Polyhedral study of mixed integer sets arising from inventory problems

“Branch-and-cut” algorithm is one of the most efficient exact approaches to solve mixed integer programs. This algorithm combines the advantages of a pure branch-and-bound approach and cutting planes scheme. Branch-and-cut algorithm computes the linear programming relaxation of the problem at each node of the search tree which is improved by the use of cuts, i.e. by the inclusion of valid inequalities. It should be taken into account that selection of strongest cuts is crucial for their effective use in branch-and-cut algorithm. In this thesis, we focus on the derivation and use of cutting planes to solve general mixed integer problems, and in particular inventory problems combined with other problems such as distribution, supplier selection, vehicle routing, etc. In order to achieve this goal, we first consider substructures (relaxations) of such problems which are obtained by the coherent loss of information. The polyhedral structure of those simpler mixed integer sets is studied to derive strong valid inequalities. Finally those strong inequalities are included in the cutting plane algorithms to solve the general mixed integer problems. We study three mixed integer sets in this dissertation. The first two mixed integer sets arise as a subproblem of the lot-sizing with supplier selection, the network design and the vendor-managed inventory routing problems. These sets are variants of the well-known single node fixed-charge network set where a binary or integer variable is associated with the node. The third set occurs as a subproblem of mixed integer sets where incompatibility between binary variables is considered. We generate families of valid inequalities for those sets, identify classes of facet-defining inequalities, and discuss the separation problems associated with the inequalities. Then cutting plane frameworks are implemented to solve some mixed integer programs. Preliminary computational experiments are presented in this direction.

A priori reformulations for joint rolling-horizon scheduling of materials processing and lot-sizing problem

In many production processes, a key material is prepared and then transformed into different final products. The lot sizing decisions concern not only the production of final products, but also that of material preparation in order to take account of their sequence-dependent setup costs and times. The amount of research in recent years indicates the relevance of this problem in various industrial settings. In this paper, facility location reformulation and strengthening constraints are newly applied to a previous lot-sizing model in order to improve solution quality and computing time. Three alternative metaheuristics are used to fix the setup variables, resulting in much improved performance over previous research, especially regarding the use of the metaheuristics for larger instances. © 2013 Elsevier Ltd. All rights reserved.

Hardy's inequality on exterior domains

Let Ω be a smooth exterior domain in ℝN and 1 < p < ∞. We prove that when p ≠ N, Hardy's LP inequality is valid on D01,p(Ω). ©2005 American Mathematical Society

Documenting reproduction and inequality : revisiting Jean Anyon’s “Social class and school knowledge”

Jean Anyon’s (1981) “Social class and school knowledge” was a landmark work in North American educational research. It provided a richly detailed qualitative description of differential, social-class-based constructions of knowledge and epistemological stance. This essay situates Anyon’s work in two parallel traditions of critical educational research: the sociology of the curriculum and classroom interaction and discourse analysis. It argues for the renewed importance of both quantitative and qualitative research on social reproduction and equity in the current policy context.

Action research for contexts of change and inequality

Undoubtedly, the past half-century has witnessed an escalation of changes in the social, political, economic and educational structures in many societies around the world. Some have seen change as a challenge and hope while, for many others, it is a source of concern and worry. Some have adopted change with gusto, while for many it is something to be resisted. Some say we live in a world and times with an increasing awareness that “times are changing”, while for some “the more things change, the more they stay the same”.

Health, endogenous time preference, and inequality : a political economy perspective

We study an overlapping-generations model in which agents' mortality risks, and consequently impatience, are endogenously determined by private and public investment in health care. Revenues allocated for public health care arc determined by a voting process. We find that the degree of substitutability between public and private health expenditures matters for macroeconomic outcomes of the model. Higher substitutability implies a “crowding-out" effect, which in turn impacts adversely on morality risks and impatience leading to lower public expenditures on health care in the political equilibrium. Consequently, higher substitutability is associated with greater polarization in wealth, and long-run distributions that are bimodal.

A political economy perspective on persistent inequality, inflation, and redistribution

In this paper we examine the dynamics of the link between inequality and inflation from a political economy perspective. We consider a simple dynamic general equilibrium model in which agents vote over the desired inflation rate in each period, and inequality is persistent. Inflation in our model is a mechanism of redistribution, and we find that the link between inequality and inflation within any period or over time depends on institutional and preference related parameters. Furthermore, we find that differences in the initial distributions of wealth can yield a diverse set of patterns for the evolution of the inflation and inequality link. Relative to existing literature, our model leads to more precise predictions about the inflation-inequality correlation. To that end, results in the extant empirical literature on the inflation and inequality link need to be interpreted with caution.

Inequality Aversion and Performance in and on the Field

The experimental literature and studies using survey data have established that people care a great deal about their relative economic position and not solely, as standard economic theory assumes, about their absolute economic position. Individuals are concerned about social comparisons. However, behavioral evidence in the field is rare. This paper provides an empirical analysis, testing the model of inequality aversion using two unique panel data sets for basketball and soccer players. We find support that the concept of inequality aversion helps to understand how the relative income situation affects performance in a real competitive environment with real tasks and real incentives.

Osteoarthritis Index delivered by mobile phone (m-WOMAC) is valid, reliable, and responsive

Objectives: To evaluate the validity, reliability and responsiveness of EDC using the WOMAC® NRS 3.1 Index on Motorola V3 mobile phones. ---------- Methods: Patients with osteoarthritis (OA) undergoing primary unilateral hip or knee joint replacement surgery were assessed pre-operatively and 3-4 months post-operatively. Patients completed the WOMAC® Index in paper (p-WOMAC®) and electronic (m-WOMAC®) format in random order. ---------- Results: 24 men and 38 women with hip and knee OA participated and successfully completed the m-WOMAC® questionnaire. Pearson correlations between the summated total index scores for the p-WOMAC® and m-WOMAC® pre- and post-surgery were 0.98 and 0.99 (p<0.0001). There was no clinically important or statistically significant between-method difference in the adjusted total summated scores, pre- and post-surgery (adjusted mean difference = 4.44, p = 0.474 and 1.73, p = 0.781). Internal consistency estimates of m-WOMAC® reliability were 0.87 – 0.98. The m-WOMAC® detected clinically important, statistically significant (p<0.0001) improvements in pain, stiffness, function and total index score. ---------- Conclusions: Sixty-two patients with hip and knee OA successfully completed EDC by Motorola V3 mobile phone using the m-WOMAC® NRS3.1 Index; completion times averaging only 1-1.5 minutes longer than the p-WOMAC® Index. Data were successfully and securely transmitted from patients in Australia to a server in the USA. There was close agreement and no significant differences between m-WOMAC® and p-WOMAC® scores. This study confirms the validity, reliability and responsiveness of the Exco InTouch engineered, Java-based m-WOMAC® Index application. EDC with the m-WOMAC® Index provides unique opportunities for using quantitative measurement in clinical research and practice.