Parallel Machine Scheduling with Batch Delivery to Two Customers

Xueling Zhong,Dakui Jiang

doi:10.1155/2015/247356

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 withmparallel machines and two customers. A set of jobs containingn1jobs from customer 1 andn2jobs 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. Ifm=2and(n1-b)(n2-b)<0, we propose a heuristic with worst-case ratio bound of 3/2, wherebis the capacity of the delivery shipment. Otherwise, the worst-case ratio bound of the heuristic we propose is2-2/(m+1).

Highlights

To meet the soaring demands of electronic devices in recent years, manufacturers in China start building new factories to increase production capacities
Two different strategies are mainly adopted by these manufacturers, one is to build a new factory at the undeveloped land near current factory and the other is to place the new factory to a different region with lower labor cost
We have studied a parallel machine scheduling model with batch delivery to two customers

Summary

Introduction

To meet the soaring demands of electronic devices in recent years, manufacturers in China start building new factories to increase production capacities. Such an objective function is adopted by Chen and Vairaktarakis [1] This problem is a variation of the integrated productiondistribution scheduling models with batch delivery to multiple customers by vehicle routing method, which is always encountered in make-to-order or time-sensitive product supply chains. In these supply chains, finished jobs are often delivered to customers immediately or shortly after the production which lead to production and distribution operations that are intimately linked with no intermediate inventory.

Notations and Preliminary Results

Conclusion