Climate policy under fat-tailed risk: an application of FUND

We apply four alternative decision criteria, two old ones and two new, to the question of the appropriate level of greenhouse gas emission reduction. In all cases, we consider a uniform carbon tax that is applied to all emissions from all sectors and all countries; and that increases over time with the discount rate. For a one per cent pure rate of the time preference and a rate of risk aversion of one, the tax that maximises expected net present welfare equals $120/tC in 2010. However, we also find evidence that the uncertainty about welfare may well have fat tails so that the sample mean exists only by virtue of the finite number of runs in our Monte Carlo analysis. This is consistent with Weitzman’s Dismal Theorem. We therefore consider minimax regret as a decision criterion. As regret is defined on the positive real line, we in fact consider large percentiles instead of the ill-defined maximum. Depending on the percentile used, the recommended tax lies between $100 and $170/tC. Regret is a measure of the slope of the welfare function, while we are in fact concerned about the level of welfare. We therefore minimise the tail risk, defined as the expected welfare below a percentile of the probability density function without climate policy. Depending on the percentile used, the recommended tax lies between $20 and $330/tC. We also minimise the fatness of the tails, as measured by the p-value of the test of the null hypothesis that recursive mean welfare is non-stationary in the number of Monte Carlo runs. We cannot reject the null hypothesis of non-stationarity at the 5 % confidence level, but come closest for an initial tax of $50/tC. All four alternative decision criteria rapidly improve as modest taxes are introduced, but gradually deteriorate if the tax is too high. That implies that the appropriate tax is an interior solution. In stark contrast to some of the interpretations of the Dismal Theorem, we find that fat tails by no means justify arbitrarily large carbon taxes.     

Modelling and application of the self-locking phenomenon in the context of a non-discrete impact clutch

This paper describes an application of the self locking phenomenon in order to realize a non-discrete impact clutch. It is used to generate velocity jumps in an underactuated robot manipulator. Due to control reasons the impacts have to be made possible at arbitrary times, which calls for a non-discrete device. Different design alternatives are listed and a numerical simulation as well as a possible mechanical design of the self-locking mechanism are presented. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the impact of advertising initiatives in supply chains

Advertising plays an important role in affecting consumer demand. Socially responsible firms are expected to use advertising judiciously, limiting advertising of “bad” products. An example is the advertising initiative adopted by several major food manufacturers to limit the advertising of unhealthy food categories to children. Such initiatives are based on the belief that less advertising will lead to less consumption of these unhealthy food categories. However, food manufacturers usually distribute products to consumers through retailers whose advertising is not restricted by those initiative programs. In this paper, we examine the effectiveness of such advertising initiative in a leader–follower supply chain with one manufacturer and one retailer. We assume that both the manufacturer and the retailer can choose to participate in the advertising initiative by reducing their advertising levels. The problem is formulated as a Stackelberg game. We show that the effectiveness of the advertising initiative critically depends on the leader’s participation in the initiative. If the leader is willing to reduce the advertising level below a threshold, the market coverage of the product can drop significantly. On the other hand, if only the follower participates in the initiative, the market coverage is likely to expand in the majority of cases. Managerial implications of this research are also discussed.     

Modelling and optimisation for sustainable development policy assessment

Earlier work on sustainable development devised a policy assessment tool that was based on a static optimisation formulation. Key ingredients in sustainable development problems are the presence of random effects and the conflict between different objectives. To accommodate these, the earlier formulation was strongly stochastic and was posed in a multi-objective framework. The purpose of this paper is to consider the extension of the work to a formulation that deploys dynamic optimisation. In particular it is the aim here to use simulations based on a large scale model to derive dynamic rather than static representations, to integrate these into the optimisation scheme and to assess the benefits.     

