Dampening bullwhip effect of order-up-to inventory strategies via an optimal control method

In this paper, we consider the bullwhip effect problem of an Order-Up-To (OUT) inventory strategy for a supply chain system. We firstly establish a new discrete-time dynamical model which is suitable to describe the OUT inventory strategy. Then, we analyze the bullwhip effect for the dynamical model of the supply chain system. We thus transform the bullwhip effect's dampening problem to a discrete-time optimal control problem. By using the Pontryagin's maximum principle, we compute the corresponding optimal control and obtain the optimal manufacturer productivity of goods. Finally, we carry out numerical simulation experiments to show that the devised optimal control strategy is useful to dampen the bullwhip effect which always happens in the supply chain system

Computation of Lacunarity from Covariance of Spatial Binary Maps

We consider a spatial binary coverage map (binary pixel image) which might represent the spatial pattern of the presence and absence of vegetation in a landscape. ‘Lacunarity’ is a generic term for the nature of gaps in the pattern: a popular choice of summary statistic is the ‘gliding-box lacunarity’ (GBL) curve. GBL is potentially useful for quantifying changes in vegetation patterns, but its application is hampered by a lack of interpretability and practical difficulties with missing data. In this paper we find a mathematical relationship between GBL and spatial covariance. This leads to new estimators of GBL that tolerate irregular spatial domains and missing data, thus overcoming major weaknesses of the traditional estimator. The relationship gives an explicit formula for GBL of models with known spatial covariance and enables us to predict the effect of changes in the pattern on GBL. Using variance reduction methods for spatial data, we obtain statistically efficient estimators of GBL. The techniques are demonstrated on simulated binary coverage maps and remotely sensed maps of local-scale disturbance and meso-scale fragmentation in Australian forests. Results show in some cases a fourfold reduction in mean integrated squared error and a twentyfold reduction in sensitivity to missing data. Supplementary materials accompanying the paper appear online and include a software implementation in the R language

Multi-temporal land-cover classification and change analysis with conditional probability networks: The case of Lesvos Island (Greece)

This study uses a series of Landsat images to map the main land-cover types on the Mediterranean island of Lesvos, Greece. We compare a single-year maximum likelihood classification (MLC) with a multi-temporal maximum likelihood classification (MTMLC) approach, with time-series class labels modelled using a first-order hidden Markov model comprising continuous and discrete variables. A rigorous validation scheme shows statistically significant higher accuracy figures for the multi-temporal approach. Land-cover change accuracies were also greatly improved by the proposed methodology: from 46% to 70%. The results show that when only two dates are used, the mapping of land use/cover is unreliable and a large number of the changes identified are due to the individual-year commission and omission errors

Counting flags in triangle-free digraphs

Motivated by the Caccetta-Haggkvist Conjecture, we prove that every digraph on n vertices with minimum outdegree 0.3465n contains an oriented triangle. This improves the bound of 0.3532n of Hamburger, Haxell and Kostochka. The main new tool we use in our proof is the theory of flag algebras developed recently by Razborov.Comment: 19 pages, 7 figures; this is the final version to appear in Combinatoric

Using natural resource inventory data to improve the management of dryland salinity in the Great Southern, Western Australia

The synoptic assessment of salinity risk and the likely costs and benefits associated with various management options is crucial to natural resource management decision-making in southern Australia. A variety of methods have been proposed and tested for assessing various aspects of salinity risks and costs, but no large region of Australia has ever had a comprehensive risk assessment across the range of biophysical and economic issues with forecasts of the effectiveness of different levels of intervention. This National Land and Water Resources Audit Implementation Project (referred to locally as Salt Scenarios 2020, or SS2020 for short) attempted to provide such an assessment (at a scale of around 1:100,000). The existing methods of monitoring and predicting salinity (based on variables derived from widely-available Landsat TM data and existing contour data; albeit with improved variable extraction from the DEMs) are being applied to the rest of the agricultural area of WA as part of the Land Monitor Project, funded in part by NHT. Collecting accurate contour data (2-metre) is a major part of the NHT project. This Audit project was proposed to allow other fundamental data sets, and especially groundwater levels from bore-hole data, to be used to significantly improve predictions in lower-rainfall areas as well as refine the predictions in the high rainfall areas. The Great Southern is an area of considerable economic and environmental value populated by 60,000 people. In 1996, it was estimated that about 30% of the cleared land and associated vegetation and water resources are at risk from becoming salt-affected over the next 30 years unless high-water use farming systems and farm forestry are adopted over large parts of the region(Ferdowsian et al., 1996). Four key questions arise with respect to the future of this region as affected by dryland salinity: •How large will the problem eventually be under current land practices? How large might it be in the year 2020? •What is at risk if the area under threat grows that large? •To what degree can we change the eventual extent of salinity with land use alternatives that are both feasible and available? •What are the costs and benefits of intervening with these alternative land uses? Ultimately, the SS2020 Project aimed to provide some guidance to state, regional and local planners and managers regarding salinity risk in the Great Southern. The analyses underpinning this guidance were based on similar data employed by NLWRA projects under Theme 2 – Dryland Salinit

