Maurício C. de Souza

Packing items to feed assembly lines

Abstract We treat a practical application of packing problems in feeding assembly lines. This study was motivated by a real situation encountered in the shop floor of a major automobile industry plant in Brazil. The assembly line feed problem (LFP) consists in how pack the items in the available containers to meet the line work centers’ requirements with a minimum total cost over the planning horizon. LFP is a variable-sized bin packing problem that has two special features: (i) a cardinality constraint on each bin’s size; and, (ii) a cost structure such that each bin’s cost varies according to the items that are packed in it. We propose an integer programming model and a GRASP heuristic for LFP. Numerical results on real-life test instances are reported.

Capacitated lot sizing and sequence dependent setup scheduling: an iterative approach for integration

We consider here the lot sizing and scheduling problem in single-level manufacturing systems. The shop floor is composed of unrelated parallel machines with sequence dependent setup times. We propose an integer programming model embedding precise capacity information due to scheduling constraints in a classical lot-sizing model. We also propose an iterative approach to generate a production plan taking into account scheduling constraints due to changeover setup times. The procedure executes two decision modules per iteration: a lot-sizing module and a scheduling module. The capacitated lot-sizing problem is solved to optimality considering estimated data and aggregate information, and the scheduling problem is solved by a GRASP heuristic. In the proposed scheme the information flow connecting the two levels is managed in each iteration. We report a set of computational experiments and discuss future work.

Skewed VNS enclosing second order algorithm for the degree constrained minimum spanning tree problem

We develop ideas to enhance the performance of the variable neighborhood search (VNS) by guiding the search in the shaking phase, and by employing the Skewed strategy. For this purpose, Second Order algorithms and Skewed functions expressing structural differences are embedded in an efficient VNS proposed in the literature for the degree constrained minimum spanning tree problem. Given an undirected graph with weights associated with its edges, the degree constrained minimum spanning tree problem consists in finding a minimum spanning tree of the given graph, subject to constraints on node degrees. Computational experiments are conducted on the largest and hardest benchmark instances found in the literature to date. We report results showing that the VNS with the proposed strategies improved the best known solutions for all the hardest benchmark instances. Moreover, these new best solutions significantly reduced the gaps with respect to tight lower bounds reported in the literature.

Variable neighborhood descent with iterated local search for routing and wavelength assignment

In this work we treat the Routing and Wavelength Assignment (RWA) with focus on minimizing the number of wavelengths to route demand requests. Lightpaths are used to carry the traffic optically between origin-destination pairs. The RWA is subjected to wavelength continuity constraints, and a particular wavelength cannot be assigned to two different lightpaths sharing a common physical link. We develop a Variable Neighborhood Descent (VND) with Iterated Local Search (ILS) for the problem. In a VND phase we try to rearrange requests between subgraphs associated to subsets of a partition of the set of lightpath requests. In a feasible solution, lightpaths belonging to a subset can be routed with the same wavelength. Thus, the purpose is to eliminate one subset of the partition. When VND fails, we perform a ILS phase to disturb the requests distribution among the subsets of the partition. An iteration of the algorithm alternates between a VND phase and a ILS phase. We report computational experiments that show VND-ILS was able to improve results upon powerful methods proposed in the literature.

Min‐degree constrained minimum spanning tree problem: complexity, properties, and formulations

This paper addresses a new combinatorial problem, the Min-Degree Constrained Minimum Spanning Tree (md-MST), that can be stated as: given a weighted undirected graph with positive costs on the edges and a node-degrees function , the md-MST is to find a minimum cost spanning tree T of G, where each node i of T either has at least a degree of or is a leaf node. This problem is closely related to the well-known Degree Constrained Minimum Spanning Tree (d-MST) problem, where the degree constraint is an upper bound instead. The general NP-hardness for the md-MST is established and some properties related to the feasibility of the solutions for this problem are presented, in particular we prove some bounds on the number of internal and leaf nodes. Flow-based formulations are proposed and computational experiments involving the associated Linear Programming (LP) relaxations are presented.

