An integrated approach to the vehicle routing and container loading problems

Real-world distribution problems raise some practical considerations that usually are not considered in a realistic way in more theoretical studies. One of these considerations is related to the vehicle capacity, not only in terms of cubic meters or weight capacity but also in terms of the cargo physical arrangements. In a distribution scene, two combinatorial optimization problems, the vehicle routing problem with time windows and the container loading problem, are inherently related to each other. This work presents a framework to integrate these two problems using two different resolution methods. The first one treats the problem in a sequential approach, while the second uses a hierarchical approach. To test the quality and efficiency of the proposed approaches, some test problems were created based on the well-known Solomon, Bischoff and Ratcliff test problems. The results of the integrated approaches are presented and compared with results of the vehicle routing problem with time windows and the container loading problem applied separately.     

On the concentrated loading of certain elastic half-space problems and related external crack problems. A new approach

Using a new integral equation connecting different types of fundamental solutions, a variety of external crack problems are solved when the crack is situated in an infinite space and occupies the region exterior to a circle, with the loading on the crack faces being of a concentrated nature. As a consequence of a particular integral representation we are also able to discuss certain “punch” problems for an elastic half-space when the punch is rigid and frictionless, with a circular cross section, but with an arbitrary base profile     

A non-conventional approach for crack problems in piezoelectric media under electromechanical loading

In this paper the elastostatic solution of an inclined crack problem has been analyzed. The approach is analogous to the one proposed over the past years for orthotropic materials by Piva andViola (1988) (Eng Fract Mech, 29: 535–548), and it may be considered an alternative to the mathematical formalisms currently used. A general expression of the stress field is determined in terms of complex potentials. The stress distribution and the displacement field in the proximity of the crack tip are finally obtained. An expression of the energy release rate is provided in terms of the field intensity factors. Numerical results are presented and discussed under different remote electro-mechanical loading conditions and varying the crack inclination. Particular attention has been focused on the effect of the lateral load on the fracture quantities and on the direction of the incipient branching angle.     

A neural network approach for batching decisions in wafer fabrication

This paper considers a stochastic batching problem for a batch process in wafer fabrication, where various numbers of wafer lots are allowed to process together in each batch, and wafer lots arrive randomly but not in a specified pattern. The objective is to determine the optimal size (number of wafer lots) of each batch with respect to the measure of minimizing the mean queueing time of wafer lots. For the problem, a multi-layer perceptron neural network model is proposed to make real-time batching control, and its effectiveness is investigated in comparison with that of the well-known minimum batch size policy.     

A bottleneck assignment approach to the multiple container loading problem

The container loading problem addresses the question of how to store several three dimensional, rectangular items (e.g. boxes) in one or more containers in such a way that maximum use is made of the container space. The multiple container problem concentrates on the situation where the consignment to be loaded cannot be accommodated in a single container. To minimize the number of required containers the repeated application of a single container approach is often suggested in the literature. In contrast, in this paper an approach based on a set partitioning formulation of the problem is presented. Within this approach a single container algorithm is used to produce alternative loading patterns. This approach easily allows introducing additional aspects, e.g. separation of boxes or complete shipment of boxes.     

Parallel machine scheduling with tool loading: a constraint programming approach

This paper presents constraint programming models that aim to solve scheduling and tool assignment problems in parallel machine environments. There are a number of jobs to be processed on parallel machines. Each job requires a set of tools, but limited number of tools are available in the system due to economic restrictions. The problem is to assign the jobs and the required tools to machines and to determine the schedule so that the makespan is minimised. Three constraint programming models are developed and compared with existing methods described in the literature.     

A heuristic-based approach to integrate the product line selection decision to the supply chain configuration

Product platform development (PPD) as an approach to mass customisation (MC) helps an organisation to reduce costs as well as ensure timely deliveries. Varieties are offered to different market segments by combining and incorporating different modules at different levels. Modules at different levels are essentially features that a customer segment is looking for. It is apparent that overall optimisation would require simultaneous consideration of not only PPD but also other supply chain constraints. In this paper, an attempt has been made to develop a mixed integer linear programming (MILP) model for sourcing, production planning, and PPD decisions. Based on analyses of the model, a heuristic solution procedure has been suggested. The heuristic developed in this paper attempts to decompose the problem and then assimilate the outputs from the simpler parts to obtain the final solution. Finally, a simple example to illustrate the solution procedure is presented.     

