c) setup resource constraints: the number of setups that can be performed simultaneously on different machines is restricted due to a limited number of setup workers. We propose a MILP formulation that captures the entire weaving process. To handle large real instances, while also speeding up an exact solver on smaller ones, we propose two heuristics that perform job-splitting and assignment of jobs to machines either greedily or by using a relaxed version of our MILP model, respectively. We evaluate the impact of our approach on real datasets under user-imposed time limits and resources (machines, workers) availability.