Scheduling parallel dedicated machines under a single non-shared resource

The scheduling problem of minimizing the makespan for m parallel dedicated machines under single resource constraints is considered. For different variants of the problem the complexity status is established. Heuristic algorithms employing the so-called group technology approach are presented and their worst-case behavior is examined. Finally, a polynomial time approximation scheme is presented for the problem with fixed number of machines.

Scheduling problems for parallel dedicated machines under multiple resource constraints

The paper considers scheduling problems for parallel dedicated machines subject to resource constraints. A fairly complete computational complexity classification is obtained, a number of polynomial-time algorithms are designed. For the problem with a fixed number of machines in which a job uses at most one resource of unit size a polynomial-time approximation scheme is offered.

Single machine scheduling and due date assignment under series-parallel precedence constraints

We consider a single machine due date assignment and scheduling problem of minimizing holding costs with no tardy jobs tinder series parallel and somewhat wider class of precedence constraints as well as the properties of series-parallel graphs.

Approximation Algorithms for a Symmetric Quadratic Knapsack Problem and its Scheduling Applications

We consider a knapsack problem to minimize a symmetric quadratic function. We demonstrate that this symmetric quadratic knapsack problem is relevant to two problems of single machine scheduling: the problem of minimizing the weighted sum of the completion times with a single machine non-availability interval under the non-resumable scenario; and the problem of minimizing the total weighted earliness and tardiness with respect to a common small due date. We develop a polynomial-time approximation algorithm that delivers a constant worst-case performance ratio for a special form of the symmetric quadratic knapsack problem. We adapt that algorithm to our scheduling problems and achieve a better performance. For the problems under consideration no fixed-ratio approximation algorithms have been previously known.