Polymathian specialise in building bespoke hosted optimisation point solutions for industry

Published Papers

Fox, M., Herden, D. Ship Scheduling of Fertilizer Products, OR Insight, June 1999

This article describes a Mixed Integer Programming model to schedule ships with a variety of fertilizer products into eight ports on Australia's eastern and southern seaboards. The objective is to minimise freight, discharge and inventory holding costs while taking into account demand for product and warehousing constraints. Major planning decisions are made on a monthly basis for a 12-15 month planning horizon. To improve run-time performance extra integer variables are introduced to provide strong cuts and binary variables are introduced gradually throughout the planning horizon over several optimisation runs. The model is used for operational planning and budgetary purposes and interfaces to the outside world through a friendly matrix generator and a modern spreadsheet system.


Hollis, B., Forbes, M., Douglas, B. 2006. Vehicle Routing and Crew Scheduling for Metropolitan Mail Distribution at Australia Post, European Journal of Operational Research 1(173) 133-150.

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.


Hollis, B., Green, P. 2012. Real-Life Vehicle Routing with Time Windows for Visual attractiveness and Operational Robustness., Volume 29, Issue 04, August 2012. (YouTube animation)

This paper describes an algorithm for producing visually attractive and operationally robust solutions to a real-life vehicle routing problem with time windows. Visually attractive and operationally robust solutions are usually synonymous with compact, nonoverlapping routes with little or no intra-route cross over. The visual attractiveness of routes, for practical routing applications, is often of paramount importance.

We present a two phase solution approach. The first phase is inspired by the sequential insertion algorithm of Solomon (1987) and includes a range of novel enhancements to ensure visually attractive solutions are produced in the face of a range of nonstandard real-life constraints: A constrained and heterogeneous vehicle fleet; tight time windows and banned delivery windows; multiple route capacity measures; driver breaks; minimum route volumes; vehicle-location compatibility rules; nonreturn to base routes; peak hour traveling times; vehicle type dependent service times; and replenishment back at the depot. The second phase is based on the guided local search algorithm of Kilby et al. (1999). It uses an augmented objective function designed to seek solutions which strike a balance between minimizing traditional cost measures, whilst maximizing the visual attractiveness of the solution.

Our two phase solution approach is particularly adept at producing solutions that both aggressively minimize the total number of routes, a feature that we believe has been missing in algorithms presented in equivalent literature, as well as minimizing traditional cost measures whilst delivering a very high degree of visual attractiveness.

The algorithm presented has been successfully implemented and deployed for the real-life, daily beverage distribution problem of Schweppes Australia Pty. Ltd. for a range of capital cities throughout Australia.


Lechner, A., Clarke, D., Weatherley, D., Fletcher, A., Erskine, P., Comber, A. The Application of the Virtual Ecologist Approach to Evaluating the Effects of Uncertainty in Plot Based Monitoring Schemes due to Landscape Spatial and Temporal Heterogeneity, 6th International Congress on Environmental Modelling and Software (iEMSs 2012)

Monitoring programs that can detect changes in ecosystem condition are critical to assessing the success of rehabilitation and detecting negative anthropogenic impacts from activities such as mining. However, vegetation communities vary considerably and may exhibit short-term condition changes that mask long-term trends. This paper describes the development of a virtual ecologist (VE) landscape and observation simulation model for time-series data (VELOS_t). VELOS_t can be used to quantify the relationship between vegetation temporal and spatial variability, measurement uncertainty and sampling design to evaluate the robustness of a particular monitoring strategy. The model has four components: i) a landscape model that uses synthetic data to describe vegetation condition; ii) a natural variation model; iii) an environmental impact model and iv) a sampling model to describe plot-based monitoring schemes. The VE model allows users to estimate the expected performance of a range of sampling designs a priori and thus estimate detection sensitivity. Using simulated vegetation data, the model assesses whether statistical analyses can distinguish patterns of vegetation abundance from the effects of the observation of these patterns. Furthermore, the VE approach is a useful in testing the uncertainty sources such as imprecise measurement of vegetation cover are easily modelled using the VE approach in comparison to analytical approaches. This paper introduces the virtual ecologist model and provides a simple example of its use to assess the robustness of monitoring scheme design for long-term trend analysis.


Fox, M. On Apportioning and Rounding, Aust Comp Jnl, Vol 11, No. 3

The apportioning and rounding problem described in Coote (February 1979) is shown to reduce to a simple linear program. The formulation defines an assignment problem capable of hand or computer solution and exhibiting maximum accuracy.