A nonholonomic approach to isoparallel problems and some applications

Isoparallel problems are a class of optimal control problems on principal fibre bundles endowed with a connection and a Riemannian metric on the base space. These problems consist of finding the shortest curve on the base among those with a given parallel transport operator. It has been shown that when the structure group of the principal bundle admits a bi-invariant metric, the normal solutions are precisely the projections of the geodesics (relative to an appropriate Riemannian metric) on the bundle. In this work we obtain a generalization of this result that holds true for any structure group, by transforming the isoparallel problem into a nonholonomic problem of a generalized type. The latter reduces to the geodesic problem if the structure group has a bi-invariant metric. We illustrate the theory with an application to the optimal control of an elastic rolling ball (the plate-ball system), relating some aspects of this problem to the dynamics of a simple pendulum. Finally, we indicate how the study of locomotion of microorganisms can benefit from this approach. This work shows how optimal control and generalized nonholonomic mechanics are related within the context of Lagrangian reduction.     

A combinatorial approach to a class of parallel-machine,continuous-time scheduling problems

The paper analyzes a manufacturing system with N non-identical, parallel machines continuously producing one product type in response to its demand. Inventory and backlog costs are incurred when tracking the demand results in inventory surpluses and shortages respectively. In addition, the production cost of a machine is incurred when the machine is not idle. The objective is to determine machine production rates so that the inventory, backlog, and production costs are minimized. For problems with demand defined as an arbitrary function of time, numerical methods are suggested to approximate an optimal solution. The complexity of the approximation methods is polynomial, while finding an exact optimal solution requires exponential time. In a case when production is to cope with a special form of a single-mode, K-level piece-wise constant demand, we prove, with the aid of the maximum principle, that the exact optimal solution can be found as a combination of analytical and combinatorial tools in O(KN ²( max {K,2N})²) time.     

A complex variable approach to electrochemical machining problems

Summary Electrochemical machining is the name given to the process of eroding metal by electrolysis. The anode in this process is a workpiece from which metal is eroded and the cathode is a shaped machine tool which is fed towards the work-piece (see Fig. 1). Erosion takes place when an electric potential is applied across the electrolyte filled gap between the tool and the workpiece. The electrolyte is pumped through the gap in order to remove the products of erosion.In this paper an attempt is made, under certain simplifying assumptions, to determine the resulting shape of the workpiece and the gap-sizes between the tool and workpiece. Basically two problems are treated in this paper; one for a plane-faced tool with complete insulation on the tool sides (see Fig. 2) and the other for an uninsulated straight sided tool (see Fig. 5). An exact complex variable technique is used and only minimal computer usage is required for final evaluations from derived analytic formulae.     

A local genetic approach to multi-objective,facility layout problems with fixed aisles

We develop a new local genetic algorithm hybridized tabu search, to solve multi-criteria facility layout problems. Within these types of problems, we consider two objectives involving material handling costs and non-material relationship requirements according to the idea of systematic layout planning. Our focus is on a particular case which involves the explicit consideration of fixed aisles and transverse passageways between sections. Numerical experiments as well as comparative tests show the great effectiveness of the proposed method in dealing with multi-criteria facility layout problems up to some moderate scales.     

A damage-plasticity interface approach to the meso-scale modelling of concrete subjected to cyclic compressive loading

Concrete is characterised by stiff inclusions in a soft matrix separated by weak interfacial transition zones (ITZs). Subjected to cyclic loading, this material exhibits a strongly nonlinear response, which is characterised by the occurrence of hysteresis loops. Furthermore, for cyclic loading, failure may occur before the equivalent strength for monotonic loading is reached. The present work investigates, whether the occurrence of permanent displacements in different phases of the meso-structure of quasi-brittle heterogeneous materials, such as concrete, leads to damage evolution during repeated loading.A new three-dimensional interface model based on a combination of damage mechanics and the theory of plasticity is proposed, which allows one to control the ratio of permanent and total inelastic displacements. The model is based on only a few material parameters, which can be directly determined by experiments.The interface model is applied to the plane-stress analysis of an idealised heterogeneous material with cylindrical inclusions and ITZs subjected to cyclic compressive stresses.     

