Scheduling precedence-constrained jobs with stochastic processing times on parallel machines

We consider parallel machine scheduling problems where the jobs are subject to precedence constraints, and the processing times of jobs are governed by independent probability distributions. The objective is to minimize the weighted sum of job completion times &;j wjC_j in expectation, where wj&; 0. Building upon an LP-relaxation by Möhring, Schulz, and Uetz (J.ACM 46 (1999), pp.924-942) and an idle time charging scheme by Chekuri, Motwani, Natarajan, and Stein (SIAM J. Comp., to appear) we derive the first approximation algorithms for this model

More-Dimensional Packing with Order Constraints

We present a first systematic study on more-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture. They can be interpreted as more-dimensional generalizations of scheduling problems. Using graph-theoretic structures to describe feasible solutions, we develop a novel exact branch-and-bound algorithm. This extends previous work by Fekete and Schepers; a key tool is a new order-theoretic characterization of feasible extensions of a partial order to a given complementarity graph that is tailor-made for use in a branch-and-bound environment. The usefulness of our approach is validated by computational results

Scheduling Scarce Resources in Chemical Engineering

The efficient utilization of scarce resources, such as machines or manpower, is major challenge within production planning in the chemical industry. We describe solution methods for a resource-constrained scheduling problem which arises at a production facility at BASF AG in Ludwigshafen. We have developed and implemented two different algorithms to solve this problem, a novel approach which is based upon Lagrangian relaxation, as well as a branch-and-bound procedure. Since the Lagrangian approach is applicable for a whole variety of resource-constrained scheduling problems, it is of interest not only for the specific problem we describe, but is of interest also for many other industrial applications. In this paper, we describe both approaches, and also report on computational results, based upon practical problem instances as well as benchmark test sets