VNS and second order heuristics for the min-degree constrained minimum spanning tree problem

Given an undirected graph with weights associated with its edges, the min-degree constrained minimum spanning tree (md-MST) problem consists in finding a minimum spanning tree of the given graph, imposing minimum degree constraints in all nodes except the leaves. This problem was recently proposed in Almeida et al. [Min-degree constrained minimum spanning tree problem: Complexity, proprieties and formulations. Operations Research Center, University of Lisbon, Working-paper no. 6; 2006], where its theoretical complexity was characterized and showed to be NP-hard. The present paper discusses variable neighborhood search (VNS) metaheuristics addressing the md-MST. A so-called enhanced version of a second order (ESO) repetitive technique is also considered, in order to guide the search in both shaking and improvement phases of the VNS method. A Kruskal based greedy heuristic adapted to the md-MST is also presented, being used within the ESO framework. VNS randomized methodologies are also discussed. These are the first heuristics to the md-MST ever proposed in the literature. Computational experiments are conducted on instances adapted from benchmark ones used in the context of the well-known degree constraint minimum spanning tree problem. These experiments have shown that randomized VNS methods enclosing an ESO algorithm can produce very interesting results. In particular, that a simpler VNS randomized methodology might be taken into account when very high dimensional instances are under consideration.

Surgical scheduling with simultaneous employment of specialised human resources

Surgical scheduling is a challenging problem faced by hospital managers. It is subject to a wide range of constraints depending upon the particular situation within any given hospital. We deal with the simultaneous employment of specialised human resources, which must be assigned to surgeries according to their skills as well as the time windows of the staff. A particular feature is that they can be assigned to two surgeries simultaneously if the rooms are compatible. The objective is to maximise the use of the operating rooms. We propose an integer model and integer programming based heuristics to address the problem. Computational experiments were conducted on a number of scenarios inspired by real data to cover different practical problem solving situations. Numerical results show that relaxations provide tight upper bounds, and relax-and-fix heuristics are successful in finding optimal or near optimal solutions.

Models and heuristics for the k ‐degree constrained minimum spanning tree problem with node‐degree costs

The k -Degree constrained Minimum Spanning Tree Problem (k -DMSTP) consists in finding a minimal cost spanning tree satisfying the condition that every node has a degree no greater than a fixed value k. Here we consider an extension where besides the edge costs, a concave cost function is associated to the degree of each node. Several integer linear programming formulations based on reformulation techniques are presented and their linear programming relaxations are compared. A GRASP heuristic to obtain feasible solutions for the problem together with a Path Relinking strategy is also described. We include computational results using instances with up to 200 nodes that give an empirical assessment of the linear programming bounds of the different models as well as the ability of using these models to solve the problems by using an Integer Linear Programming package. The results also show that the proposed GRASP heuristic appears to perform rather well for this type of problems.

md-MST is NP-hard for d≥3

Abstract Let G = ( V , E ) be a connected weighted undirected graph. Given a positive integer d, the Min-Degree Constrained Minimum Spanning Tree (md-MST) problem consists in finding a spanning tree T for G having minimum total edge cost and such as each node i in the tree either has degree at least d or is a leaf node. In the present work we prove that this recently introduced combinatorial problem is NP-hard in general.

Cycle-based algorithms for multicommodity network flow problems with separable piecewise convex costs

This invention relates to novel hydrophilic, crosslinked, polyurea-urethane, solid, discrete particles formed by adding in droplet form a hydrophilic prepolymer comprising an isocyanate-capped polyol or mixtures thereof wherein said polyol or mixture of polyols has a reaction functionality greater than two, the total of said polyol present having an ethylene oxide content of at least 40 weight percent, before capping to a large excess of a stirred aqueous reactant. The resultant solid particles can be molded into various shapes as desired or used for coating or adhesive applications.