Analysis of linear trade models and relation to scale economies

We discuss linear Ricardo models with a range of parameters. We show that the exact boundary of the region of equilibria of these models is obtained by solving a simple integer programming problem. We show that there is also an exact correspondence between many of the equilibria resulting from families of linear models and the multiple equilibria of economies of scale models.

Robust solutions to multi-objective linear programs with uncertain data

In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for the radius of robust feasibility guaranteeing constraint feasibility for all possible scenarios within a specified uncertainty set under affine data parametrization. We then present numerically tractable optimality conditions for minmax robust weakly efficient solutions, i.e., the weakly efficient solutions of the robust counterpart. We also consider highly robust weakly efficient solutions, i.e., robust feasible solutions which are weakly efficient for any possible instance of the objective matrix within a specified uncertainty set, providing lower bounds for the radius of highly robust efficiency guaranteeing the existence of this type of solutions under affine and rank-1 objective data uncertainty. Finally, we provide numerically tractable optimality conditions for highly robust weakly efficient solutions.

Comparison of the implicit enumeration method and the branch-and-bound method for logical design

Bibliography: p. 91-94.

Optimal networks with NOR-OR gates and Wired OR logic /

Originally presented as the author's thesis (M.S.), University of Illinois at Urbana-Champaign.

A study of certain factors affecting computation times in designing optimal NOR networks by the implicit enumeration method using the feed-forward formulation /

Bibliography: p. 27-29.

Optimization and Machine Learning Frameworks for Complex Network Analysis

Thesis (Ph.D.)--University of Washington, 2016-06

Vehicle routing and crew scheduling for metropolitan mail distribution at Australia Post

This paper presents a new multi-depot combined vehicle and crew scheduling algorithm, and uses it, in conjunction with a heuristic vehicle routing algorithm, to solve the intra-city mail distribution problem faced by Australia Post. First we describe the Australia Post mail distribution problem and outline the heuristic vehicle routing algorithm used to find vehicle routes. We present a new multi-depot combined vehicle and crew scheduling algorithm based on set covering with column generation. The paper concludes with a computational investigation examining the affect of different types of vehicle routing solutions on the vehicle and crew scheduling solution, comparing the different levels of integration possible with the new vehicle and crew scheduling algorithm and comparing the results of sequential versus simultaneous vehicle and crew scheduling, using real life data for Australia Post distribution networks.

A mathematical model for assembly line balancing model to consider disordering sequence of workstations

Purpose – A binary integer programming model for the simple assembly line balancing problem (SALBP), which is well known as SALBP-1, was formulated more than 30 years ago. Since then, a number of researchers have extended the model for the variants of assembly line balancing problem.The model is still prevalent nowadays mainly because of the lower and upper bounds on task assignment. These properties avoid significant increase of decision variables. The purpose of this paper is to use an example to show that the model may lead to a confusing solution. Design/methodology/approach – The paper provides a remedial constraint set for the model to rectify the disordered sequence problem. Findings – The paper presents proof that the assembly line balancing model formulated by Patterson and Albracht may lead to a confusing solution. Originality/value – No one previously has found that the commonly used model is incorrect.

Zero weights and non-zero slacks:different solution to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.

An operational research-based integrated approach for mass evacuation planning of a city

Large-scale disasters are constantly occurring around the world, and in many cases evacuation of regions of city is needed. ‘Operational Research/Management Science’ (OR/MS) has been widely used in emergency planning for over five decades. Warning dissemination, evacuee transportation and shelter management are three ‘Evacuation Support Functions’ (ESF) generic to many hazards. This thesis has adopted a case study approach to illustrate the importance of integrated approach of evacuation planning and particularly the role of OR/MS models. In the warning dissemination phase, uncertainty in the household’s behaviour as ‘warning informants’ has been investigated along with uncertainties in the warning system. An agentbased model (ABM) was developed for ESF-1 with households as agents and ‘warning informants’ behaviour as the agent behaviour. The model was used to study warning dissemination effectiveness under various conditions of the official channel. In the transportation phase, uncertainties in the household’s behaviour such as departure time (a function of ESF-1), means of transport and destination have been. Households could evacuate as pedestrians, using car or evacuation buses. An ABM was developed to study the evacuation performance (measured in evacuation travel time). In this thesis, a holistic approach for planning the public evacuation shelters called ‘Shelter Information Management System’ (SIMS) has been developed. A generic allocation framework of was developed to available shelter capacity to the shelter demand by considering the evacuation travel time. This was formulated using integer programming. In the sheltering phase, the uncertainty in household shelter choices (either nearest/allocated/convenient) has been studied for its impact on allocation policies using sensitivity analyses. Using analyses from the models and detailed examination of household states from ‘warning to safety’, it was found that the three ESFs though sequential in time, however have lot of interdependencies from the perspective of evacuation planning. This thesis has illustrated an OR/MS based integrated approach including and beyond single ESF preparedness. The developed approach will help in understanding the inter-linkages of the three evacuation phases and preparing a multi-agency-based evacuation planning evacuation

Online trendy topics detection in microblogs with selective user monitoring under cost constraints

As microblog services such as Twitter become a fast and convenient communication approach, identification of trendy topics in microblog services has great academic and business value. However detecting trendy topics is very challenging due to huge number of users and short-text posts in microblog diffusion networks. In this paper we introduce a trendy topics detection system under computation and communication resource constraints. In stark contrast to retrieving and processing the whole microblog contents, we develop an idea of selecting a small set of microblog users and processing their posts to achieve an overall acceptable trendy topic coverage, without exceeding resource budget for detection. We formulate the selection operation of these subset users as mixed-integer optimization problems, and develop heuristic algorithms to compute their approximate solutions. The proposed system is evaluated with real-time test data retrieved from Sina Weibo, the dominant microblog service provider in China. It's shown that by monitoring 500 out of 1.6 million microblog users and tracking their microposts (about 15,000 daily) with our system, nearly 65% trendy topics can be detected, while on average 5 hours earlier before they appear in Sina Weibo official trends.

CAPS in Z(2,n)

We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small n.

Optimal Decision Rules in Logical Recognition Models

The task of smooth and stable decision rules construction in logical recognition models is considered. Logical regularities of classes are defined as conjunctions of one-place predicates that determine the membership of features values in an intervals of the real axis. The conjunctions are true on a special no extending subsets of reference objects of some class and are optimal. The standard approach of linear decision rules construction for given sets of logical regularities consists in realization of voting schemes. The weighting coefficients of voting procedures are done as heuristic ones or are as solutions of complex optimization task. The modifications of linear decision rules are proposed that are based on the search of maximal estimations of standard objects for their classes and use approximations of logical regularities by smooth sigmoid functions.

A Fast Algorithm for Weber Problem on a Grid

AMS subject classification: 90B80.