A heuristic approach on the facility layout problem based on game theory

Facility layout problems are related to the location of all facilities in a plant. Numerous research works related to facility layout have been published. The applicability of these various existing models may be limited by the fact that they all ignore competitive reactions to one's actions. In addition to external competitors, some internal problems of system such as material handling system design affect layout designs. For considering these effects, some researchers have investigated multi-objective approaches that in most cases lead to the optimisation of a weighted sum of score functions. The poor practicability of such an approach is due to the difficulty of normalising these functions and quantifying the weights. To the extent that competitors do react to a firm's actions and also the facility layout problem considers several conflicting objectives by distinct decision makers in the firm, the existing models may be oversimplifications of reality. In this paper, we modelled such a facility layout problem with conflicting objectives under a duopoly Bertrand competition as a game and solved it with a proposed simulated annealing meta-heuristic. Results obtained from solving some numerical examples confirm the effectiveness of the proposed model for the layout design.     

Damage in MMCs using the GMC: theoretical formulation

In this work the incorporation of damage in the material behavior is investigated. Damage is incorporated into the generalized cells model (GMC), and applied to metal-matrix composites (MMCs). The local incremental damage model of Voyiadjis and Park is used here in order to account for damage in each subcell separately. The resulting micromechanical analysis establishes elasto-plastic constitutive equations that govern the overall behavior of the damaged composite. The elasto-plastic constitutive model is first derived in the undamaged configuration for each constituent of the metal-matrix composite. The plasticity model used here is based on the existence of a yield surface and flow rule. The relationships are then transformed for each constituent to the damaged configuration by applying the local incremental constituent damage tensors. The overall damaged quantities are then obtained by applying the local damage concentration factors obtained by employing the rate of displacement and traction continuity conditions at the interface between subcells and between neighboring repeating cells in the generalized cells model. Examples are solved numerically in order to explore the physical interpretation of the proposed theory for a unit cell composite element.     

Towards a richer evolutionary game theory

Most examples of the application of evolutionary game theory to problems in biology involve highly simplified models. I contend that it is time to move on and include much more richness in models. In particular, more thought needs to be given to the importance of (i) between-individual variation; (ii) the interaction between individuals, and hence the process by which decisions are reached; (iii) the ecological and life-history context of the situation; (iv) the traits that are under selection, and (v) the underlying psychological mechanisms that lead to behaviour. I give examples where including variation between individuals fundamentally changes predicted outcomes of a game. Variation also selects for real-time responses, again resulting in changed outcomes. Variation can select for other traits, such as choosiness and social sensitivity. More generally, many problems involve coevolution of more than one trait. I identify situations where a reductionist approach, in which a game is isolated from is ecological setting, can be misleading. I also highlight the need to consider flexibility of behaviour, mental states and other issues concerned with the evolution of mechanism.     

The warehouse scheduling problem: formulation and algorithms

The Warehouse Scheduling Problem is a deterministic multi-item inventory problem with a restriction on warehouse floor space available. We formulate a mixed integer nonlinear programming problem for the objective of minimizing long run inventory holding and order costs per unit of time. We integrate algorithms for staggering orders, described in companion papers, with a heuristic to choose the order sequences. The result is called Sequenced Staggering. We describe a new algorithm to generate order frequencies, called the powers-of-two-factor-of-three technique, as a generalization of Roundy's roundoff technique for powers-of-two policies. We report on a computational study of four hybrid algorithms for solving the warehouse scheduling problem, including the competing algorithm of Gallego, Queyranne, and Simchi-Levi. Based on these results, we recommend the combination of powers-of-two frequencies with Sequenced Staggering.     

Variational formulation of a nonstationary heat-conduction problem

Belorus Polytechnic Academy, Minsk. Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 62, No. 1, pp. 130–139, January, 1992.     

Lagrangian heuristic-based neighbourhood search for the multiple-choice multi-dimensional knapsack problem

This article addresses a Lagrangian heuristic-based neighbourhood search for the multiple-choice multi-dimensional knapsack problem, an NP-hard combinatorial optimization problem. The problem is solved by using a cooperative approach that uses a local search for exploring a series of neighbourhoods induced from the Lagrangian relaxation. Each neighbourhood is submitted to an optimization process using two alternative strategies: reducing and moving strategies. The reducing strategy serves to reduce the current search space whereas the moving strategy explores the new search space. The performance of the proposed approach is evaluated on benchmark instances taken from the literature. Its obtained results are compared with those reached by some recent methods available in the literature. New solutions have been obtained for almost 80% of the instances tested.     

