A decision model for natural oil buying policy under uncertainty

A manufacturer, in a fast moving consumer goods industry, buys Natural oils from a number of oil suppliers world-wide. The prices of these oils are the major raw material cost in producing the consumer goods, which are also sold world-wide. The volatility in the international prices of the Natural oils has signi¯cant impact on the planning and budgets decisions. Since the oils are bought and the ¯nished products are sold in markets throughout the world, the manufacturer is exposed to a variety of market uncertainties and the resulting risks. These uncertainties are the raw material prices, the demand and the therefore the selling prices for the finished goods- all of which influence the profitability of the manufacturing firm. The risks can be minimised by entering into futures contract of appropriate duration, that is, by following a schedule of "forward"' purchase of oil (with specific series of future delivery dates) with the oil suppliers. We formulate this problem as a two-stage Stochastic Program (SP) using the futures and the spot prices for the Natural oil. This SP model gives robust decisions that hedge against the uncertainties in the Natural oil prices and the demand for the finished products. The uncertainty in the oil prices and the demand are modelled through a scenario generator. We have constructed a decision support system (DSS) that integrates the SP model, the scenario generator and the solution algorithm. This DSS also provides the decision maker a profile of the risk and return exposures for different policies

Modelling of mathematical programs: An analysis of strategy and an outline description of a computer assisted system

The salient components of the mathematical programming modeling activity are first analysed. Earlier generation systems such as program generators and procedural (modelling) languages are briefly discussed. A proposal for a computer assisted modelling scheme is then put forward. The proposed system contrasts with the earlier approaches in that no computer programming expertise is required on the part of the modeller. A mathematical programming model is usually constructed by progressive definition of dimensions, data tables, model variables, model constraints and the matrix coefficients which connect the last two entities. The philosophy and design of the experimental system supports this approach to model description. This aspect is illustrated by a few examples. The introduction of computer assistance in structuring of the data and the resulting model is novel and is in line with recent developments in friendly and flexible user interface

Computer assisted mathematical programming

A Computer Assisted Mathematical Programming (Modelling) System (CAMPS) is described in this paper. The system uses program generator techniques for model creation and contrasts with earlier approaches which use a special purpose language to construct models. Thus no programming skill is required to formulate a model. In designing the system we have first analysed the salient components of the mathematical programming activity. A mathematical programming model is usually constructed by progressive definition of dimensions, data tables, model variables, model constraints and the matrix coefficients which connect the last two entities. Computer assistance is provided to structure the data and the resulting model in the above sequence. In addition to this novel feature and the automatic documentation facility, the system is in line with recent developments, and incorporates a friendly and flexible user interface

THE EFFECT OF CMV INFECTION ON PROGRESSION OF HUMAN-IMMUNODEFICIENCY-VIRUS DISEASE IN A COHORT OF HEMOPHILIC MEN FOLLOWED FOR UP TO 13 YEARS FROM SEROCONVERSION

The effect of prior infection with cytomegalovirus (CMV) on progression of HIV disease in a cohort of 111 men with haemophilia was studied after 13 years followup. The relative hazards associated with CMV positivity on progression to AIDS, death and a CD4 count of 0.05 x 10(9)/l were 2.28, 2.42 and 2.34, respectively. CMV seropositive patients were significantly older than the seronegative and this was controlled for by using a Cox proportional hazards model. The relative hazards for the three endpoints decreased to 1.89, 1.82 and 1.93 respectively and were marginally non-significant (P = 0.05, 0.08 and 0.08 for the three endpoints respectively). We conclude that this cohort continues to show evidence of a 'co-factor' effect associated with prior infection with CMV which is confounded by age but not completely explained by age differences. The potential biological significance of these results is discussed in the context of recent controlled clinical trials which show a survival benefit from long-term high-dose acyclovir, a drug with activity in vivo against CMV and other herpesviruses

The rate of CD4 decline as a determinant of progression to AIDS independent of the most recent CD4 count

