Brand positioning under lexicographic choice rules

This paper discusses a brand positioning model in which two brands of a product are to be positioned in a price-quality space under a new behavioral assumption. This assumption asserts that customers determine the highest-quality product within their reservation price and purchase it, provided its quality does not fall short of a minimum standard. The model also includes producers' costs that are incurred for delivering a certain quality. We first delineate reaction functions for the optimal location of one brand, give a location of its competitor. We then show that Nash equilibria do not exist as long as price and quality are both variable. Finally, we consider a two phase model: in the first phase, the duopolists sequentially choose their quality levels under the assumption that both competitors know that in the second phase, a Nash equilibrium in prices follows. Single-variable mathematical programming formulations are presented to solve the problem. A numerical example is also given to illustrate the working of the model.     

Technology choice under several uncertainty sources

We analyze a model of irreversible investment with two sources of uncertainty. A risk-neutral decision maker has the choice between two mutually exclusive projects under input price and output price uncertainty. We propose a complete study of the shape of the rational investment region and we prove that it is never optimal to invest when the alternative investments generate the same payoff independently of its size. A key feature of this bidimensional degree of uncertainty is thus that the payoff generated by each project is not a sufficient statistic to make a rational investment. In this context, our analysis provides a new motive for waiting to invest: the benefits associated with the dominance of one project over the other. As an illustration, we apply our methodology to power generation under uncertainty.     

Predicted violations of the invariance principle in choice under uncertainty

A basic and distinctive prediction of regret theory is that certain variations in the juxtaposition of the consequences of alternative actions will tend to affect preferences between them in a particular way. This paper presents a body of experimental evidence which tests that prediction.The evidence in this paper comes from experimental work financed by the Economic and Social Research Council (U.K.), Awards B 00 23 2127 and B 00 23 2163. The author would also like to thank the British Academy and the University of York for assistance with the costs of travel and attendance at the Symposium.     

An outranking method under uncertainty

The uncertainty of consequences and the imprecision of data often imply, in multicriteria decision problems, the use of probability distributions to characterize the evaluation of each action with respect to eacg criterion. To keep as much information as possible, the analysis should treat directly these probability distributions instead of reducing them to single values such as mean or median. In this context, the paper proposes a multicriteria procedure which transforms these distributive evaluations of actions, according to decisionmaker's preferences, in order to progress to a ranking of these actions. The procedure consists, for each couple of actions, to construct a distributive preference degree with respect to each criterion and a distributive outranking degree over all criteria. These distributive outranking degrees are then explored in order to rank the actions, totally or partially.     

An average lexicographic value for cooperative games

For games with a non-empty core the Alexia value is introduced, a value which averages the lexicographic maxima of the core. It is seen that the Alexia value coincides with the Shapley value for convex games, and with the nucleolus for strongly compromise admissible games and big boss games. For simple flow games, clan games and compromise stable games an explicit expression and interpretation of the Alexia value is derived. Furthermore it is shown that the reverse Alexia value, defined by averaging the lexicographic minima of the core, coincides with the Alexia value for convex games and compromise stable games.     

在未来收益不确定下的期权定价模型

§ 1　 IntroductionAt present,some high-technology(high-tech) firms such as information,software,pharmaceutical et al,are rapidly growing at home and abroad.The firm' s stock price hasbeen bid upward irrationally by individual day traders.Some managers see the currentfren-zy as a spectacularexample ofmarketbubble.The marketbubble can' tbe explained by theaverage rate of growth,butithas reacted on the developmentprospect of high-tech firms.Existing net cash flow method cannot properly capture …     

With uncertainty by choice of zero dynamics

We propose an approach to output stabilization of multiply connected control systems with uncertainty based on structural decomposition of the original system and asymptotic invariance methods. The proposed approach solves the stabilization problem for minimum-phase systems. Bounds are obtained on the rate of convergence of the stabilization algorithms. Conditions are derived expanding the class of vector controlled systems with uncertainty that are stabilizable by asymptotic invariance methods.     

Foundations of lexicographic utility

This paper presents an alternative mathematical characterization of lexicographic utility to the one given by Chipman (1960). A natural constructivistic procedure on imposing a lexicographic ordering on the product space of natural numbers is pursued. The consequences on the topological structure of such a space are examined.     

Automorphisms of lexicographic products

The automorphism group Γ(P) of a partially ordered set P consists of all permutations on P that preserve order (and have order preserving inverses). In this paper we raise, and partially answer, the question: How is the automorphism group of the lexicographic product (P × Q) of two orders (P and Q) related to the automorphism groups of the factors, P and Q?We show that the wreath product Γ(Q) wr ΓP) is always contained in Γ(P × Q). We find necessary and sufficient conditions for Γ(P × Q) to equal Γ(Q) wr Γ(P), and when P and Q are finite, we find a complete characterization of Γ(P × Q) in terms of Γ(P), Γ(Q) and properties of P and Q.     

