Exploring the trade-off between immediate gratification and delayed network externalities in the consumption of information goods

Our motivation for this paper originates from recent advances in consumption and payment technologies available for mobile commerce. Ubiquitous computing is enabling consumers worldwide to reach digital content and services whenever and wherever they request it. This capability further fuels “impatience” in consumption of such information goods. We model such consumer behavior using a hyperbolic discounting approach. A subset of these products, especially software, also inherit delayed network externalities as part of their consumption characteristics. This builds a tension between decision to consume now or to expedite consumption. We build a stylized model to assess the impact of immediate gratification on the profit maximizing behavior of a monopolist firm which produces an information good with network externalities. We find that serving “impatient” consumers is always profitable for a monopolist. For lower levels of network externalities, the monopolist can increase first period and decrease second period prices in equilibrium. As network externalities effect increases, prices converge to the traditional market (with exponential discounters) levels.     

Existence of optimal stationary policies in average reward Markov decision processes with a recurrent state

We consider discrete-timeaverage reward Markov decision processes with denumerable state space andbounded reward function. Under structural restrictions on the model the existence of an optimal stationary policy is proved; both the lim inf and lim sup average criteria are considered. In contrast to the usual approach our results donot rely on the average regard optimality equation. Rather, the arguments are based on well-known facts fromRenewal Theory.This research was supported in part by the Consejo Nacional de Ciencia y Tecnologia (CONACYT) under Grants PCEXCNA 040640 and 050156, and by SEMAC under Grant 89-1/00ifn$.     

Existence and computation of optimal tolls in multiclass network equilibrium problems

In this work we provide a simple proof of the existence of optimal tolls for multiclass network equilibrium problems where the value-of-time parameter varies continuously throughout the population. The main argument, based on a finite-dimensional reformulation of the problem, also allows us to determine in a simple fashion revenue minimizing link toll vectors.     

Testing of a large-scale network optimization program

This paper describes the experimental results of testing a large-scale program for solving minimum-cost network flow problems. With this program, general structure transshipment problems with over ten thousand nodes and thirty thousand arcs have been easily solved without resorting to auxiliary storage. The algorithm is a variant of the primal revised simplex method; the computer code is called LPNET illustrating the close connection between linear programming and network graphs. This approach substantially improves computer processing timeand core storage, especially for relatively large network problems. The results of these experiments are provided. It is emphasized that an organized experimental design and a detailed series of empirical tests are crucial for an efficient implementation.Research supported in part by TRW Systems Group and Harvard Business School.     

The expected number of extreme points of a random linear program

There has been increasing attention recently on average case algorithmic performance measures since worst case measures can be qualitatively quite different. An important characteristic of a linear program, relating to Simplex Method performance, is the number of vertices of the feasible region. We show 2 ⁿ to be an upper bound on the mean number of extreme points of a randomly generated feasible region with arbitrary probability distributions on the constraint matrix and right hand side vector. The only assumption made is that inequality directions are chosen independently in accordance with a series of independent fair coin tosses.We would like to thank the Institute of Pure and Applied Mathematics in Rio de Janeiro for supporting the authors' collaboration that led to this paper.     

Designing a sustainable closed-loop supply chain network based on triple bottom line approach: A comparison of metaheuristics hybridization techniques

Recently, there is a growing concern about the environmental and social footprint of business operations. While most of the papers in the field of supply chain network design focus on economic performance, recently, some studies have considered environmental dimensions.     

Reducing mosquito-borne disease outbreak size: The relative importance of contact and transmissibility in a network model

The complex biological and environmental factors involved in the transmission of mosquito-borne diseases in humans have made their control elusive in many instances. Conceptual models contribute to gain insight and help to reduce the risk of taking poor managerial decisions. The focus of this paper is to compare, using a contact network model, the impact that perturbation of the number infectious contacts and of transmissibility have on the size of an outbreak. We illustrate the analysis on a contact network parametrized with data that associates humans and the mosquito Culex quinquefasciatus, a vector for lymphatic filariasis. The model suggests that, if the values corresponding to transmissibility and number of infectious contacts is relatively large, variations in the size of an outbreak are significantly in favor of control measures to reduce infectious contacts.     

