The problem of scheduling G groups of jobs on m unrelated parallel machines is considered. Each group consists of several identical jobs. Implicit in a schedule is a partition of a group into batches; all jobs of a batch are processed jointly. It is possible for diierent batches of the same group to be processed concurrently on diierent machines. However, at any time, a batch can be processed o...

We consider the problem of allocating a single server to families of jobs with random service times and due dates. Furthermore, a setup is required when the server switches from one job family to another. We address the problems of minimizing expected weighted ow time, expected maximum lateness, and total weighted tardiness with emphasis on problems for which it is assumed that each family can ...

We characterize optimal policies for the problem of allocating a single server to a set of jobs from N families. Each job is an instance of demand for an item and is associated with a family, a holding cost rate, and a mean processing time. Setup times are required to switch from one family to another, but not within a family. We consider the case in which the order of jobs within the family is...

Background: Breast cancer is the most frequently diagnosed cancer and the leading global cause of cancer death among women worldwide. Radiotherapy plays a significant role in treatment of breast cancer and reduces locoregional recurrence and eventually improves survival. The treatment fields applied for breast cancer treatment include: tangential, axillary, supraclavicular and internal mammary ...

This paper presents a new mathematical model for the problem of scheduling part families and jobs within each part family in a flow line manufacturing cell where the setup times for each family are sequence dependent and it is desired to minimize the maximum completion time of the last job on the last machine (makespan) while processing parts (jobs) in each family together. Gaining an optimal s...

This paper addresses a complex parallel machine scheduling problem with jobs divided into operations and grouped in families. Non-anticipatory family setup times are held at the beginning of each batch, defined by combination one setup-time sequence from unique family. Other aspects also considered problem, such as release dates for machines, operation’s sizes, machine’s eligibility capacity. W...

This paper presents several procedures for scheduling identical parallel machines with family setups when the objective is to minimize total tardiness. These procedures are tested on several problem sets with varying numbers of families, jobs and machines, varying setup time distributions and various levels of due date tightness and variability. The results show that genetic algorithms are the ...