Modelling of linguistic variables in multicriteria energy policy support

The climate change and the increasing complexity of the energy sector along with the prerequisite for sustainability have broadened the energy policy shaping field by bringing out new challenges. Decision support tools and methods, such as Multicriteria Decision Aid (MCDA), are necessary for energy policy, in the pursuit of appropriate approaches necessary to support the restructuring of the energy sector, concerning patterns of energy extraction, generation, transformation and use, from unsustainable to sustainable forms of development. Papers devoted to the investigation of MCDA models using linguistic variables for energy policy support seem to be not available in the international literature. The scope of this paper is to explore different linguistic representation and computational models in MCDA that are or can be applied to energy policy support and to establish a clear linkage between them. This paper argues that MCDA methodologies with direct computation on linguistic variables can support energy policy frameworks, bridging the gap between energy policy makers thinking, reasoning, representation and computing. Finally, current trends, open questions and prospects in this topic are pointed out.     

Modelling advertising budgeting and allocation decisions using modified multinomial logit market share models

Previous research suggests that a multinomial logit model of market share (MNL) is inappropriate for equilibrium analyses of advertising competition. This article shows that when employing simple transformations of the advertising effort, the modified MNL model becomes useful in representing situations of diminishing returns to advertising and appropriate for advertising equilibrium analyses without additional difficulties in its empirical estimation. Using the modified MNL model, optimal advertising budgets together with their allocation over time are derived for both the cases of concave and S-shaped attraction (response) functions in a symmetric oligopoly.     

Modelling for policy assessment in the natural gas industry

The selection of a method for policy assessment in a particular industry varies according to the characteristics of the issues involved. In the natural gas industry, each component has its own specific features and, when analysed as a single whole, a synthesized modelling approach may turn appropriate. This paper shows that in some instances, the integration of modelling methodologies might be of great value for understanding, evaluating and formulating energy policy. Here we address methodological issues that have been considered for the assessment of policy options in the natural gas industry in Colombia. We focus on both modelling and policy, specifically with respect to industry sustainability, and also on environmental impacts.     

Optimal investment policy: An application of Stokes' theorem

An application of the Stokes' theorem is illustrated by solving the two-state problem, with inequality constraints, of Dobell and Ho concerning the optimal investment of resources. Whenever applicable, the Stokes' theorem approach seems to be elegant and parsimonious.     

Optimization of planning an advertising campaign of goods and services

A generalization of the mathematical model and operations research problems formulated on its basis, which were presented in [1] in the framework of an approach to planning an advertising campaign of goods and services, is considered, and corresponding nonlinear programming problems with linear constraints are formulated.     

Pure-strategy Nash equilibria in an advertising game with interference

Two manufacturers produce substitutable goods for a homogeneous market. The advertising efforts of the two manufacturers determine the demand for the goods and interfere negatively with each other. The demand of each good is a piecewise linear function of the product goodwill, and the latter is a linear function of advertising efforts. In a game with two competing profit-maximizing manufacturers who have access to a set of several advertising media, the pure-strategy Nash equilibria are characterized and their existence is shown.     

Dual problem of optimizing an orthotropic cylindrical shell

The problem of optimizing the weight of an orthotropic cylindrical shell is examined, using the duality theory of geometrical programing.     

On the impact of initial performance on the effectiveness of advertising pulsation policies

Using a modified version of a Vidale–Wolfe model, proposed by Little, this paper examines the impact of initial sales rate on the performance of a variety of discrete, piecewise-continuous advertising policies for a finite planning horizon. The deployment of a non-discounted measure of performance reveals, irrespective of the shape of the advertising response function, that when the initial sales rate is different from zero at the beginning of the planning period: (1) a firm would be better off concentrating its advertising effort at the end rather than at the beginning of the planning period for a Blitz Policy (BP), (2) for an Advertising Pulsing/Maintenance Policy (APMP), it is more lucrative for a firm to alternate between a lower level of advertising followed by higher level (low–high) in a cyclic manner rather than to cycle the opposite way (high–low), and (3) in the presence of an initial sales rate, the pattern of the optimal advertising policy determined by dynamic programming can be significantly different from its alternative counterpart in its absence. In addition, it has been demonstrated, among other theoretical findings, that, for any given mean rate of advertising, the mean sales is bounded from below and is a decreasing function of the length of the planning horizon. Numerical examples are introduced to illustrate and reinforce the above research findings.     

