An exact algorithm for the network pricing problem

This work focuses on an improved exact algorithm for addressing an NP-hard network pricing problem. The method involves an efficient and partial generation of candidate solutions, a recursive scheme for generating improved upper bounds, and a column generation procedure for solving the network-structured subproblems. Its efficiency is assessed against both randomly generated instances involving three distinct topologies as well as instances based on real life situations in telecommunication and freight transportation.     

Jointly pricing and ordering for a multi-product multi-constraint newsvendor problem with supplier quantity discounts

We present an extension to the multi-product newsvendor problem by incorporating the retailer’s pricing decision as well as considering supplier quantity discount. The objective is to maximize the expected profit of the retailer through jointly determining the ordering quantities and selling prices for the products, subject to multiple capacity constraints. We formulate the problem as a Generalized Disjunctive Programming (GDP) model and develop a Lagrangian heuristic approach for its solution. Randomly produced instances involving up to 1000 products are used to test the proposed approach. Computational results show that the Lagrangian heuristic approach can present very good solutions to all instances in reasonable time.     

An iterative scheme for solving nonlinear equations with monotone operators

An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A discrete version of the Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with monotone operators is proposed and its convergence is proved. A discrepancy principle is proposed and justified. A priori and a posteriori stopping rules for the iterative scheme are formulated and justified. AMS subject classification (2000)  47J05, 47J06, 47J35, 65R30     

An almost monotone approximation for a nonlinear two‐point boundary value problem

Almost monotone approximation is proposed for nonlinear two‐points problem. A general framework is given for studying the existence and uniqueness of numerical solutions. A discrete approximation with high accuracy is constructed. Nonlinear Jacobi iteration and Gauss–Seidel iteration are introduced to save work. The continuous approximation is also considered. The numerical results show the advantages of such an approach. This revised version was published online in August 2006 with corrections to the Cover Date.     

An optimization problem for nonlinear Steklov eigenvalues with a boundary potential

In this paper, we analyze an optimization problem for the first (nonlinear) Steklov eigenvalue plus a boundary potential with respect to the potential function which is assumed to be uniformly bounded and with fixed L¹$L^1$-norm.     

Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters

We study a model linear convection-diffusion-reaction problem where both the diffusion term and the convection term are multiplied by small parameters ε_d and ε_c, respectively. Depending on the size of the parameters the solution of the problem may exhibit exponential layers at both end points of the domain. Sharp bounds for the derivatives of the solution are derived using a barrier-function technique. These bounds are applied in the analysis of a simple upwind-difference scheme on Shishkin meshes. This method is established to be almost first-order convergent, independently of the parameters ε_d and ε_c.     

An efficient approach for solving the lot-sizing problem with time-varying storage capacities

We address the dynamic lot size problem assuming time-varying storage capacities. The planning horizon is divided into T periods and stockouts are not allowed. Moreover, for each period, we consider a setup cost, a holding unit cost and a production/ordering unit cost, which can vary through the planning horizon. Although this model can be solved using O(T³) algorithms already introduced in the specialized literature, we show that under this cost structure an optimal solution can be obtained in O(T log T) time. In addition, we show that when production/ordering unit costs are assumed to be constant (i.e., the Wagner–Whitin case), there exists an optimal plan satisfying the Zero Inventory Ordering (ZIO) property.     

An infinite horizon stochastic maximum principle for discounted control problem with Lipschitz coefficients

In the present work, a stochastic maximum principle for discounted control of a certain class of degenerate diffusion processes with global Lipschitz coefficient is investigated. The value function is given by a discounted performance functional, leading to a stochastic maximum principle of semi-couple forward–backward stochastic differential equation with non-smooth coefficients. The proof is based on the approximation of the Lipschitz coefficients by smooth ones and the approximation of the infinite horizon adjoint process.     

An explicit solution for an instantaneous two-phase Stefan problem with nonlinear thermal coefficients

We consider a nonlinear heat conduction problem for a semi-infinitematerial x > 0, with phase-change temperature T₁, an initialtemperature T₂ (> T₁) and a heat flux of the type q (t) =q₀/t imposed on the fixed face x = 0. We assume that the volumetricheat capacity and the thermal conductivity are particular nonlinearfunctions of the temperature in both solid and liquid phases. We determine necessary and/or sufficient conditions on the parametersof the problem in order to obtain the existence of an explicitsolution for an instantaneous nonlinear twophase Stefan problem(solidification process).     

An algorithm for solving a two-person game with information transfer

An algorithm for solving a two-person game with information transfer is proposed. The algorithm is based on a special linear programming problem. An example is given.     

An assignment problem for a parallel queueing system with two heterogeneous servers

In this paper, we consider an optimization problem for a parallel queueing system with two heterogeneous servers. Each server has its own queue and customers arrive at each queue according to independent Poisson processes. Each service time is independent and exponentially distributed. When a customer arrives at queue 1, the customers in queue 1 can be transferred to queue 2 by paying an assignment cost which is proportional to the number of moved customers. Holding cost is a function of the pair of queue lengths of the two servers. Our objective is to minimize the expected total discounted cost. We use the dynamic programming approach for this problem. Considering the pair of queue lengths as a state space, we show that the optimal policy has a switch over structure under some conditions on the holding cost.     

Enhanced formulations and branch-and-cut for the two level network design problem with transition facilities

We consider a new combinatorial optimization problem that combines network design and facility location aspects. Given a graph with two types of customers and two technologies that can be installed on the edges, the objective is to find a minimum cost subtree connecting all customers while the primary customers are served by a primary subtree that is embedded into the secondary subtree. In addition, besides fixed link installation costs, facility opening costs, associated to each node where primary and secondary subtree connect, have to be paid. The problem is called the Two Level Network Design Problem with Transition Facilities (TLNDF).