The role of retailer’s performance in optimal wholesale price discount policies

The main goal of this paper is to model the effects of wholesale price control on manufacturer’s profit, taking explicitly into account the retailer’s sales motivation and performance. We consider a stylized distribution channel where a manufacturer sells a single kind of good to a single retailer. Wholesale price discounts are assumed to increase the retailer’s motivation thus improving sales. We study the manufacturer’s profit maximization problem as an optimal control model where the manufacturer’s control is the discount on wholesale price and retailer’s motivation is one of the state variables. In particular in the paper we prove that an increasing discount policy is optimal for the manufacturer when the retailer is not efficient while efficient retailers may require to decrease the trade discounts at the end of the selling period. Computational experiments point out how the discount on wholesale price passed by the retailer to the market (pass-through) influences the optimal profit of the manufacturer.     

The role of the water temperature in the optimal management of marine aquaculture

This paper analyses the influence of the water temperature over the optimal management of aquaculture farms. A fish growth model is presented and included in a general profit optimisation framework. Results reveal a positive influence of the average water temperature over the optimal harvesting time. The optimal ration size exhibits an uneven path with an upward phase in the warmer season followed by downward phase in winter time. An application for the seabream culture in the Mediterranean countries shows harvesting time and ration size very dependent on the water temperature and the stocking date. The risk involved with uncertainty of the environmental conditions is also estimated, which could explain the difference between the predicted optimal harvesting sizes and the real practice in commercial culture.     

Optimal dividend payments under a time of ruin constraint: Exponential claims

We consider the optimal dividends problem under the Cramér–Lundberg model with exponential claim sizes subject to a constraint on the expected time of ruin. We introduce the dual problem and show that the complementary slackness conditions are satisfied, thus there is no duality gap. Therefore the optimal value function can be obtained as the point-wise infimum of auxiliary value functions indexed by Lagrange multipliers. We also present a series of numerical examples.     

Reliable design of a logistics network under uncertainty: A fuzzy possibilistic-queuing model

This paper proposes a bi-objective model for designing a reliable network of bi-directional facilities in logistics network under uncertainties. For this purpose, the model utilizes an effective reliability approach to find a robust logistics network design. The objectives of the model are to minimize the total costs and the expected transportation costs after failures of bi-directional facilities of the logistics network. To solve the model, a new solution approach is proposed by combining queuing theory, fuzzy possibilistic programming and fuzzy multi-objective programming. Finally, the computational experiments are provided to illustrate the effectiveness of the proposed model and solution approach.     

The minmax regret gradual covering location problem on a network with incomplete information of demand weights

The gradual covering location problem seeks to establish facilities on a network so as to maximize the total demand covered, allowing partial coverage. We focus on the gradual covering location problem when the demand weights associated with nodes of the network are random variables whose probability distributions are unknown. Using only information on the range of these random variables, this study is aimed at finding the “minmax regret” location that minimizes the worst-case coverage loss. We show that under some conditions, the problem is equivalent to known location problems (e.g. the minmax regret median problem). Polynomial time algorithms are developed for the problem on a general network with linear coverage decay functions.     

Improved program planning with formal models? The case of high risk crop farming in Northeast Germany

In this paper we explore whether the incorporation of systematic time series analyses and mathematical optimization procedures in the practical planning process has the potential to improve production program decisions. The cases of four German cash crop farms are investigated over six planning periods. In order to avoid solutions that simply exceed the farmer’s risk tolerance, the apparently accepted variance of the observed program’s total gross margin is used as an upper bound in the optimization. For each of the 24 planning occasions, the formal model is used to generate optimized alternative programs. The total gross margins that could have been realized if the formally optimized programs had been implemented are then compared to those that were actually realized. We find that the farmers could have increased their total gross margins significantly if—instead of using simple routines and rules of thumb—they had used adequate methods of statistical analysis combined with the formal optimization model. Norbert Hirschauer thanks the German Research Foundation (DFG) for the opportunity to work on this paper during a research leave.     