A hybrid heuristic for the multiple choice multidimensional knapsack problem

In this article, a new solution approach for the multiple choice multidimensional knapsack problem is described. The problem is a variant of the multidimensional knapsack problem where items are divided into classes, and exactly one item per class has to be chosen. Both problems are NP-hard. However, the multiple choice multidimensional knapsack problem appears to be more difficult to solve in part because of its choice constraints. Many real applications lead to very large scale multiple choice multidimensional knapsack problems that can hardly be addressed using exact algorithms. A new hybrid heuristic is proposed that embeds several new procedures for this problem. The approach is based on the resolution of linear programming relaxations of the problem and reduced problems that are obtained by fixing some variables of the problem. The solutions of these problems are used to update the global lower and upper bounds for the optimal solution value. A new strategy for defining the reduced problems is explored, together with a new family of cuts and a reformulation procedure that is used at each iteration to improve the performance of the heuristic. An extensive set of computational experiments is reported for benchmark instances from the literature and for a large set of hard instances generated randomly. The results show that the approach outperforms other state-of-the-art methods described so far, providing the best known solution for a significant number of benchmark instances.     

Bridging humanitarian operations management and organisational theory

The aim of the editorial note is to introduce the scope of this special issue (SI). We explain our editorial approach and provide a brief summary of eight articles included in the SI following multiple rounds of reviews. Finally, we outline future research questions which stemmed out of the discussions of this SI.     

C-K design theory: an advanced formulation

C-K theory is a unified Design theory and was first introduced in 2003 (Hatchuel and Weil 2003). The name “C-K theory” reflects the assumption that Design can be modelled as the interplay between two interdependent spaces with different structures and logics: the space of concepts (C) and the space of knowledge (K). Both pragmatic views of Design and existing Design theories define Design as a dynamic mapping process between required functions and selected structures. However, dynamic mapping is not sufficient to describe the generation of new objects and new knowledge which are distinctive features of Design. We show that C-K theory captures such generation and offers a rigorous definition of Design. This is illustrated with an example: the design of Magnesium-CO₂ engines for Mars explorations. Using C-K theory we also discuss Braha and Reich’s topological structures for design modelling (Braha and Reich 2003). We interpret this approach as special assumptions about the stability of objects in space K. Combining C-K theory and Braha and Reich’s models opens new areas for research about knowledge structures in Design theories. These findings confirm the analytical and interpretative power of C-K theory.

Mathematical formulation of the stefan problem

The Stefan problem describes the conduction of heat in a medium involving a solid-liquid phase change at a prescribed melting temperature. Considerations of physical, mathematical and numerical experiences with such problems all imply that enthalpy (not temperature) is the natural dependent variable to specify the solution. Our discussion centers on the physical interpretation of the multi-valued Heaviside “function” which arises in the mathematical formulation as the fraction of water. We show that this permits the consideration of (possibly large) regions of mush at the melting temperature and of problems with internally distributed sources of heat. Moreover, in order for such problems to be well-posed, this fraction of water must necessarily be specified initially in the part of the region at the melting temperature.     

An improved strain gradient plasticity formulation with energetic interfaces: theory and a fully implicit finite element formulation

A fully implicit backward-Euler implementation of a higher order strain gradient plasticity theory is presented. A tangent operator consistent with the numerical update procedure is given. The implemented theory is a dissipative bulk formulation with energetic contribution from internal interface to model the behavior of material interfaces at small length scales. The implementation is tested by solving some examples that specifically highlight the numerics and the effect of using the energetic interfaces as higher order boundary conditions. Specifically, it is demonstrated that the energetic interface formulation is able to mimic a wide range of plastic strain conditions at internal boundaries. It is also shown that delayed micro-hard conditions may arise under certain circumstances such that an interface at first offers little constraints on plastic flow, but with increasing plastic deformation will develop and become a barrier to dislocation motion.     

Cooperative parallel adaptive neighbourhood search for the disjunctively constrained knapsack problem

This article investigates the use of parallel computing for solving the disjunctively constrained knapsack problem. The proposed parallel computing model can be viewed as a cooperative algorithm based on a multi-neighbourhood search. The cooperation system is composed of a team manager and a crowd of team members. The team members aim at applying their own search strategies to explore the solution space. The team manager collects the solutions from the members and shares the best one with them. The performance of the proposed method is evaluated on a group of benchmark data sets. The results obtained are compared to those reached by the best methods from the literature. The results show that the proposed method is able to provide the best solutions in most cases. In order to highlight the robustness of the proposed parallel computing model, a new set of large-scale instances is introduced. Encouraging results have been obtained.     