A tactical model for resource allocation and its application to advertising budgeting

Models for optimal product positioning have received considerable attention by marketing researchers and marketing scientists over the past decade. Typically, optimizing models take the viewpoint that the manager wishes to find a specific vector of product attribute levels that, in the face of competitors’ product profiles, maximizes the firm’s market share (or, perhaps, return) over some designated planning horizon. This class of models emphasizes long run strategic modeling.In contrast, the authors introduce a tactical, short-term model, called SALIENCE, whose purpose is to allocate sales efforts in such a way as to increase the relative importance of attributes for which the sponsoring firm’s current product has a (possibly temporary) differential advantage. In this case emphasis is on short-run, tactical decision making.We describe the SALIENCE model, both informally and mathematically. The model is applied, illustratively, to a real (disguised) study of overnight air shipment delivery.     

Intervention analysis to identify significant exposures in pulsing advertising campaigns: an operative procedure

The purpose of this paper is to develop an operational method to detect the most effective exposures in the context of a given pulsing advertising campaign. For most effective, are intended those exposures that produce a statistically significant increase in the level of a response variable, either temporarily or permanently. The method consists in specifying an intervention model for the response variable, where the significant exposures are selected on the basis of a probabilistic criterion, and is empirically evaluated by using brandlevel data from five advertising tracking studies that also include the actual spending schedules. Given a pulsing advertising campaign, the proposed method serves both as an a-posteriori improvement of the campaign itself and as an a-priori additional information for programming future scheduling. Mathematics Subject Classification: 62M10.     

Optimal advertising/ordering policy and finance mode selection for a capital-constrained retailer with stochastic demand

In this paper, we discuss how a capital-constrained retailer determines his optimal advertising/ordering policy and selects his financing mode when he faces the following modes: no financing service, bank financing, and supplier/mixed financing. For each mode, we construct an optimization model and present a method for how the retailer determines his corresponding optimal advertising and ordering policies in the terms of his initial capital level. Furthermore, we derive the conditions of retailer selecting the optimal financing mode based on both his initial capital level and the interest rates of the financing services. We show that when the retailer is relatively “poor,” he prefers bank financing mode if the bank interest rate is lower than the supplier, otherwise mixed financing mode; when he is moderately “rich,” he only selects supplier financing mode if the bank interest rate is greater than a threshold value and otherwise bank financing mode; however, when he is relatively “rich,” he always chooses bank financing mode even if the bank interest rate is higher than the supplier. We conduct numerical studies to illustrate the theoretical results and find adopting financing service significantly improves the retailer’s performance especially when he has relatively low initial capital level.     

Evaluating the profitability of advertising for heavily advertised brands: an empirical study

Even companies with large advertising budgets are sceptical of OR models in advertising—such models often appear overly complex, unrealistic and costly to use. Here a simple econometric model is proposed which utilises existing company data. The parameters are estimated for the five leading brands in a sector of the German alcoholic drinks market. Estimates of the short and long run advertising elasticities are made and optimum advertising appropriations are calculated.     

Modelling handling operations in grocery retail stores: an empirical analysis

Shelf stacking represents the daily process of manually refilling the shelves with products from new deliveries. For most retailers, handling operations are labour-intensive and often very costly. This paper presents an empirical study of the shelf-stacking process in grocery retail stores. We examine the complete process at the level of individual sub-activities and study the main factors that affect the execution time of this common operation. Based on the insights from different sub-activities, a prediction model is developed that allows estimating the total stacking time per order line, solely on the basis of the number of case packs and consumer units. The model is tested and validated using real-life data from two European grocery retailers and serves as a useful tool for evaluating the workload required for the usual shelf-stacking operations. Furthermore, we illustrate the benefits of the model by analytically quantifying the potential time savings in the stacking process, and present a lot-sizing analysis to demonstrate the opportunities for extending inventory control rules with a handling component.