Integrated Job Scheduling with Parallel-Batch Processing and Batch Deliveries

Abstract

This paper studies an integrated scheduling problem which consists of production and distribution stages. Jobs are processed on a parallel-batch machine in the production stage, and then transported to customers in the distribution stage. The aim is to find an integrated schedule in the two stages with the objective to optimize both total delivery time and total transportation cost. We focus on two models with either unbounded or bounded batch processing capacity in the production stage. In both models we assume sufficient vehicles each with infinite transportation capacity. For the unbounded model, we derive an $O\left( {g{{\left( {{n \mathord{\left/ {\vphantom{n g}} \right. \kern-\nulldelimiterspace} g}} \right)}^{2g}}} \right)$ time dynamic programming algorithm where g ≥ 1 and n are the number of customers and jobs respectively. For the bounded model, we focus on a special case with m different processing times of jobs, and present an $O\left( {{n^3}{2^{3m}}} \right)$ time algorithm.