PhD Theses

Hollis, B. PhD Thesis, Vehicle and Crew Routing and Scheduling. 2010

This thesis is concerned with various aspects of vehicle and crew routing and scheduling. In particular: the integration of vehicle routing with simultaneous vehicle and crew scheduling; simultaneous vehicle and crew scheduling with time windows; and vehicle routing with time windows for visual attractiveness and operational robustness. It is comprised of the solution techniques to a subset of the real world problems I have had the opportunity to apply myself to in my professional career to date, that met the requirements for inclusion in an industry-based PhD thesis: involving substantial new and innovative research; being a real world problem where the solutions produced would be implemented and the software within which the research was embodied deployed; and combining the willingness of the customer to allow publication including the use and release of internal company data. This thesis is comprised of three articles, included as chapters without alteration, submitted for publication in various peer reviewed journals. It also incorporates a chapter containing an updated literature review covering the intervening period between submission of the articles and submission of this thesis and a chapter containing a brief summary of the most significant contributions and findings from the three articles.


Conference Proceedings

Hancock, W., 2012. Modeling the Gravity Flow of rock using the Discrete Element Method, In: Massmin2012, Sudbury.

A numerical model for flow using the Discrete Element Method (ESyS-Particle) was developed and validated against data reported in recent literature. An analysis of a range of flow models was conducted showing features of flow which are normally difficult to observe or measure in physical models or operating cave mines. Porosity and velocity data describe a movement zone which is very dense within the plug flow region and grows in waves of compaction and decompaction. The model was then extended to incorporate a wide size distribution of blocky particles able to interlock with each other. Results show a significant divergence from the ellipsoid of flow theory to one of a more turbulent and haphazard nature.


Weatherley, D., Boros, V., Hancock, W., Abe, S., 2010. Scaling benchmark of esys-particle for elastic wave propagation simulations. In: Escience, 2010 IEEE Sixth International Conference on e-Science. pp. 277-283.

The Discrete Element Method (DEM) is a popular particle-based numerical method for simulating geophysical processes including earthquakes, rock breakage and granular flow. Often simulations consisting of thousands of particles have insufficient resolution to reproduce the micromechanics of many geophysical processes, requiring millions of particles in some instances. The high computational expense of the DEM precludes execution of such problem sizes on desktop PCs. ESyS-Particle is a parallel implementation of the DEM, designed for execution on cluster supercomputers. Three-dimensional spatial domain decomposition is implemented using the MPI for interprocess communications. We present results of scaling benchmarks in which problem size per worker remains constant. As the number of workers increases from 27 to 1000, execution time remains near-constant, permitting simulations of 8.7M particles in approximately the same real time as simulations comprising 240K particles.


Hancock, W., Weatherley, D., Chitombo, G., 2010. Large-scale simulations of gravity flow in block caving. In: Potvin, Y. (Ed.), Caving 2010. Perth, pp. 553-566.


Integrating Vehicle Routing, Vehicle Scheduling and Crew Scheduling, Column Generation 2008

General Publications

Fox, M. Further Reduction of the Konno-Yamazaki Mean-Absolute Deviation Portfolio Optimization Model, Social Science Research Network, 2014

The purpose of this note is to present a further reduction of the model presented by Konno and Yamazaki (1991). In their paper the number of nonzero assets in the optimal solution is bounded by the number of model rows, 2T + 2, where T is the number of time periods (assuming no upper limit on the investment in an asset). Further analysis based on the work of Feinstein and Thapa (1993) shows that one set of T constraints is redundant, leading to an upper bound on nonzero assets of T + 2.


Acknowledgements

Acknowledgement: Clarke, D. Short-Term Memory Maintenance of Object Locations during Active Navigation: Which Working Memory Subsystem Is Essential?

The goal of the present study was to examine the extent to which working memory supports the maintenance of object locations during active spatial navigation. Participants were required to navigate a virtual environment and to encode the location of a target object. In the subsequent maintenance period they performed one of three secondary tasks that were designed to selectively load visual, verbal or spatial working memory subsystems. Thereafter participants re-entered the environment and navigated back to the remembered location of the target. We found that while navigation performance in participants with high navigational ability was impaired only by the spatial secondary task, navigation performance in participants with poor navigational ability was impaired equally by spatial and verbal secondary tasks. The visual secondary task had no effect on navigation performance. Our results extend current knowledge by showing that the differential engagement of working memory subsystems is determined by navigational ability.