Ramón Alvarez-Valdés

Project scheduling with resource constraints: A branch and bound approach

Abstract This paper describes a branch and bound algorithm for project scheduling with resource constraints. The algorithmis based on the idea of using disjunctive arcs for resolving conflicts that are created whenever sets of activities have to be scheduled whose total resource requirements exceed the resource availabilities in some periods. Four lower bounds are examined. The first is a simple lower bound based on longest path computations. The second and third bounds are derived from a relaxed integer programming formulation of the problem. The second bound is based on the Linear Programming relaxation with the addition of cutting planes, and the third bound is based on a Lagrangean relaxation of the formulation. This last relaxation involves a problem which is a generalization of the longest path computation and for which an efficient, though not polynomial, algorithm is given. The fourth bound is based on the disjunctive arcs used to model the problem as a graph. We report computational results on the performance of each bound on randomly generated problems involving up to 25 activities and 3 resources.

Reactive GRASP for the strip-packing problem

This paper presents a greedy randomized adaptive search procedure (GRASP) for the strip packing problem, which is the problem of placing a set of rectangular pieces into a strip of a given width and infinite height so as to minimize the required height. We investigate several strategies for the constructive and improvement phases and several choices for critical search parameters. We perform extensive computational experiments with well-known instances which have been previously reported, first to select the best alternatives and then to compare the efficiency of our algorithm with other procedures. The results show that the GRASP algorithm outperforms recently reported metaheuristics.

Design and implementation of a course scheduling system using Tabu Search

Abstract Building a course timetable is a difficult and lengthy task which universities devote a large amount of human and material resources to every year. We have developed a computer package to solve this problem. The program runs on a PC and the user may set the objectives and parameters from among a wide range of possibilities. It has a user-friendly interface for the user to input the relevant data and obtain the corresponding results. The optimization process is based on a set of heuristic algorithms. The core is a Tabu Search procedure for which several strategies have been developed and tested in order to get a fast and powerful algorithm. The first tests of the package have produced satisfactory results.

A Maximal-Space Algorithm for the Container Loading Problem

In this paper, a greedy randomized adaptive search procedure (GRASP) for the container loading problem is presented. This approach is based on a constructive block heuristic that builds upon the concept of maximal space, a nondisjoint representation of the free space in a container. This new algorithm is extensively tested over the complete set of Bischoff and Ratcliff problems [Bischoff, E. E., M. S. W. Ratcliff. 1995. Issues in the development of approaches to container loading. Omega23 377--390], ranging from weakly heterogeneous to strongly heterogeneous cargo, and outperforms all the known nonparallel approaches that, partially or completely, have used this set of test problems. When comparing against parallel algorithms, it is better on average but not for every class of problem. In terms of efficiency, this approach runs in much less computing time than that required by parallel methods. Thorough computational experiments concerning the evaluation of the impact of algorithm design choices and internal parameters on the overall efficiency of this new approach are also presented.

A tabu search algorithm for large-scale guillotine (un)constrained two-dimensional cutting problems

Abstract In this paper we develop several heuristic algorithms for the two-dimensional cutting problem (TDC) in which a single stock sheet has to be cut into a set of small pieces, while maximising the value of the pieces cut. They can be considered to be general purpose algorithms because they solve the four versions of the TDC: weighted and unweighted, constrained and unconstrained. We begin by proposing two constructive procedures based on simple bounds obtained by solving one-dimensional knapsack problems. We then use these constructive algorithms as building blocks for more complex procedures. We have developed a greedy randomised adaptive search procedure (GRASP) which is very fast and obtains good results for both constrained and unconstrained problems. We have also developed a more complex tabu search algorithm that obtains high quality results in moderate computing times. Finally, we have implemented a path relinking procedure to improve the final results of the above algorithms. For the computational results we have used the set of large-scale test problems collected and generated by Fayard et al. (J. Oper. Res. Soc. 49 (1998) 1270). Scope and purpose The two-dimensional cutting problem (TDC) consists of cutting a single rectangular stock sheet into a set of small rectangular pieces of given sizes and values to maximise the total value of the pieces cut. This problem has a wide range of commercial and industrial applications, whenever a sheet of wood, glass, paper or metal has to be cut. The TDC problem can also be considered as a subproblem of more general cutting problems, involving several available stock sheets of different sizes. In this paper we develop several heuristic algorithms for solving TDC problems. The computational results show that they produce high-quality results in short computing times.

Neighborhood structures for the container loading problem: a VNS implementation

This paper presents a Variable Neighborhood Search (VNS) algorithm for the container loading problem. The algorithm combines a constructive procedure based on the concept of maximal-space, with five new movements defined directly on the physical layout of the packed boxes, which involve insertion and deletion strategies.The new algorithm is tested on the complete set of Bischoff and Ratcliff problems, ranging from weakly to strongly heterogeneous instances, and outperforms all the reported algorithms which have used those test instances.

A BRANCH AND BOUND ALGORITHM FOR THE STRIP PACKING PROBLEM

We propose a new branch and bound algorithm for the two dimensional strip packing problem, in which a given set of rectangular pieces have to be packed into a strip of given width and infinite length so as to minimize the required height of the packing. We develop lower bounds based on integer formulations of relaxations of the problem as well as new bounds based on geometric considerations, and reduce the tree search with some dominance criteria. An extensive computational study shows the relative efficiency of the bounds and the good performance of the exact algorithm.

A tabu search algorithm for a two-dimensional non-guillotine cutting problem

In this paper we study a two-dimensional non-guillotine cutting problem, the problem of cutting rectangular pieces from a large stock rectangle so as to maximize the total value of the pieces cut. The problem has many industrial applications whenever small pieces have to be cut from or packed into a large stock sheet. We propose a tabu search algorithm. Several moves based on reducing and inserting blocks of pieces have been defined. Intensification and diversification procedures, based on long-term memory, have been included. The computational results on large sets of test instances show that the algorithm is very efficient for a wide range of packing and cutting problems.

A heuristic to schedule flexible job-shop in a glass factory

We describe the design and implementation of a scheduling system in a glass factory. The factory produces a large variety of manufactured glass objects in a complex process ranging from melting the glass in the furnaces and blowing it automatically or manually to decorating, assembling and packing it. The structure basically corresponds to a flexible job-shop scheduling problem with some special characteristics. On the one hand, dealing with hot liquid glass imposes no-wait constraints on some operations. On the other hand, skilled workers performing some manual tasks are modelled as special machines. The system produces approximate solutions in very short computing times, trying to minimize a non-regular criterion defined by the user and based on due dates. It can be used to establish delivery dates for new customer orders, taking into account current machine workloads, or to schedule a set of orders, trying to meet given customer due dates.

A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems

This paper presents a greedy randomized adaptive search procedure (GRASP) for the constrained two-dimensional non-guillotine cutting problem, the problem of cutting the rectangular pieces from a large rectangle so as to maximize the value of the pieces cut. We investigate several strategies for the constructive and improvement phases and several choices for critical search parameters. We perform extensive computational experiments with well-known instances previously reported, first to select the best alternatives and then to compare the efficiency of our algorithm with other procedures.