A Note on Scheduling Problems with Irregular Starting Time Costs

In [9], Maniezzo and Mingozzi study a project scheduling problem with irregular starting time costs. Starting from the assumption that its computational complexity status is open, they develop a branch-and-bound procedure, and identify special cases that are solvable in polynomial time. In this note, we review three previously established, related results which show that the general problem is solvable in polynomial time

Incremental and encoding formulations for Mixed Integer Programming

The standard way to represent a choice between n alternatives in Mixed Integer Programming is through n binary variables that add up to one. Unfortunately, this approach commonly leads to unbalanced branch-and-bound trees and diminished solver performance. In this paper, we present an encoding formulation framework that encompasses and expands existing approaches to mitigate this behavior. Through this framework, we generalize the incremental formulation for piecewise linear functions to any finite union of polyhedra with identical recession cones

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

Resource constrained project scheduling with time windows: A branching scheme based on dynamic release dates

We propose a branch-and-bound algorithm for resource-constrained project scheduling where any two of jobs can be linked by arbitrary minimal and maximal time lags. The jobs have to be scheduled non-preemptively, and while in process, they require several limited resources. The objective is to find a feasible schedule which minimizes the project makespan. Different branch-and-bound algorithms have been previously proposed - either based on constraint propagation techniques, or based on the idea to branch over so-called resource conflicts which are resolved by introducing additional precedence constraints. Our approach also follows the latter principle. The new idea is to resolve resource conflicts only locally by a dynamic update of job release dates instead of introducing precedence constraints. This gives rise to a reduction of both computation time and memory requirements in every node of the enumeration tree, however, at the expense of a loss of information. Nevertheless, enriched by preprocessing, strong dominance rules, and a flexible search strategy, our computational results show that the algorithm performs better than previous branch-and-bound algorithms, and is competitive with a very recent constraint propagation approach as well as tailor-made heuristics, also for large-scale instances

Mixed Integer Linear Programming Formulation Techniques

A wide range of problems can be modeled as Mixed Integer Linear Programming (MIP) problems using standard formulation techniques. However, in some cases the resulting MIP can be either too weak or too large to be effectively solved by state of the art solvers. In this survey we review advanced MIP formulation techniques that result in stronger and/or smaller formulations for a wide class of problems