Power-Aware Routing and Network Design with Bundled Links: Solutions and Analysis

The paper deeply analyzes a novel network-wide power management problem, called Power-Aware Routing and Network Design with Bundled Links (PARND-BL), which is able to take into account both the relationship between the power consumption and the traffic throughput of the nodes and to power off both the chassis and even the single Physical Interface Card (PIC) composing each link. The solutions of the PARND-BL model have been analyzed by taking into account different aspects associated with the actual applicability in real network scenarios: (i) the time for obtaining the solution, (ii) the deployed network topology and the resulting topology provided by the solution, (iii) the power behavior of the network elements, (iv) the traffic load, (v) the QoS requirement, and (vi) the number of paths to route each traffic demand. Among the most interesting and novel results, our analysis shows that the strategy of minimizing the number of powered-on network elements through the traffic consolidation does not always produce power savings, and the solution of this kind of problems, in some cases, can lead to spliting a single traffic demand into a high number of paths

Sequencing and Routing in a Large Warehouse with High Degree of Product Rotation

The paper deals with a sequencing and routing problem originated by a real-world application context. The problem consists in defining the best sequence of locations to visit within a warehouse for the storage and/or retrieval of a given set of items during a specified time horizon, where the storage/retrieval location of an item is given. Picking and put away of items are simultaneously addressed, by also considering some specific requirements given by the layout design and operating policies which are typical in the kind of warehouses under study. Specifically, the considered sequencing policy prescribes that storage locations must be replenished or emptied one at a time by following a specified order of precedence. Moreover, two fleet of vehicles are used to perform retrieving and storing operations, whose routing is restricted to disjoint areas of the warehouse. We model the problem as a constrained multicommodity flow problem on a space-time network, and we propose a Mixed-Integer Linear Programming formulation, whose primary goal is to minimize the time traveled by the vehicles during the time horizon. Since large-size realistic instances are hardly solvable within the time limit commonly imposed in the considered application context, a matheuristic approach based on a time horizon decomposition is proposed. Finally, we provide an extensive experimental analysis aiming at identifying suitable parameter settings for the proposed approach, and testing the matheuristic on particularly hard realistic scenarios. The computational experiments show the efficacy and the efficiency of the proposed approach

Assigning and sequencing storage locations under a two level storage policy: optimization model and matheuristic approach

We deal with a storage location problem in a warehouse where items of different product types are released by the production area and need to be stored. Capacitated storage locations have to be assigned to each product type to store the corresponding items. Items of different product types cannot share the same storage location, i.e., each storage location can be assigned to at most one product type. In addition, a suitable sequencing of the assigned storage locations must be devised for each product type. Each sequence will provide both the order with which the storage locations will be filled up during the storing operations, and also the order of visit of the storage locations during the successive order picking phase. A motivation is that, separately per product type, an order picking based on the time of permanence of the items in the warehouse has to be pursued. Moreover, the chosen sequencing influences the availability of additional storage on the top of the assigned storage locations. In fact, for each product type, an additional extra storage can be made available on top of pairs of consecutive storage locations in the sequence, which depends on the two storage locations at the ground level. The goal is to maximize the storage capacity still available after the assignment of the storage locations. After proving the NP-Hardness of the considered problem, we model it in terms of a multicommodity flow problem with additional constraints on an auxiliary graph, and we propose a Mixed-Integer Linear Programming model for its mathematical formulation. A matheuristic approach, based on the sequential resolution of multicommodity flow subproblems, is then presented. The proposed methodology is applied to a case study related to a large warehouse with a high stock rotation index in tissue logistics, which motivated our study. Computational results on a wide test bed related to such a real application context show the efficiency and efficacy of the proposed approach

An approximation algorithm for computing longest paths

We show how the color-coding method by Alon, Yuster and Zwick, in its version specialized to compute simple paths of a specified cardinality k, can be extended to address the presence of arc lengths (the existence of such an extension was outlined by the authors for a more general color-coding algorithm, but it was not explicitely described, and its time complexity was not discussed). The extension is then used to derive approximation results for the general longest path problem

Joint assignment, scheduling and routing models to Home Care optimization: a pattern based approach

