Logistic costs case study—an ABC approach

Activity based costing (ABC) represents a radical departure from the traditional cost accounting systems. The ABC methodology, rather than allocating costs to individual units, identifies the activities that consume resources, matching costs to the level of such activities. The key aspect of this methodology is the development of the models that represent a logical and quantifiable relationship between the utilisation of resources, the performance of activities, and the products or services that they provide. With these models one can simultaneously mirror the flow of orders and products along the logistic chain, capturing the costs at a level of desegregation that enables the analysis of profit by type of client, market segment and distribution channel. This application of ABC costing to a logistic operator illustrates the main difficulties and benefits of this approach.     

Optimal preventive maintenance scheduling of thermal generating units in power systems —A survey of problem formulations and solution methods

Preventive maintenance scheduling of thermal generating units occupies a significant place in power system operation and expansion planning; at the same time it is a challenging optimization problem. The purpose of this paper is to analyse essential features of the maintenance scheduling problem, including imposed constraints and various objectives, as well as to present the results of the research work done in this field using operational research methods. Papers published during last fifteen years are discussed, with special regard for the applied optimization techniques.     

Local models—an approach to distributed multi-objective optimization

When solving real-world optimization problems, evolutionary algorithms often require a large number of fitness evaluations in order to converge to the global optima. Attempts have been made to find techniques to reduce the number of fitness function evaluations. We propose a novel framework in the context of multi-objective optimization where fitness evaluations are distributed by creating a limited number of adaptive spheres spanning the search space. These spheres move towards the global Pareto front as components of a swarm optimization system. We call this process localization. The contribution of the paper is a general framework for distributed evolutionary multi-objective optimization, in which the individuals in each sphere can be controlled by any existing evolutionary multi-objective optimization algorithm in the literature.     

Reed‐muller codes: an ideal theory approach

By using techniques from commutative algebra such as the ideal of a set of points, the a‐invariant, the Hilbert function, and the Koszul complex, the main results about the Generalized and Projective Reed‐Muller codes are obtained.     

Toward net-zero carbon manufacturing operations: an onsite renewables solution

A growing number of manufacturing firms are striving to achieve eco-friendly operations through onsite wind or solar generation. This paper proposes a zero-carbon power supply model to guide the integration of onsite renewable energy into manufacturing facilities. We intend to address two fundamental questions: (1) Is it cost-effective to deploy onsite wind turbines and solar photovoltaics (PVs) systems to achieve net-zero carbon environmental performance? (2) Is the renewable generation system able to meet the electricity demand despite the power intermittency? To answer these questions, we formulate a stochastic optimization model to minimize the levelized cost of onsite renewable energy. The goal is achieved by optimizing the sizing of wind and solar generating units. The proposed energy solution is tested in ten cities around the world under diverse climatic conditions. While PV is still expensive, we conclude that manufacturers could realize zero-carbon emissions at affordable cost provided the local wind speed is above 5 m/s.     

Logic and rationality in OR interventions: an examination in the light of the ‘critical rationalist’ approach

Historically OR has conceived of itself as a professional practice giving rational, objective advice rooted in the ethos of science. However, the claim of science to rationality and objectivity has wilted under the onslaught of relativist and post-modern attack. One proposed philosophy of science seeks to avoid such problems by adopting a strictly objectivist approach. Critical rationalism (CR), the philosophy originated by Karl Popper, attempts to eliminate all inductive, justificatory and merely subjective claims by the ruthless application of deductive logic. The philosophical development of the CR approach to practice is currently a work-in-progress; however, it is an approach that should on the face of it find favour with OR, particularly for those who want to claim that OR is logically rational. The paper, drawing on the work of David Miller, explores how such an approach can be applied in the OR context. It concludes that although as CR suggests it may be possible to drive out inductive and justificatory claims in OR, subjective choice is an essential element of managerial decision-making and cannot be ignored or assumed away. The paper identifies some of the challenges that confront philosophers of practice if OR is to take the insights of CR to heart, suggests some possible responses, and identifies areas for future research.     

Time decay of maxwell—klein—gordon equations in 4—dimensional minkowski space

Abstract. In this paper I derive a gauge invariant decay estimate of the solutions of massive Maxwell—Klein—Gordon fields equations in the 4—dimensional Minkowski space, provided that the initial energy of the system is bounded. This estimate implies that the Klein—Gordon field decays to zero in the local L² norm. I also show that the local energy decays. The proof is based on gauge invariant energy identities.     