Conceptual design optimization of rectilinear building frames: A knapsack problem approach

This article presents an automated technique for preliminary layout (conceptual design) optimization of rectilinear, orthogonal building frames in which the shape of the building plan, the number of bays and the size of unsupported spans are variables. It adopts the knapsack problem as the applied combinatorial optimization problem, and describes how the conceptual design optimization problem can be generally modelled as the unbounded multi-constraint multiple knapsack problem. It discusses some special cases, which can be modelled more efficiently as the single knapsack problem, the multiple-choice knapsack problem or the multiple knapsack problem. A knapsack contains sub-rectangles that define the floor plan and the location of columns. Particular conditions or preferences for the conceptual design can be incorporated as constraints on the knapsacks and/or sub-rectangles. A bi-objective knapsack problem is defined with the aim of obtaining a conceptual design having minimum cost and maximum plan regularity (minimum structural eccentricity). A multi-objective ant colony algorithm is formulated to solve the combinatorial optimization problem. A numerical example is included to demonstrate the application of the present method and the robustness of the algorithm.     

An iterative rounding search-based algorithm for the disjunctively constrained knapsack problem

This article proposes an iterative rounding search-based algorithm for approximately solving the disjunctively constrained knapsack problem. The problem can be viewed as a variant of the well-known knapsack problem with some sets of incompatible items. The algorithm considers two key features: a rounding strategy applied to the fractional variables of a linear relaxation and a neighbouring strategy used for improving the quality of the solutions at hand. Both strategies are iterated into a process based on adding a series of (i) valid cardinality constraints and (ii) lower bounds used for bounding the objective function. The proposed algorithm is analysed computationally on a set of benchmark instances of the literature. The proposed algorithm outperforms the Cplex solver and the results obtained improve on most existing solutions.     

Three-dimensional absolute nodal co-ordinate formulation: plate problem

In this investigation, an absolute nodal co-ordinate dynamic formulation is developed for the large deformations and rotations of three-dimensional plate elements. In this formulation, no infinitesimal or finite rotations are used as nodal co-ordinates, instead global displacements and slopes are used as the plate coordinates. Using this interpretation of the plate coordinates the new method does not require the use of co-ordinate transformation to define the global inertia properties of the plates. The resulting mass matrix is the same constant matrix that appears in linear structural dynamics. The stiffness matrix, on the other hand, is a non-linear function of the nodal co-ordinates of the plate even in the case of a linear elastic problem. It is demonstrated in this paper that, unlike the incremental finite element formulations, the proposed method leads to an exact modelling of the rigid body inertia when the plate element moves as a rigid body. It is also demonstrated that by using the proposed method the conventional plate element shape function has a complete set of rigid body modes that can describe an exact arbitrary rigid body displacement. Using this fact, plate elements in the proposed new formulation can be considered as isoparametric elements. As a consequence, an arbitrary rigid body motion of the element results in zero strain. © 1997 John Wiley & Sons, Ltd.     

Impact of policy incentives on electric vehicles development: a system dynamics-based evolutionary game theoretical analysis

Clean Technologies and Environmental Policy - A system dynamics-based evolutionary game theoretical analysis is proposed to examine the impact of policy incentives, i.e., price subsidy and taxation...     

Optimizing centralized inventory operations in a cooperative game theory setting

For single period inventory models with normally distributed, correlated individual demands we examine the problem of minimizing the cost of inventory centralization as a function of the covariance matrix. In a stable centralized setting there are no incentives for any party to break-away -- referred to as nonempty core conditions. For the allocated benefits in inventory centralization, nonempty core conditions are always satisfied. In this paper we discuss a step by step greedy optimization procedure which computes an optimal centralization solution. The procedure manipulates the correlations without changing the mean or the variance at each store. We do not just accept that in the centralized setting the parties are better-off but for the first time provide the analysis of how to maximize their collective benefits.     

Regularization of the solution of the inverse heat-conduction problem in a variational formulation

A version of the solution allowing numerical minimization of the target functional to be eliminated is considered.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 52, No. 6, pp. 991–995, June, 1987.