Weighted tardiness minimization for unrelated machines with sequence-dependent and resource-constrained setups

TL;DR

This paper addresses a complex scheduling problem involving unrelated machines, sequence-dependent setups, and resource constraints, proposing a combined MILP, metaheuristics, and CP approach to minimize total weighted tardiness effectively.

Contribution

It introduces a novel problem variant with practical relevance, develops a relaxed MILP for bounds, and extends heuristics with CP to handle complex constraints efficiently.

Findings

Metaheuristics with MILP bounds outperform in various instances.

The approach significantly reduces tardiness in practical textile manufacturing scenarios.

Different methods show strengths depending on problem parameters.

Abstract

Motivated by the need of quick job (re-)scheduling, we examine an elaborate scheduling environment under the objective of total weighted tardiness minimization. The examined problem variant moves well beyond existing literature, as it considers unrelated machines, sequence-dependent and machine-dependent setup times and a renewable resource constraint on the number of simultaneous setups. For this variant, we provide a relaxed MILP to calculate lower bounds, thus estimating a worst-case optimality gap. As a fast exact approach appears not plausible for instances of practical importance, we extend known (meta-)heuristics to deal with the problem at hand, coupling them with a Constraint Programming (CP) component - vital to guarantee the non-violation of the problem's constraints - which optimally allocates resources with respect to tardiness minimization. The validity and versatility of employing different (meta-)heuristics exploiting a relaxed MILP as a quality measure is revealed by our extensive experimental study, which shows that the methods deployed have complementary strengths depending on the instance parameters. Since the problem description has been obtained from a textile manufacturer where jobs of diverse size arrive continuously under tight deadlines, we also discuss the practical impact of our approach in terms of both tardiness decrease and broader managerial insights.