Parallel Machine Scheduling with Batch Delivery to Two Customers

Abstract EN

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 m parallel machines and two customers.

A set of jobs containing n1 jobs from customer 1 and n2 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 m=2 and (n1-b)(n2-b)<0, we propose a heuristic with worst-case ratio bound of 3/2, where b is the capacity of the delivery shipment.

Otherwise, the worst-case ratio bound of the heuristic we propose is 2-2/(m+1).