Optimizing glass coating lines: MIP model and valid inequalities

Glass coating is a specific transformation aiming at improving glass performance. The work presented in this paper deals with the determination of the optimal configuration of the production lines used to perform this operation. We propose a first MIP formulation of the problem and then discuss several types of valid inequalities for improving it. The main idea is to exploit explicit or implicit binary exclusion constraints to derive stronger valid inequalities: the maximal clique constraints. Efficient (polynomial time) separation algorithms exploiting special structure of the problem are described, giving rise to a cutting-plane generation procedure for strengthening the initial formulation. The computational study carried out shows that, with the enhanced formulation, good solutions can be obtained within reasonable computation times using currently available integer programming software.     

New approaches to nurse rostering benchmark instances

This paper presents the results of developing a branch and price algorithm and an ejection chain method for nurse rostering problems. The approach is general enough to be able to apply it to a wide range of benchmark nurse rostering instances. The majority of the instances are real world applications. They have been collected from a variety of sources including industrial collaborators, other researchers and various publications. The results of entering these algorithms in the 2010 International Nurse Rostering Competition are also presented and discussed. In addition, incorporated within both algorithms is a dynamic programming method which we present. The algorithm contains a number of heuristics and other features which make it very effective on the broad rostering model introduced.     

Balancing modular transfer lines with serial-parallel activation of spindle heads at stations

The paper deals with an as yet unexplored combinatorial optimization problem concerning balancing complex transfer lines in the machining/process environment. In contrast to similar problems for assembly lines, in transfer line balancing, tasks are grouped into blocks. All tasks of each block are executed simultaneously (in parallel) by one piece of equipment (spindle head). For the transfer lines considered in this paper, spindle heads at each station are activated in serial-parallel order. The set of all available spindle heads is known beforehand. Precedence, cycle time, compatibility, and parallelism constraints for the blocks and tasks are given. The line investment cost is estimated by the sum of block and station costs. The problem is to assign all tasks (using the available blocks) such that all constraints are respected and line investment cost is at a minimum. This paper focuses on solving the problem via a branch-and-bound algorithm. An approach for obtaining an efficient lower bound is offered, based on a reduction of the initial problem to a set partitioning problem. Computational experiments reveal that the proposed approach is efficient mathematically and can be used to solve practical transfer line design problems of a medium size.     

Global optimization for sum of geometric fractional functions

This paper presents an efficient branch and bound algorithm for globally solving sum of geometric fractional functions under geometric constraints, which arise in various practical problems. By using an equivalent transformation and a new linear relaxation technique, a linear relaxation programming problem of the equivalent problem is obtained. The proposed algorithm is convergent to the global optimal solution by means of the subsequent solutions of a series of linear programming problems. Numerical results are reported to show the feasibility of our algorithm.     

Branched immersions and braids

Branch points of a real 2-surface Σ in a 4-manifold M generalize branch points of complex curves in complex surfaces: for example, they can occur as singularities of minimal surfaces. We investigate such a branch point p when Σ is topologically embedded. It defines a link L(p), the components of which are closed braids with the same axis up to orientation. If Σ is closed without boundary, the contribution of p to the degree of the normal bundle of Σ in M can be computed on the link L(p), in terms of the algebraic crossing numbers of its components and of their linking numbers with one another.      

A computational comparison of some branch and bound methods for indefinite quadratic programs

The aim of this paper is to discuss different branch and bound methods for solving indefinite quadratic programs. In these methods the quadratic objective function is decomposed in a d.c. form and the relaxations are obtained by linearizing the concave part of the decomposition. In this light, various decomposition schemes have been considered and studied. The various branch and bound solution methods have been implemented and compared by means of a deep computational test.      

Solving the car sequencing problem via Branch & Bound

In a mixed-model assembly line, varying models of the same basic product are to be produced in a facultative sequence. This results to a short-term planning problem where a sequence of models is sought which minimizes station overloads. In practice – e.g. the final assembly of cars – special sequencing rules are enforced which restrict the number of models possessing a certain optional feature k to r_k within a subsequence of s_k successive models. This problem is known as car sequencing. So far, employed solution techniques stem mainly from the field of Logic and Constraint Logic Programming. In this work, a special Branch & Bound algorithm is developed, which exploits the problem structure in order to reduce combinatorial complexity.     

Flow Shop排序问题Fm|prmu|∑w_jC_j的分枝定界法

本文讨论FlowShop排序问题Fm|prmu|∑ωjCj给出了求解该问题的一个分枝定界法．     

A zero-inventory production and distribution problem with a fixed customer sequence

In this paper, we study the zero-inventory production and distribution problem with a single transporter and a fixed sequence of customers. The production facility has a limited production rate, and the delivery truck has non-negligible traveling times between locations. The order in which customers may receive deliveries is fixed. Each customer requests a delivery quantity and a time window for receiving the delivery. The lifespan of the product starts as soon as the production for a customer’s order is finished, which makes the product expire in a constant time. Since the production facility and the shipping truck are limited resources, not all the customers may receive the delivery within their specified time windows and/or within product lifespan. The problem is then to choose a subset of customers from the given sequence to receive the deliveries to maximize the total demand satisfied, without violating the product lifespan, the production/distribution capacity, and the delivery time window constraints. We analyze several fundamental properties of the problem and show that these properties can lead to a fast branch and bound search procedure for practical problems. A heuristic lower bound on the optimal solution is developed to accelerate the search. Empirical studies on the computational effort required by the proposed search procedure comparing to that required by CPLEX on randomly generated test cases are reported.     

Airport management: taxi planning

The Taxi Planning studies the aircraft routing and scheduling on the airport ground. This is a dynamic problem, which must be updated almost every time that a new aircraft enters or exits the system. Taxi Planning has been modelled using a linear multicommodity flow network model with side constraints and binary variables. The flow capacity constraints are used to represent the conflicts and competence between aircrafts using a given airport capacity. The “Branch and Bound” and “Fix and Relax” methodologies have been used. The computational tests have been run at the Madrid-Barajas airport, using actual data from the airport traffic.