Minimizing sequence-dependent setup costs in feeding batch processes under due date restrictions

Abstract

This paper addresses the minimization of sequence-dependent setup costs in feeding batch processes. Since feeding batch processes often supply subsequent time-critical stages with modules, hard due date restrictions have to be met. It is common that feeding batch processes possess a specific structure of setup costs that are proportional to resulting machine state differences. If each job has a different batch type, the integration of hard due dates leads to a problem that is equivalent to a specific variant of the Line-TSPTW with general processing times and deadlines. We show that this well-known problem, whose complexity status has been unknown for a long time, is binary $\mathcal{NP }$-hard. Although the more relevant version with a constant number of batch types is known to be strongly polynomial, no practically applicable exact solution method can be found in the literature. Therefore, this paper proposes new solution algorithms. Specifically, Dynamic Programming and Branch&Bound approaches are developed. By making use of a modified problem definition, a new enumeration scheme, and a specifically designed dominance rule, even complex problem instances with up to 200 jobs are optimally solved by a new best-first Branch&Bound algorithm. Apart from a detailed complexity analysis, the efficiency of the proposed approaches is validated by computational experiments.