A multilevel block incomplete cholesky preconditioner for solving normal equations in linear least squares problems

An incomplete factorization method for preconditioning symmetric positive definite matrices is introduced to solve normal equations. The normal equations are form to solve linear least squares problems. The procedure is based on a block incomplete Cholesky factorization and a multilevel recursive strategy with an approximate Schur complement matrix formed implicitly. A diagonal perturbation strategy is implemented to enhance factorization robustness. The factors obtained are used as a preconditioner for the conjugate gradient method. Numerical experiments are used to show the robustness and efficiency of this preconditioning technique, and to compare it with two other preconditioners.     

On the summability of the formal solutions for some PDEs with irregular singularity

In this Note, we consider some classes of nonlinear partial differential equations with regular singularity with respect to t=0 and irregular one with respect to x=0. Our purpose is to establish a result which is similar to the k-summability property, known in the case of singular ordinary differential equations. We can prove that, except at most a countable set, the formal solution is Borel summable or k-summable with respect to x in all other directions. To cite this article: Z. Luo et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

A large-scale application of the partial coverage uncapacitated facility location problem

The traditional, uncapacitated facility location problem (UFLP) seeks to determine a set of warehouses to open such that all retail stores are serviced by a warehouse and the sum of the fixed costs of opening and operating the warehouses and the variable costs of supplying the retail stores from the opened warehouses is minimized. In this paper, we discuss the partial coverage uncapacitated facility location problem (PCUFLP) as a generalization of the uncapacitated facility location problem in which not all the retail stores must be satisfied by a warehouse. Erlenkotter's dual-ascent algorithm, DUALOC, will be used to solve optimally large (1600 stores and 13?000 candidate warehouses) real-world implemented PCUFLP applications in less than two minutes on a 500?MHz PC. Furthermore, a simple analysis of the problem input data will indicate why and when efficient solutions to large PCUFLPs can be expected.     

Effect of coordinated replenishment policies on quality

Coordinated replenishment is a supply chain policy that affects many operational performance measures, including cost, lead time, and quality. In this paper, we develop a mathematical model of a simplified supply chain in which conformance quality is one of the supplier's decision variables and both the supplier and its customer are trying to minimize expected annual cost. Our expected cost model includes the important quality costs (appraisal, prevention, internal failure, and external failure) as well as holding, set-up, and ordering costs. Our results indicate that coordination leads to a decline in total cost but that coordination does not necessarily lead to an improvement in quality. In other words, buyers who are using coordinated replenishment may be trading higher quality for lower cost.     

An optimal replenishment policy for items with inventory-level-dependent demand and fixed lifetime under the LIFO policy

In a recent paper, Hwang and Hahn considered inventory replenishment problems for an item with an inventory-level-dependent demand rate and a fixed lifetime. They developed an EQQ model under the situation of considering the first-in–first-out (FIFO) issuing policy. First, this paper reconsiders Hwang and Hann's problem by employing the last-in–first-out (LIFO) issuing policy, which is more practical in the retail industry. An inventory model is developed. Secondly, the concavity of the objective function is proved. Thirdly, this paper presents conditions where the present model has a unique optimal solution and a method for finding the global optimal solution. A simple solution procedure and sensitivity analyses of parameters are also provided.     

An algorithm to locate perinatal facilities in the municipality of Rio de Janeiro

In order to reduce infant mortality in the municipality of Rio de Janeiro it is desired to encourage all mothers-to-be to attend the appropriate health care facilities. A 3-level hierarchical prenatal–neonatal health care system is described together with a basic model for optimising accessibility to facilities. A genetic algorithm to solve the basic model is developed and some numerical experience reported. Extensions to the basic model and planned future research are briefly indicated.     

Machine assignment in a nonlinear multi-product flowline

A group of machines for processing a set of jobs in a manufacturing system is often located in a serial line. An efficient strategy for locating these machines such that the total travel distance or the cost of transporting the jobs is minimized is desired. In this research, the assumption of a linear line with equally spaced machine location is relaxed. This research addressed problems of locating unique machines. It is found that the machine distances possess unique properties in this type of a problem. Utilizing these properties, heuristic strategies are proposed to obtain efficient solution where optimal methods are expected to be computationally prohibitive. A lower bound for the optimum solution is also proposed. Results are encouraging.     

A column generation approach for the timetabling problem of Greek high schools

A column generation (CG) approach for the solution of timetabling problems is presented. This methodology could be used for various instances of the timetabling problem, although in this paper the solution of the high-school situation in Greece is presented. The results obtained show clearly that the CG approach that has been extremely successful in recent years in the solution of airline crew scheduling problems could also be very efficient and robust for the solution of timetabling problems. Several large timetabling problems corresponding to real problems have been successfully solved, with the solutions obtained feasible and of very high quality in accordance with the problem definition. In addition, none of the solutions contained any idle hour for any of the teachers, which was one of the main goals of this optimization effort.     

Tuning inventory policy parameters in a small chemical company

A project to improve inventory management in a small UK chemical company is described. A research group comprising university academics and company managers for logistics and information technology examined current practices and analysed a database of historical records of business operations of the company. Based on the analysis, a scheme to categorise stock and set ordering policies to optimise inventory costs was developed. Some comments are made on process issues and the learning that took place.