NP-hardness of the single-variable-resource scheduling problem to minimize the total weighted completion time

NP-hardness of the single-variable-resource scheduling problem to minimize the total weighted completion time

Baker and Nuttle [1] studied the following single-variable-resource scheduling problem: sequencing n jobs for processing by a single resource to minimize a function of job completion times, when the availability of the resource varies over time. When the objective function to be minimized is the total weighted completion time, Baker and Nuttle conjectured that the problem is NP-hard. We show in...

Scheduling with Rejection to Minimize the Total Weighted Completion Time∗

In this paper, we address the scheduling problem with rejection in which we can choose a subset of jobs to process. Choosing not to process any job incurs a corresponding penalty. We consider the following problem for the first time: scheduling with rejection to minimize the total weighted completion time with the constraint of total penalties on identical parallel machines, where the number of...

Customer Order Scheduling to Minimize Total Weighted Completion Time

In this paper we study the scheduling problem in which each customer order consists of several jobs of different types, which are to be processed on m facilities. Each facility is dedicated to the processing of only one type of jobs. All jobs of an order have to be delivered to the customer at the same time. The objective is to schedule all the orders to minimize the total weighted order comple...

Scheduling Identical Parallel Machines to Minimize Total Weighted Completion Time

Two agents single machine scheduling problem with total completion time and total weighted completion time objectives