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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 247356, 6 pages
http://dx.doi.org/10.1155/2015/247356
Research Article

Parallel Machine Scheduling with Batch Delivery to Two Customers

1Department of Internet Finance and Information Engineering, Guangdong University of Finance, Guangzhou 510520, China
2College of Management and Economics, Tianjin University, Tianjin 300072, China

Received 1 May 2015; Revised 22 August 2015; Accepted 31 August 2015

Academic Editor: Sergio Teggi

Copyright © 2015 Xueling Zhong and Dakui Jiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In some make-to-order supply chains, the manufacturer needs to process and deliver products for customers at different locations. To coordinate production and distribution operations at the detailed scheduling level, we study a parallel machine scheduling model with batch delivery to two customers by vehicle routing method. In this model, the supply chain consists of a processing facility with parallel machines and two customers. A set of jobs containing jobs from customer 1 and jobs from customer 2 are first processed in the processing facility and then delivered to the customers directly without intermediate inventory. The problem is to find a joint schedule of production and distribution such that the tradeoff between maximum arrival time of the jobs and total distribution cost is minimized. The distribution cost of a delivery shipment consists of a fixed charge and a variable cost proportional to the total distance of the route taken by the shipment. We provide polynomial time heuristics with worst-case performance analysis for the problem. If and , we propose a heuristic with worst-case ratio bound of 3/2, where is the capacity of the delivery shipment. Otherwise, the worst-case ratio bound of the heuristic we propose is .