A multi-agency project of the Western Australian Salinity Action Plan supported by the Natural Heritage Trust

Land Monitor is a multi-agency project of the Western Australian Salinity Action Plan supported by the Natural Heritage Trust. It will provide land managers and administrators with baseline salinity and vegetation data for monitoring changes over time, and land height data from which contours accurate to two metre intervals can be produced. The Project will also provide estimates of areas at risk from secondary or future salinisation. Land Monitor will cover the 18 million hectares of agricultural area of south-west, Western Australia. Sequences of calibrated Landsat Thematic Mapper satellite images integrated with landform information derived from height data, ground truthing and other existing mapped data sets are used as the basis for monitoring changes in salinity and woody vegetation. Heights are derived on a 10m grid from stereo aerial photography flown at 1:40,000 scale, using soft-copy automatic terrain extraction (image correlation) techniques. Proposed Land Monitor products include salinity maps, predicted salinity maps, enhanced imagery, vegetation status maps and spectral / temporal statistics. These products will be available in a range of formats and scales, from paddock, farm to catchment and shire scales to suit customer needs

The Land Monitor Project

The Land Monitor Project is providing information over the southwest agricultural region of WA. It is assembling and processing sequences of Landsat TM data, a new highresolution digital elevation model (DEM) and other spatial data to provide monitoring information on the area of salt-affected land, and on changes in the area and status of perennial vegetation over the period 1988-2000. Land Monitor is a multi-agency project of the Western Australian Salinity Action Plan supported by the Natural Heritage Trust. The Project will also providing estimates of areas at risk from secondary or future salinisation, based on the historical salinity maps and a set of landform variables derived from the high resolution DEM. Sequences of calibrated Landsat Thematic Mapper satellite images integrated with landform information derived from height data, ground truthing and other existing mapped data are used as the basis for monitoring changes in salinity and woody vegetation. Procedures for accurate registration and calibration were developed by CSIRO Mathematical and Information Sciences (CMIS), as were the data integration procedures for salinity mapping and prediction. For the DEM, heights are derived on a 10m grid from stereo aerial photography flown at 1:40,000 scale, using soft-copy automatic terrain extraction (image correlation) techniques. Land Monitor products include: high resolution DEMs; calibrated sequences of Landsat imgery; present and historical salinity maps; predicted salinity maps; maps of change in vegetation status and spectral/temporal statistics. These products are available in a range of formats and scales, from paddock to catchment and shire scales to suit customer needs

A new generic open pit mine planning process with risk assessment ability

Conventionally, mining industry relies on a deterministic view, where a unique mine plan is determined based on a single resource model. A major shortfall of this approach is the inability to assess the risk caused by the well-known geological uncertainty, i.e. the in situ grade and tonnage variability of the mineral deposit. Despite some recent attempts in developing stochastic mine planning models which have demonstrated promising results, the industry still remains sceptical about this innovative idea. With respect to unbiased linear estimation, kriging is the most popular and reliable deterministic interpolation technique for resource estimation and it appears to remain its popularity in the near future. This paper presents a new systematic framework to quantify the risk of kriging-based mining projects due to the geological uncertainties. Firstly, conditional simulation is implemented to generate a series of equally-probable orebody realisations and these realisations are then compared with the kriged resource model to analyse its geological uncertainty. Secondly, a production schedule over the life of mine is determined based on the kriged resource model. Finally, risk profiles of that production schedule, namely ore and waste tonnage production, blending grade and Net Present Value (NPV), are constructed using the orebody realisations. The proposed model was applied on a multi-element deposit and the result demonstrates that that the kriging-based mine plan is unlikely to meet the production targets. Especially, the kriging-based mine plan overestimated the expected NPV at a magnitude of 6.70% to 7.34% (135 M$to 151 M$). A new multivariate conditional simulation framework was also introduced in this paper to cope with the multivariate nature of the deposit. Although an iron ore deposit is used to prove the concepts, the method can easily be adapted to other kinds of mineral deposits, including surface coal mine