The design of efficient Home Care Services is a quite recent and challenging problem motivated by the ever increasing age of population and the consequent need to reduce hospitalization costs. We are given a weekly planning horizon, a set of operators each characterized by a skill and a set of patients each requiring a set of visits also characterized by a skill. We propose an integrated model that jointly addresses the following problems: (i) the assignment of operators to patients guaranteeing the appropriate levels of skill; (ii) the scheduling of visits in the planning horizon; and (iii) the determination of a set of tours indicating the sequence of patients each operator must visit in every day of the week. Several variants of this model are investigated. All of them use the pattern as a key tool to formulate the problem. A pattern is an a priori given profile specifying a possible schedule for a given set of visits possibly characterized by differnt skills. Computational results on a set of real instances are analysed. They show that the selection of the pattern generation policy is crucial to solve large instances efficiently

A New Algorithm for Reoptimizing Shortest Paths When the Arc Costs Change

We propose an algorithm which reoptimizes shortest paths in a very general situation, that is when any subset of arcs of the input graph is aected by a change of the arc costs, which can be either lower or higher than the old ones. This situation is more general than the ones addressed in the literature so far

Dual Algorithms for the Shortest Path Tree Problem

We consider dual approaches for the Shortest Path Tree Problem. After a brief introduction to the problem, we review the most important dual algorithms which have been described in the literature for its solution, and propose a new family of dual ascent algorithms. In these algorithms, "local" and "global" dual updating operations are performed at the nodes in order to enlarge a partial shortest path tree, which at the beginning contains only the root node, until a shortest path tree is found. Several kinds of dual updating operations are proposed, which allow one to derive different dual algorithms from a general schema. One of them, in particular, which is based only on global operations, can be viewed as a dual interpretation of Dijkstra's classical algorithm. Due to their structure, all the proposed approaches are suitable for parallel implementations. They are also suitable for reoptimization approaches, when the computation of shortest paths from different root nodes i..

The One-Dimensional Cutting Stock Problem: a linear programming algorithm based on hyperflows

Cutting stock problems have been deeply investigated in the last thirty years due to their wide range of applications as well as to their nice structure. The one dimensional problem (CSP) consists in cutting out of the minumum number of standard lengths the required number of pieces for each demand length. An ILP formulation, known as the multicut model, where there is a variable for each feasible way of cutting a standard length and a constraint for each demand length, has been the model of reference since the column generation problem was formulated as a knapsack in 1965 by Gilmore and Gomory. Further investigations studied the gap between the multicut model objective function and its linear relaxation [11], which gave theorical foundations to the many rounding heuristics for the standard case, while a remarkable number of heuristics have been proposed to tackle particular cases arising in production processes. Nevertheless, the problem structure has never been exploited in order to ..

Hyperflow Models

We consider the Minimum cost hyperflow problem, a generalization of the minimum cost flow problems on standard and on generalized graphs. In order to solve this problem, a specialization of the primal Simplex Algorithm, named the Hypergraph Simplex Algorithm, has been recently proposed. Here, the results of a wide experimentation on random hypergraphs and on some kinds of structured hypergraphs are reported. In the experimentation, a C implementation of the Hypergraph Simplex Algorithm has been compare wth the primal version of CPLEX code, by obtaining rather interesting results. In fact, when the hypergraph size increases, our code runs faste than CPLEX; in particular, its solution time is a rather slow increasing fnction of the hypergraph size. The problem under consideration has very interesting applications, which can be modelled and solved in terms of hypergraph flows. These include Multicommodity flows and applications in the area of flexible manufacturing systems, like the One-Dimensional Cutting Stock Problem and Assembly Problems. In particular, it is shown how to model Assembly Problems with a given degree, say k, of parallelism (i.e. when k parallel identical machinesare available for the execution of the operations) in terms of hyperflows. Finally, some Economic Applications are formulated and interpreted in terms of minimum cost hyperflow problems

Robust Portfolio Asset Allocation: models and algorithmic approaches

Many financial optimization problems involve future values of security prices, interest rates and exchange rates which are not known in advance, but can only be forecasted or estimated. Such problems fit perfectly into the framework of Robust Optimization that, given optimization problems with uncertain parameters, looks for solutions that will achieve good objective function values for the realization of these parameters in given uncertainty sets.In finance, Robust Optimization offers vehicles to incorporate the estimation of uncertain parameters into the decision making process.This is true, for example, in portfolio asset allocation. Starting from the robust counterparts of the classical mean-variance portfolio problems, in this paper we review some mathematical models that have been recently proposed in the literature to address uncertainty in portfolio asset allocation problems. For some of these, we focus also on algorithmic approaches and computataional issues. Finally, we analyze the relationship between robustness and risk measures