Strange: An interactive method for multi-objective linear programming under uncertainty

In the field of investment planning within a time horizon, problems typically involve multiple objectives, and basic data are uncertain. In a large number of cases, these decision problems can be written as linear programming problems in which time dependent uncertainties affect the coefficients and the right hand side of constraints. Given the possibility of defining plausible scenarios on basic data, discrete sets of such coefficients are given, each with its subjective probability of occurrence. The corresponding structure is then characteristic for Multi-Objective Stochastic Linear Programming (MOSLP).In the paper, an interactive procedure is described to obtain a best compromise for such a MOSLP problem. This algorithm, called Strange, extends the Stem method to take the random aspects into account. It involves in particular, the concepts of stochastic programming with recourse. In its interactive steps, the efficiency projection techniques are used to provide the decision-maker with detailed graphical information on efficient solution families.As an illustration of the successive steps, a didactic example is solved in some detail, and the results of a case study in energy planning are given.     

An application of Lagrangian relaxation to a capacity planning problem under uncertainty

A supply chain network-planning problem is presented as a two-stage resource allocation model with 0-1 discrete variables. In contrast to the deterministic mathematical programming approach, we use scenarios, to represent the uncertainties in demand. This formulation leads to a very large scale mixed integer-programming problem which is intractable. We apply Lagrangian relaxation and its corresponding decomposition of the initial problem in a novel way, whereby the Lagrangian relaxation is reinterpreted as a column generator and the integer feasible solutions are used to approximate the given problem. This approach addresses two closely related problems of scenario analysis and two-stage stochastic programs. Computational solutions for large data instances of these problems are carried out successfully and their solutions analysed and reported. The model and the solution system have been applied to study supply chain capacity investment and planning.     

Dynamic journeying under uncertainty

We introduce a journey planning problem in multi-modal transportation networks under uncertainty. The goal is to find a journey, possibly involving transfers between different transport services, from a given origin to a given destination within a specified time horizon. Due to uncertainty in travel times, the arrival times of transport services at public transport stops are modeled as random variables. If a transfer between two services is rendered unsuccessful, the commuter has to reconsider the remaining path to the destination. The problem is modeled as a Markov decision process in which states are defined as paths in the transport network. The main contribution is a backward induction method that generates an optimal policy for traversing the public transport network in terms of maximizing the probability of reaching the destination in time. By assuming history independence and independence of successful transfers between services we obtain approximate methods for the same problem. Analysis and numerical experiments suggest that while solving the path dependent model requires the enumeration of all paths from the origin to the destination, the proposed approximations may be useful for practical purposes due to their computational simplicity. In addition to on-time arrival probability, we show how travel and overdue costs can be taken into account, making the model applicable to freight transportation problems.     

Online purchasing under uncertainty

Suppose there is a collection of independent uniform random variables, and a hypergraph of target structures on the vertex set . We would like to purchase a target structure at small cost, but we do not know all the costs x_i ahead of time. Instead, we inspect the random variables x_i one at a time, and after each inspection, choose to either keep the vertex i at cost x_i, or reject vertex i forever. In the present paper, we consider the case where is the edge‐set of a complete graph (or digraph), and the target structures are the spanning trees of a graph, spanning arborescences of a digraph, the paths between a fixed pair of vertices, perfect matchings, Hamilton cycles or the cliques of some fixed size.     

Forestry management under uncertainty

The forest harvest and road construction planning problem consists fundamentally of managing land designated for timber production and divided into harvest cells. For each time period the planner must decide which cells to cut and what access roads to build in order to maximize expected net profit. We have previously developed deterministic mixed integer linear programming models for this problem. The main contribution of the present work is the introduction of a multistage Stochastic Integer Programming model. This enables the planner to make more robust decisions based on a range of timber price scenarios over time, maximizing the expected value instead of merely analyzing a single average scenario. We use a specialization of the Branch-and-Fix Coordination algorithmic approach. Different price and associated probability scenarios are considered, allowing us to compare expected profits when uncertainties are taken into account and when only average prices are used. The stochastic approach as formulated in this work generates solutions that were always feasible and better than the average solution, while the latter in many scenarios proved to be infeasible.     

Optimisation under hybrid uncertainty

Fuzzy Stochastic Optimisation is emerging as a subfield of Mathematical programming, the disciplinary matrix of which consists of analysis of mathematical programs under fuzziness and randomness along with methods for solving them. The “primum movens” of this paper is to describe a unifying methodological approach, that is suitable for finding a satisfying solution of a mathematical program in the presence of fuzzy data and random variables. Properties of fuzzy random variables (FRVs) serve as the backdrop to this approach which also lends itself better to handling mathematical programs with fuzzy random coefficients. For the paper to be somewhat self-contained, the notion of FRV is briefly discussed and a synopsis of Fuzzy Stochastic Optimisation provided. A systematically solved example aimed at illustrating the proposed approach is also included.     

Cooperation under interval uncertainty

In this paper, the classical theory of two-person cooperative games is extended to two-person cooperative games with interval uncertainty. The core, balancedness, superadditivity and related topics are studied. Solutions called ψ ^α-values are introduced and characterizations are given.