in this paper, shortest path design problem (spdp) in which the path is incident to all cells is considered. the bi-directional path is one of the known types of configuration of networks for automated guided vehi-cles (agv).to solve this problem, two algorithms are developed. for each algorithm an integer linear pro-gramming (ilp) is determined. the objective functions of both algorithms are t...

is the objective function to be optimized over P . Whenever all variables in (1.1) are restricted to be integral, the problem is known as a linear integer programming (IP) problem. Conversely, a pure linear programming (LP) problem results when all variables in (1.1) are restricted to be real valued. As is frequently the case for MIP, instead of attempting to optimize (1.3) directly over P , it...

In this paper we present a computational comparison of four different flow formulations for the capacitated location-routing problem. We introduce three new flow formulations for the problem, namely a two-index two-commodity flow formulation, a three-index vehicle-flow formulation and a three-index two-commodity flow formulation. We also consider the known two-index vehicle-flow formulation and...

Combinatorial optimization problems can often be formulated as mixed integer linear programming problems, as discussed in Section 1.4.1.1 in this encyclopedia. They can then be solved using branch-and-cut, which is an exact algorithm combining branch-and-bound (see Section 1.4.1.2 of this encyclopedia) and cutting planes (see Section 1.4.3 of this encyclopedia). The basic idea is to take a line...

The software system ABACUS is an object-oriented framework for the implementation of branch-and-cut and branch-and-price algorithms. This paper describes the design of ABACUS including the design principles and the most important classes.

The software system ABACUS is an object-oriented framework for the implementation of branch-and-cut and branch-and-price algorithms. This paper describes the design of ABACUS including the design principles and the most important classes.

We introduce Horizon Decomposition in the context of Dantzig-Wolfe Decomposition, and apply it to the Capacitated Lot-Sizing Problem with Setup Times. We partition the problem horizon in contiguous overlapping intervals and create subproblems identical to the original problem, but of smaller size. The user has the flexibility to regulate the size of the master problem and the subproblem via two...

In this paper, a strict formulation of a generalization of the classical pick up and delivery problem is presented. Here, we add the flexibility of providing the option for passengers to transfer from one vehicle to another at specific locations. As part of the mathematical formulation, we include transfer nodes where vehicles may interact interchanging passengers. Additional variables to keep ...

We propose a new heuristic for pure 0–1 programs, which finds feasible integer points by enumerating extended facets of the octahedron, the outer polar of the unit hypercube. We give efficient algorithms to carry out the enumeration, and we explain how our heuristic can be embedded in a branch-and-cut framework. Finally, we present computational results on a set of pure 0–1 programs taken from ...