Can an a priori error estimate for an approximate solution of an ill-posed problem be comparable with the error in data?

For a linear operator equation of the first kind with perturbed data, it is shown that the global (on typical sets) a priori error estimate for its approximate solution can have the same order as that for the approximate data only if the operator of the problem is normally solvable. If the operator of the problem is given exactly, this is possible only if the problem is well-posed (stable).     

An exact solution method for unconstrained quadratic 0–1 programming: a geometric approach

We explore in this paper certain rich geometric properties hidden behind quadratic 0–1 programming. Especially, we derive new lower bounding methods and variable fixation techniques for quadratic 0–1 optimization problems by investigating geometric features of the ellipse contour of a (perturbed) convex quadratic function. These findings further lead to some new optimality conditions for quadratic 0–1 programming. Integrating these novel solution schemes into a proposed solution algorithm of a branch-and-bound type, we obtain promising preliminary computational results.     

On the entropy solution to an elliptic problem in anisotropic Sobolev–Orlicz spaces

For a certain class of anisotropic elliptic equations with the right-hand side from L ₁ in an arbitrary unbounded domains, the Dirichlet problem with an inhomogeneous boundary condition is considered. The existence and uniqueness of the entropy solution in anisotropic Sobolev–Orlicz spaces are proven.     

Correlation stress testing for value-at-risk: an unconstrained convex optimization approach

Correlation stress testing is employed in several financial models for determining the value-at-risk (VaR) of a financial institution’s portfolio. The possible lack of mathematical consistence in the target correlation matrix, which must be positive semidefinite, often causes breakdown of these models. The target matrix is obtained by fixing some of the correlations (often contained in blocks of submatrices) in the current correlation matrix while stressing the remaining to a certain level to reflect various stressing scenarios. The combination of fixing and stressing effects often leads to mathematical inconsistence of the target matrix. It is then naturally to find the nearest correlation matrix to the target matrix with the fixed correlations unaltered. However, the number of fixed correlations could be potentially very large, posing a computational challenge to existing methods. In this paper, we propose an unconstrained convex optimization approach by solving one or a sequence of continuously differentiable (but not twice continuously differentiable) convex optimization problems, depending on different stress patterns. This research fully takes advantage of the recently developed theory of strongly semismooth matrix valued functions, which makes fast convergent numerical methods applicable to the underlying unconstrained optimization problem. Promising numerical results on practical data (RiskMetrics database) and randomly generated problems of larger sizes are reported.     

Designing an efficient supply chain network with uncertain data: a robust optimization—data envelopment analysis approach

Designing a supply chain network (SCN) is an important issue for organizations in competitive markets. In this paper, a novel robust SCN that considers the efficiencies and costs simultaneously is proposed. In order to estimate the efficiency of the producers and distributors, data envelopment analysis (DEA) model is incorporated into SCN. Moreover, to handle the uncertainty in data, a scenario-based robust optimization approach is applied. The proposed model finds out the efficient location of producers and distributors and determines the amount of purchases from each supplier in uncertain conditions. To illustrate the application of the proposed model, a numerical example is solved and results are analyzed.     

A parametric solution for simple stress—strength model of failure with an application

Estimation of P(R ⩽ S) is considered for the simple stress—strength model of failure. Using the Pareto and Power distributions together with their combined form a useful parametric solution is obtained and is illustrated numerically. It is shown that these models are also applicable when only the tails of distributions for R and S are considered. An application to the failure study concerning the fractures is also included     

Differential forms in Carnot groups: a Γ-convergence approach

Carnot groups (connected simply connected nilpotent stratified Lie groups) can be endowed with a complex (E ₀ ^* , d _c ) of “intrinsic” differential forms. In this paper we prove that, in a free Carnot group of step κ, intrinsic 1-forms as well as their intrinsic differentials d _c appear naturally as limits of usual “Riemannian” differentials d _ε , ε >?0. More precisely, we show that L ²-energies associated with ε ^?κ d _ε on 1 forms Γ-converge, as ε → 0, to the energy associated with d _c .