Hybrid Meta-heuristics with VNS and Exact Methods: Application to Large Unconditional and Conditional Vertex p-Centre Problems

Large-scale unconditional and conditional vertex p-centre problems are solved using two meta-heuristics. One is based on a three-stage approach whereas the other relies on a guided multi-start principle. Both methods incorporate Variable Neighbourhood Search, exact method, and aggregation techniques. The methods are assessed on the TSP dataset which consist of up to 71,009 demand points with p varying from 5 to 100. To the best of our knowledge, these are the largest instances solved for unconditional and conditional vertex p-centre problems. The two proposed meta-heuristics yield competitive results for both classes of problems

Neighbourhood Reduction in Global and Combinatorial Optimization: The Case of the p-Centre Problem

Neighbourhood reductions for a class of location problems known as the vertex (or discrete) and planar (or continuous) p-centre problems are presented. A brief review of these two forms of the p-centre problem is first provided followed by those respective reduction schemes that have shown to be promising. These reduction schemes have the power of transforming optimal or near optimal methods such as metaheuristics or relaxation-based procedures, which were considered relatively slow, into efficient and exciting ones that are now able to find optimal solutions or tight lower/upper bounds for larger instances. Research highlights of neighbourhood reduction for global and combinatorial optimisation problems in general and for related location problems in particular are also given

Dynamics of a Cournot Duopoly Game with a Generalized Bounded Rationality

In this paper, the dynamics of Cournot duopoly game with a generalized bounded rationality is considered. The fractional bounded rationality of the Cournot duopoly game is introduced. The conditions of local stability analysis of equilibrium points of the game are derived. The effect of fractional marginal profit on the game is investigated. The complex dynamics behaviors of the game are discussed by numerical computation when parameters are varied

An Enhancement of Daskin's algorithm for solving P-centre problem

An Enhancement to the exact algorithm of Daskin (1995) to solve the vertex P- center problem is proposed. A simple enhancement which uses tighter initial lower and upper bounds, and a more appropriate binary search method are introduced to reduce the number of subproblems to be solved. These ideas are tested on a well known set of problems from the literature (i.e., TSP-Lib problems) with encouraging results

A Bulk Service Queue with a Choice of Service and Re-Service under Bernoulli Schedule

This paper investigates the queueing process of a bulk service queueing system under Bernoulli schedule. It also generalizes some known scenarios concerning the choice of service and re-service types. The queueing process is studied both in discrete time and in continuous time. Performance measures are derived and used to implement an optimal management policy of the system

Enhancements to Two Exact Methods for the Vertex P-Centre Problem.

Enhancements to two exact algorithms from the literature to solve the vertex P-center problem are proposed. In the first approach modifications of some steps are introduced to reduce the number of ILP iterations needed to find the optimal solution. In the second approach a simple enhancement which uses tighter initial lower and upper bounds, and a more appropriate binary search method are proposed to reduce the number of subproblems to be solved. These ideas are tested on two well known sets of problems from the literature (i.e., OR-Lib and TSP-Lib problems) with encouraging result

Dynamic Effects Arise Due to Consumers’ Preferences Depending on Past Choices

We analyzed a dynamic duopoly game where players adopt specific preferences. These preferences are derived from Cobb–Douglas utility function with the assumption that they depend on past choices. For this paper, we investigated two possible cases for the suggested game. The first case considers only focusing on the action done by one player. This action reduces the game’s map to a one-dimensional map, which is the logistic map. Using analytical and numerical simulation, the stability of fixed points of this map is studied. In the second case, we focus on the actions applied by both players. The fixed points, in this case, are calculated, and their stability is discussed. The conditions of stability are provided in terms of the game’s parameters. Numerical simulation is carried out to give local and global investigations of the chaotic behavior of the game’s map. In addition, we use a statistical measure, such as entropy, to get more evidences on the regularity and predictability of time series associated with this case

Optimal control of production inventory systems with deteriorating items

This paper is concerned with the optimal control of a production inventory system with deteriorating items. It is assumed that the deterioration rate follows the two-parameter Weibull distribution. The continuous-review and periodic-review policies are investigated. In each case, optimality conditions are derived. Also, numerical illustrative examples are presented

A New Class of Bivariate Gompertz Distributions and its Mixture

Abstract A new class of bivariate Gompertz distributions is presented in this paper. The model introduced here is of Marshall-Olkin type. The used procedure is based on a latent random variable with exponential distribution. A mixture of the suggested bivariate distributions is also derived. The obtained results in this paper generalize those of MarshallOlkin bivariate exponential distribution and other present in the literature

Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control

Many researchers have used quadratic utility function to study its influences on economic games with product differentiation. Such games include Cournot, Bertrand, and a mixed-type game called Cournot-Bertrand. Within this paper, a cubic utility function that is derived from a constant elasticity of substitution production function (CES) is introduced. This cubic function is more desirable than the quadratic one besides its amenability to efficiency analysis. Based on that utility a two-dimensional Cournot duopoly game with horizontal product differentiation is modeled using a discrete time scale. Two different types of games are studied in this paper. In the first game, firms are updating their output production using the traditional bounded rationality approach. In the second game, firms adopt Puu’s mechanism to update their productions. Puu’s mechanism does not require any information about the profit function; instead it needs both firms to know their production and their profits in the past time periods. In both scenarios, an explicit form for the Nash equilibrium point is obtained under certain conditions. The stability analysis of Nash point is considered. Furthermore, some numerical simulations are carried out to confirm the chaotic behavior of Nash equilibrium point. This analysis includes bifurcation, attractor, maximum Lyapunov exponent, and sensitivity to initial conditions