Hybrid algorithms for the earliness–tardiness single-machine multiple orders per job scheduling problem with a common due date

Department of Mathematics and Computer Science, University of Hagen, 58097 Hagen, Germany.

^* Corresponding author: Lars.Moench@fernuni-hagen.de

Received: 31 May 2017
Accepted: 27 April 2018

Abstract

In this paper, we study an earliness–tardiness scheduling problem for a single machine that is motivated by process conditions found in semiconductor wafer fabrication facilities (wafer fabs). In modern 300-mm wafer fabs, front opening unified pods (FOUPs) transfer wafers. The number of FOUPs is limited to avoid a congestion of the Automated Material Handling System. Several orders can be grouped in one FOUP. A nonrestrictive common due date for all the orders is assumed. Only orders that belong to the same family can be processed together in a single FOUP at the same time. We present a Mixed Integer Linear Programming (MILP) formulation for this problem. Moreover, we show that this scheduling problem is NP-hard. We propose several simple heuristics based on dispatching rules and assignment strategies from bin packing. Moreover, genetic algorithms are designed that assign the orders to the set of early and tardy orders, respectively. In addition, a random key genetic algorithm (RKGA) is described that proposes order sequences. The different algorithms are hybridized with job formation and sequencing heuristics. A more specialized algorithm that is based on the generalized assignment problem is presented for the special case of a single order family. Results of computational experiments based on randomly generated problem instances are presented. They demonstrate that the genetic algorithms perform well with respect to solution quality and computing time under a broad range of experimental conditions.