A modied branch and cut procedure for resource portfolio problem under relaxed resource dedication policy

Multi-project scheduling problems are characterized by the way resources are managed in the problem environment. The general approach in multi-project scheduling literature is to consider resource capacities as a common pool that can be shared among all projects without any restrictions or costs. The way the resources are used in a multi-project environment is called resource management policy and the aforementioned assumption is called Resource Sharing Policy in this study. The resource sharing policy is not a generalization for multi-project scheduling environments and different resource management policies maybe defined to identify characteristics of different problem environments. In this study, we present a resource management policy which prevents sharing of resources among projects but allows resource transfers when a project starts after the completion of another one. This policy is called the Relaxed Resource Dedication (RRD) Policy in this study. The general resource capacities might or might not be decision variables. We will treat here the case where the general available amounts of resources are decision variables to be determined subject to a limited budget. We call this problem as the Resource Portfolio Problem (RPP). In this study, RPP is investigated under RRD policy and a modified Branch and Cut (B&C)procedure based on CPLEX is proposed. The B&C procedure of CPLEX is modified with different branching strategies, heuristic solution approaches and valid inequalities. The computational studies presented demonstrate the effectiveness of the proposed solution approaches

Towards Verifying Nonlinear Integer Arithmetic

We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. More precisely, we give n^{O(1)} size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result

A combination of different resource management policies in a multi-project environment

Multi-project problem environments are defined according to the way resources are managed in the problem environment, which is called the resource management policy (RMP) in this study. Different resource management policies can be defined according to the characteristics of the projects and/or resources in the problem environment. The most common RMP encountered in the multi-project scheduling literature is the resource sharing policy (RSP), where resources can be shared among projects without any costs or limitations. This policy can be seen as an extreme case since there is a strong assumption of unconstrained resource sharing. Another RMP can be defined as the other extreme such that resources cannot be shared among projects, which is called the resource dedication policy (RDP). The last RMP considered in this study is between these two policies where resources are dedicated but can be transferred among projects when a project finishes, the dedicated resources to this project can be transferred to another one starting after the finish of the corresponding project. This RPM is called the resource transfer policy (RTP). In this study we investigate a problem environment where all these three types of RPM are present. Additionally, the general resource capacities are taken as decision variables that are constrained by a given general budget. We call this multi-project environment as the Generalized Resource Portfolio Problem (GRPP). We have investigated this problem and proposed an iterative solution approach based on exact solution methods which determines the general resource capacities from the budget, resource dedications, resource sharing and resource transfer decisions and schedules the individual projects. Computational results for over forty test problems are reported

On Neighborhood Tree Search

We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by exploring different paths of the tree in a heuristic way. We show that allowing the search to 'backtrack' to a previously visited solution and resuming the iterative variable neighborhood descent by 'pruning' the already explored neighborhood branches leads to the design of effective and efficient search heuristics. We describe this idea by discussing its basic design components within a generic algorithmic scheme and we propose some simple and intuitive strategies to guide the search when traversing the neighborhood tree. We conduct a thorough experimental analysis of this approach by considering two different problem domains, namely, the Total Weighted Tardiness Problem (SMTWTP), and the more sophisticated Location Routing Problem (LRP). We show that independently of the considered domain, the approach is highly competitive. In particular, we show that using different branching and backtracking strategies when exploring the neighborhood tree allows us to achieve different trade-offs in terms of solution quality and computing cost.Comment: Genetic and Evolutionary Computation Conference (GECCO'12) (2012

The determinants of multinational banking during the first globalization, 1870-1914

What determined the multinational expansion of European banks in the pre1914 era of globalization? And how were banks' foreign investments related to other facets of the globalizing world economy such as trade and capital flows? The paper reviews both the contemporary and historical literature, and empirically investigates these issues by using an original panel data based on a sample of more than 50 countries. The dependent variable, aiming at measuring the intensity of crossborder activities operated by banks from foreign locations, is the number of foreign branches and subsidiaries of British, French and German banks. Explanatory variables are mainly selected on the base of the eclectic theory of multinational banking, but also include geographical factors (as suggested by gravity models) and institutional indicators advanced by recent studies inspired by new institutional economics, such as legal families and adherence to the Gold Standard. These regressors captures the impact of economic integration (trade and capital flows), informational development, institutional and economic characteristics of the hostmarket, as well as exchange rate and country risk factors, on banks' foreign investment decisions. The results suggest that, due to its prevailing 'colonial' features, pre1914 multinational banking does not fit easily into augmented gravity models. The role of trade as a key determinant of banks expansion overseas is qualified, and both institutional factors as well as competitive interaction emerge as critical determinants of banks' decisions to invest in foreign countries. Moreover, the systematic comparison of determinants of foreign investiments of banks from major core countries reveals that multinational banking was not a homogenous phenomenon, as banks of different nationality responded differently to economic, geographical and institutional factor

Order acceptance and scheduling in a single-machine environment: exact and heuristic algorithms.

In this paper, we develop exact and heuristic algorithms for the order acceptance and scheduling problem in a single-machine environment. We consider the case where a pool consisting of firm planned orders as well as potential orders is available from which an over-demanded company can select. The capacity available for processing the accepted orders is limited and orders are characterized by known processing times, delivery dates, revenues and the weight representing a penalty per unit-time delay beyond the delivery date promised to the customer. We prove the non-approximability of the problem and give two linear formulations that we solve with CPLEX. We devise two exact branch-and-bound procedures able to solve problem instances of practical dimensions. For the solution of large instances, we propose six heuristics. We provide a comparison and comments on the efficiency and quality of the results obtained using both the exact and heuristic algorithms, including the solution of the linear formulations using CPLEX.Order acceptance; Scheduling; Single machine; Branch-and-bound; Heuristics; Firm planned orders;