We consider the problem of scheduling a set of n tasks on m processors under precedence, communication, and global system energy constraints to minimize makespan. We extend existing scheduling models to account for energy usage and give convex programming algorithms that yield essentially the same results as existing algorithms that do not consider energy, while adhering to a strict energy bound.

The vehicle routing problem is a combinatorial optimization and integer programming problem seeking to service a number of customers with a fleet of vehicles. Vehicle routing problem has many applications in the fields of transportation, distribution and logistics. In this study, the vehicle routing problem subject to precedence constraints has been modeled as the Travelling Salesman Problem (T...

We consider the preemptive and non-preemptive problems of scheduling jobs with precedence constraints on parallel machines with the objective to minimize the sum of (weighted) completion times. We investigate an online model in which the scheduler learns about a job when all its predecessors have completed. For scheduling on a single machine, we show matching lower and upper bounds of Θ(n) and ...

Process discovery has emerged as a powerful approach to support the analysis and the design of complex processes. It consists of analyzing a set of traces registering the sequence of tasks performed along several enactments of a transactional system, in order to build a process model that can explain all the episodes recorded over them. An approach to accomplish this task is presented which can...

This paper considers the complexity and the correlation of scheduling unit-time jobs on identical parallel machines and unit-time ow-shop scheduling under precedence constraints. It is shown that, in the case of chain-like precedence constraints, the nonpre-emptive parallel-machines problem and the ow-shop problem to minimize maximum or total completion time can be solved in polynomial time, an...

In traditional precedence-constrained scheduling a task is ready to execute when all its predecessors are complete. We call such a task an AND task. In this paper we allow certain tasks to be ready when just one of their predecessors is complete. These tasks are known as OR tasks. We analyze the complexity of two types of real-time AND/OR task scheduling problems. In the rst type of problem, al...

We introduce a variation of the scheduling with precedence constraints problem that has applications to molecular folding and production management. We are given a bipartite graph H = (B,S). Vertices in B are thought of as goods or services that must be bought to produce items in S that are to be sold. An edge from j ∈ S to i ∈ B indicates that the production of j requires the purchase of i. Ea...

We discuss the problem of sequencing precedence-constrained jobs on a single machine to minimize the average weighted completion time. This problem has attracted much attention in the mathematical programming community since Sidney’s pioneering work in 1975 (Sidney, J. B. 1975. Decomposition algorithms for single machine scheduling with precedence relations and deferral costs. Operations Resear...