A time-predefined local search approach to exam timetabling problems

In recent years the processing speed of computers has increased dramatically. This in turn has allowed search algorithms to execute more iterations in a given amount of real-time. Does this necessarily always lead to an improvement in the quality of final solutions? This paper is devoted to the investigation of that question. We present two variants of local search where the search time can be set as an input parameter. These two approaches are: a time-predefined variant of simulated annealing and an adaptation of the “great deluge” method. We present a comprehensive series of experiments which show that these approaches significantly outperform the previous best results (in terms of solution quality) on a range of benchmark exam timetabling problems. Of course, there is a price to pay for such better results: increased execution time. We discuss the impact of this trade-off between quality and execution time. In particular we discuss issues involving the proper estimation of the algorithm's execution time and the assessment of its importance.     

A hybrid-element approach to crack problems in plane elasticity

The hybrid-element concept and the complex variable technique have been adopted for constructing a special super-element to be used jointly with conventional finite elements for the analysis of elastic stress intensity factors for plane cracks. The use of the complex variable technique permits the proper consideration of the stress intensity at the crack tip, and it also leads to very efficient programming. The use of such a super-element in the finite element solution has been shown to be highly accurate when only a very coarse element mesh is used near the crack.     

A combined heuristic approach to dynamic lot sizing problems

A combined heuristic approach for dynamic lot sizing problems has been proposed. The combined heuristic is based on the performance analysis of the Silver-Meal heuristic on different problem sizes and demand patterns. The heuristic performs extremely well on average, and has a worst case performance ratio of two.     

A tool based approach to checking logical consistency in accident reports

In this paper, we present a technique to analyse consistency in accident reports. This is achieved using the prototype verification system. The relevant evidence and the rules for normal behaviour are coded as axioms. These axioms are then used to identify the cause of the accident. The key aspect of our work is to describe the system using a notion of states and state predicates. We show that our technique can be used in conjunction with other formal methods used to analyse accident reports.     

A matrix-based approach to properness and inversion problems for rational surfaces

We present a matrix-based approach for deciding if the parameterization of an algebraic space surface is invertible or not, and for computing the inverse of the parametrization if it exists.     

A genetic approach to solve numerical problems in the Preisach model identification

This paper introduces an identification procedure of the classical and modified scalar Preisach models based on genetic algorithms. It can be used when a reduced set of experimental data is known. The main advantage of this approach is the numerical stability of the solution. The results show that the coupling between our genetic identification procedure and the modified scalar Preisach model is able to reproduce the experimental behavior of different magnetic soft steels.     

A simple approach to solve boundary-value problems in gradient elasticity

Summary We outline a procedure for obtaining solutions of certain boundary value problems of a recently proposed theory of gradient elasticity in terms of solutions of classical elasticity. The method is applied to illustrate, among other things, how the gradient theory can remove the strain singularity from some typical examples of the classical theory.     

A new approach to solving stochastic programming problems with recourse

A new numerical approach to the solution of two-stage stochastic linear programming problems is described and evaluated. The approach avoids the solution of the first-stage problem and uses the underlying deterministic problem to generate a sequence of values of the first-stage variables which lead to successive improvements of the objective function towards the optimal policy. The model is evaluated using an example in which randomness is described by two correlated factors. The dynamics of these factors are described by stochastic processes simulated using lattice techniques. In this way, discrete distributions of the random parameters are assembled. The solutions obtained with the new iterative procedure are compared with solutions obtained with a deterministic equivalent linear programming problem. It is concluded that they are almost identical. However, the computational effort required for the new approach is negligible compared with that needed for the deterministic equivalent problem.