Emilio Cerdá

Efficient Solution Concepts and Their Relations in Stochastic Multiobjective Programming

In this work, different concepts of efficient solutions to problems of stochastic multiple-objective programming are analyzed. We center our interest on problems in which some of the objective functions depend on random parameters. The existence of different concepts of efficiency for one single stochastic problem, such as expected-value efficiency, minimum-risk efficiency, etc., raises the question of their quality. Starting from this idea, we establish some relationships between the different concepts. Our study enables us to determine what type of efficient solutions are obtained by each of these concepts.

Stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems

In this work, we deal with obtaining efficient solutions for stochastic multiobjective programming problems. In general, these solutions are obtained in two stages: in one of them, the stochastic problem is transformed into its equivalent deterministic problem, and in the other one, some of the existing generating techniques in multiobjective programming are applied to obtain efficient solutions, which involves transforming the multiobjective problem into a problem with only one objective function. Our aim is to determine whether the order in which these two transformations are carried out influences, in any way, the efficient solution obtained. Our results show that depending on the type of stochastic criterion followed and the statistical characteristics of the initial problem, the order can have an influence on the final set of efficient solutions obtained for a given problem.

Relations among Several Efficiency Concepts in Stochastic Multiple Objective Programming

In this paper, the resolution of stochastic multiple objective programming problems is studied. The existence of random parameters in the objective functions has resulted in the definition of several efficient solution concepts for such problems in the literature. We will focus our attention in the study of some of these concepts, namely, minimum risk and s probability. Once these concepts are defined, the relations among the sets of efficient solutions obtained are studied.

Waiting Lists for Surgery

Health waiting lists in general and surgical waiting list in particular are a problem for the majority of the European countries with a National Health System. In this chapter, the problem of the waiting lists for surgery from a general perspective in the scope of the health management in the European Union (EU) is analyzed. Also, applying mathematical programming techniques, we intend to design the real performance of surgical services at a local general hospital offering the decision maker a suitable methodology that allows us to analyze whether or not it is possible to improve the running of the services, taking into account all the real constraints, e.g., space, staff availability, waiting time upper limit, or financial support.

Analysis and comparisons of some solution concepts for stochastic programming problems

The aim of this study is to analyse the resolution of Stochastic Programming Problems in which the objective function depends on parameters which are continuous random variables with a known distribution probability. In the literature on these questions different solution concepts have been defined for problems of these characteristics. These concepts are obtained by applying a transformation criterion to the stochastic objective which contains a statistical feature of the objective, implying that for the same stochastic problem there are different optimal solutions available which, in principle, are not comparable. Our study analyses and establishes some relations between these solution concepts.

Analytical solution for a class of learning by doing models with multiplicative uncertainty

We find the closed form optimal solution for a class of learning by doing models, where multiplicative uncertainty is introduced in a piecewise linear cost reduction function. Previous literature does not find the closed form optimal solution for these models. We consider a monopolist, facing a linear demand function. The optimal policy for the resulting problem is shown to be piecewise linear and continuous. The optimal output increases with unit cost for certain values of the latter. Numerical examples are provided.

Learning by doing in a T-period production planning: Analytical solution

Abstract The firms in many industries shift down the production cost function as they accumulate experience (learning by doing). The intertemporal production decision of the firm under learning by doing can be formulated as a Dynamic Optimization problem. Though properties of the solution to that problem are known, in general this analytical solution has not been presented in the literature. In this paper we present the analytical solution for a class of discrete time T-period learning by doing problems. This allows us to gain insight into practical aspects such as determining when current losses are expected to occur or when the firm will become fully efficient. Examples are provided.

Modeling Multifunctional Agroforestry Systems with Environmental Values: Dehesa in Spain and Woodland Ranches in California

The high environmental and amenity values of Mediterranean oak woodlands influence the response of the public and landowners to market forces and to public policies for the management of oak woodland areas. In California and in Spain, woodlands with a Quercus overstory open enough to allow the development of a significant grassy or shrubby understory harbor exceptional levels of biodiversity, provide watershed and habitat, sequester carbon, offer historically meaningful landscapes, and are pleasing to the eye. For historic reasons, and because of the social and environmental values of the woodlands for their owners, large private holdings based on sylvo-pastoral enterprises have and will have a crucial role in the future of the woodlands. Simple financial models for predicting landowner behavior based on response to market forces do not explain landowner retention of oaks without incorporation of landowner consumption of environmental and amenity values from the property, because landowner utility for oaks is not fully accounted for. By the same token, predicting the best afforestation approach considering carbon sequestration alone without consideration of the biodiversity and amenity values of native oaks risks an over-valuation of planting alien species that could have negative environmental and social consequences. Reforestation models for carbon sequestration that do not incorporate biodiversity and public amenity values might favor plantings of alien species such as eucalyptus, however, this does not take into account the high public and private consumption values of native oaks.

Optimal control for forest management and conservation analysis in dehesa ecosystems

This paper presents a deterministic finite time horizon dynamic optimisation model aimed to determine optimal paths for artificial plantations and natural regeneration of two main tree species in dehesa multiple use ecosystems, holm oak (Quercus ilex L.) and cork oak (Q. suber L.). Whilst dehesa forest sustainability problems associated to exhaustive use of grazing resources have been indirectly approached by European Union authorities, providing support for artificial plantations over treeless land, no mention is made to natural regeneration techniques. In this sense, the formulated model allows for natural regeneration of already established ageing stands as a complement or even a substitute of actual reforestation practices. The proposed methodology is neither designed to determine optimal rotation of tree species nor optimal decorticating or pruning cycles of cork oaks and holm oaks, respectively. Instead, this information enters the model exogenously through knowledge of region specific silvicultural cycles for those commercially relevant tree species, and the optimisation program acts as an optimal land use allocator and thus a practical tool for policy analysis purposes. In addition to existing cost benefit analysis applications in dehesa ecosystems, the presented model allows in one side efficient evaluation of long term management dynamics —thus oak woodlands sustainability can be tested for sufficiently large time horizons—, and in the other, management decisions, instead of being forced through predefined scenarios, correspond to the optimal actions a decision agent would take from the complete set of feasible possibilities given actual land use and tree age distributions.

When does "Learning by Doing" generate current losses?

Abstract. We study under which conditions a learning by doing effect in the industry causes a monopolist to operate at a loss for some initial periods. Those conditions involve a parameter of the learning process, the slope of inverse demand function and the discount parameter. In order to get results, we explore the analytical solution to a T-period learning by doing model, which is also a novelty. Numerical examples are presented.