On degeneracy and collapsing in the construction of the set of objective values in a multiple objective linear program

In this paper an algorithm is developed to generate all nondominated extreme points and edges of the set of objective values of a multiple objective linear program. The approach uses simplex tableaux but avoids generating unnecessary extreme points or bases of extreme points. The procedure is based on, and improves, an algorithm Dauer and Liu developed for this problem. Essential to this approach is the work of Gal and Kruse on the neighborhood problem of determining all extreme points of a convex polytope that are adjacent to a given (degenerate) extreme point of the set. The algorithm will incorporate Gal's degeneracy graph approach to the neighborhood problem with Dauer's objective space analysis of multiple objective linear programs.     

The role of epithelial ion transport in taste transduction: A network thermodynamic model

The sensation of taste is mediated by electrical events in taste bud cells, which are embedded in the tongue epithelium. Prior to about 1981, many taste researchers regarded the tongue epithelium as virtually impermeable to most substances including small electrolytes. Taste transduction was assumed to be due to equilibrium adsorption of tastants to receptors on the taste cell membrane. More recent experiments show that, in the case of salt taste, the electrical events associated with transduction are due to ion flow across membranes rather than ion binding to a receptor. We wished to determine if standard assumptions about topology and membrane ion transport processes in high resistance (“tight”) epithelia apply to the tongue for a range of salt concentrations on the tongue surface. A model of the tongue epithelium was developed based on an earlier network model of ion transport in a kidney tight epithelium. The model has 4 membranes with series and parallel pathways and 3 transported ions. The model successfully simulates some aspects of both steady-state and transient transepithelial electrical measurements observed in vitro for a wide range (50–2000 mM) of NaCl concentrations. This is the concentration range of interest for gustation. The earlier kidney model had not been applied to hyperosmotic NaCl concentrations. The simulations indicate that common epithelial transport mechanisms can account for some phenomena important in taste transduction. They also indicate that the Na⁺ channels in taste cells have different properties than those typical in other tight epithelia.     

The role of constraints in a segregation model: The symmetric case

In this paper we study the effects of constraints on the dynamics of an adaptive segregation model introduced by Bischi and Merlone (2011) [3]. The model is described by a two dimensional piecewise smooth dynamical system in discrete time. It models the dynamics of entry and exit of two populations into a system, whose members have a limited tolerance about the presence of individuals of the other group. The constraints are given by the upper limits for the number of individuals of a population that are allowed to enter the system. They represent possible exogenous controls imposed by an authority in order to regulate the system. Using analytical, geometric and numerical methods, we investigate the border collision bifurcations generated by these constraints assuming that the two groups have similar characteristics and have the same level of tolerance toward the members of the other group. We also discuss the policy implications of the constraints to avoid segregation.     

A conic quadratic formulation for a class of convex congestion functions in network flow problems

In this paper we consider a multicommodity network flow problem with flow routing and discrete capacity expansion decisions. The problem involves trading off congestion and capacity assignment (or expansion) costs. In particular, we consider congestion costs involving convex, increasing power functions of flows on the arcs. We first observe that under certain conditions the congestion cost can be formulated as a convex function of the capacity level and the flow. Then, we show that the problem can be efficiently formulated by using conic quadratic inequalities. As most of the research on this problem is devoted to heuristic approaches, this study differs in showing that the problem can be solved to optimum by branch-and-bound solvers implementing the second-order cone programming (SOCP) algorithms. Computational experiments on the test problems from the literature show that the continuous relaxation of the formulation gives a tight lower bound and leads to optimal or near optimal integer solutions within reasonable CPU times.