the heterogeneous fixed fleet open vehicle routing problem (hffovrp) is one of the most significant extension problems of the open vehicle routing problem (ovrp). the hffovrp is the problem of designing collection routes to a number of predefined nodes by a fixed fleet number of vehicles with various capacities and related costs. in this problem, the vehicle doesn’t return to the depot after se...

a considerable problem in competitive trade world is choosing the best supply chain. as a result in much more serious circumstances of competitions looking for the best supplier for manufacturing, for preparing raw material, is very significant. meantime suppliers have different scenarios to be fulfilled, such as changing selection variables like lead-time, transportation cost and transportatio...

network location models comprise one of the main categories of location models. these models have various applications in regional and urban planning as well as in transportation, distribution, and energy management. in a network location problem, nodes represent demand points and candidate locations to locate the facilities. if the links network is unchangeably determined, the problem will be ...

We consider a production planning problem where the production process creates a mixture of desirable products and undesirable byproducts. In this production process, at any point in time the fraction of the mixture that is an undesirable byproduct increases monotonically as a function of the cumulative mixture production up to that time. The mathematical formulation of this continuous-time pro...

one of the important issues in transportation and logistics systems is vehicle routing problem (vrp). the vehicle routing problem is concerned with finding efficient routes of minimum total cost, beginning and ending at a central depot, for a fleet of vehicles to serve a number of customers. on the other hand, as a result of the increasing environmental concerns, economic problems and pressure ...

In this paper, we investigate the use of an exact primal-dual penalty approach within the framework of an interior-point method for nonconvex nonlinear programming. This approach provides regularization and relaxation, which can aid in solving ill-behaved problems and in warmstarting the algorithm. We present details of our implementation within the loqo algorithm and provide extensive numerica...

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear...

In the context of a variation of the standard UFL (Uncapacitated Facility Location) problem, but with an objective function that is a separable convex quadratic function of the transportation costs, we present some techniques for improving relaxations of MINLP formulations. We use a disaggregation principal and a strategy of developing model-specific valid inequalities (some nonlinear), which e...

Interior-point methods for nonlinear programming have been demonstrated to be quite efficient, especially for large scale problems, and, as such, they are ideal candidates for solving the nonlinear subproblems that arise in the solution of mixed-integer nonlinear programming problems via outer approximation. However, traditionally, infeasible primal-dual interior-point methods have had two main...

A Nonlinear Mixed Integer Programming approach is presented to select the number of membrane modules required in the extraction and stripping sectors of a Non Dispersive Solvent Extraction Plant for effluent treatment and metal recovery. The differential equations that model each membrane module are discretized using orthogonal collocation on finite elements leading to an algebraic system of eq...