The data of two cohort studies of HIV-infected individuals were used to examine whether the rate of CD4 decline is a determinant of HIV progression, independent of the most recent CD4 count. Time from seroconversion to clinical AIDS was the main outcome measure. Rates of CD4 decline were estimated using the ordinary least squares regression method. AIDS incidences were compared in individuals who had previously experienced either a steeper or a less steep rate of CD4 decline. Cox proportional hazards model including a time-dependent covariate for the rate of CD4 decline was performed. The rate of prior CD4 decline was significantly associated with the risk of developing AIDS independently from the most recent CD4 count, with a 2 % increase in hazard of AIDS (P < 0.01) for a difference of 10 cells/mm(3) in the estimated yearly drop in CD4 count. This finding gives scientific credit to the belief that individuals with a prior steeper CD4 decline consistently have a higher subsequent risk of developing AIDS than those with a less steep prior decline

Tools for reformulating logical forms into zero-one mixed integer programs (MIPS)

A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Programming (ILP) formulation or a Mixed Integer Programming (MIP) formulation is presented. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. A prototype user interface by which logical forms can be reformulated and the corresponding MIP constructed and analysed within an existing Mathematical Programming modelling system is illustrated. Finally, the steps to formulate a discrete optimisation model in this way are demonstrated by means of an example

Revisiting lagrange relaxation (LR) for processing large-scale mixed integer programming (MIP) problems

Lagrangean Relaxation has been successfully applied to process many well known instances of NP-hard Mixed Integer Programming problems. In this paper we present a Lagrangean Relaxation based generic solver for processing Mixed Integer Programming problems. We choose the constraints, which are relaxed using a constraint classification scheme. The tactical issue of updating the Lagrange multiplier is addressed through sub-gradient optimisation; alternative rules for updating their values are investigated. The Lagrangean relaxation provides a lower bound to the original problem and the upper bound is calculated using a heuristic technique. The bounds obtained by the Lagrangean Relaxation based generic solver were used to warm-start the Branch and Bound algorithm; the performance of the generic solver and the effect of the alternative control settings are reported for a wide class of benchmark models. Finally, we present an alternative technique to calculate the upper bound, using a genetic algorithm that benefits from the mathematical structure of the constraints. The performance of the genetic algorithm is also presented

Imaging Water Dissociation on TiO₂(110)

Scanning tunneling microscopy has been used to identify the adsorption site of H₂O on TiO₂(110)-(1 x 1) at 150 K, and to monitor the site of the dissociation products at 290 K. Water adsorbs onto the rows of fivefold coordinated Ti atoms at 150 K, dissociating by 290 K to form bridging but not terminal hydroxyls. This points to the involvement of bridging O vacancies in the dissociation pathway

Computer assisted modelling of linear, integer and separable programming problems

For mathematical programming (MP) to have greater impact upon the decision making process, MP software systems must offer suitable support in terms of model communication and modelling techniques . In this paper modelling techniques that allow logical restrictions to be modelled in integer programming terms are described and their implications discussed. In addition it is demonstrated that many classes of non-linearities which are not variable separable may be reformulated in piecewise linear form. It is shown that analysis of bounds is necessary in the following three important contexts: model reduction, formulation of logical restrictions as 0-1 mixed integer programs and reformulation of nonlinear programs as variable separable programs, It is observed that as well as incorporating an interface between the modeller and the optimiser there is a need to make available to the modeller software facilities which support the modelling techniques described here

Persistence of two genotypes of Neisseria gonorrhoeae during transmission.

Isolates of Neisseria gonorrhoeae were tested using a highly discriminatory typing method, opa typing, to examine the genetic diversity over a 2-year study period of isolates from all consecutive patients with gonorrhea attending the Genitourinary Medicine clinic in Sheffield, United Kingdom. Two opa genotypes were detected throughout the 2-year time period and comprised 41% of all strains tested. The persistence of two opa types was investigated further to determine the apparent genetic stability, by examining the ability of isolates to undergo intragenic and intergenic recombination and mutation in vitro. Intragenic recombination or mutation involving the opa genes of N. gonorrhoeae in the selected isolates was not detected, but intergenic recombination did occur. opa genes of N. gonorrhoeae in vivo appear to diversify primarily through intergenic recombination. Intergenic recombination in vivo would require the presence of a mixed gonococcal infection, in which an individual is concurrently colonized with more than one strain of N. gonorrhoeae. We propose that the level of diversity of opa genotypes in a population is linked to the degree of sexual mixing of individuals and the incidence of mixed infections of N. gonorrhoeae