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

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

On a batch arrival queuing system equipped with a stand-by server during vacation periods or the repairs times of the main server

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2011 Hindawi PublishingWe study a queuing system which is equipped with a stand-by server in addition to the main server. The stand-by server provides service to customers only during the period of absence of the main server when either the main server is on a vacation or it is in the state of repairs due to a sudden failure from time to time. The service times, vacation times, and repair times are assumed to follow general arbitrary distributions while the stand-by service times follow exponential distribution. Supplementary variables technique has been used to obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average number of customers, and the average waiting time in the queue while the MathCad software has been used to illustrate the numerical results in this work

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

Introducing new constructs for data modelling and column generation in LP modelling languages

Through popular implementation of structured query language (SQL) and query-by-example(QBE) relational databases have become the de-facto industry standard for data modelling.We consider the indices, sets, and the declarative form of Linear Programming (LP) modelling languages and introduce new constructs which provide direct link to the database systems. The models constructed in this way are data driven and display a dynamicstructure. We then show how this approach can be naturally extended to include column generation features stated in procedural forms within an otherwise declarative modelling paradigm

Sets and indices in linear programming modelling and their integration with relational data models

LP models are usually constructed using index sets and data tables which are closely related to the attributes and relations of relational database (RDB) systems. We extend the syntax of MPL, an existing LP modelling language, in order to connect it to a given RDB system. This approach reuses existing modelling and database software, provides a rich modelling environment and achieves model and data independence. This integrated software enables Mathematical Programming to be widely used as a decision support tool by unlocking the data residing in corporate databases

A review of portfolio planning: Models and systems

In this chapter, we first provide an overview of a number of portfolio planning models which have been proposed and investigated over the last forty years. We revisit the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. A piecewise linear approximation of the problem through a reformulation involving diagonalisation of the quadratic form into a variable separable function is also considered. A few other models, such as, the Mean Absolute Deviation (MAD), the Weighted Goal Programming (WGP) and the Minimax (MM) model which use alternative metrics for risk are also introduced, compared and contrasted. Recently asymmetric measures of risk have gained in importance; we consider a generic representation and a number of alternative symmetric and asymmetric measures of risk which find use in the evaluation of portfolios. There are a number of modelling and computational considerations which have been introduced into practical portfolio planning problems. These include: (a) buy-in thresholds for assets, (b) restriction on the number of assets (cardinality constraints), (c) transaction roundlot restrictions. Practical portfolio models may also include (d) dedication of cashflow streams, and, (e) immunization which involves duration matching and convexity constraints. The modelling issues in respect of these features are discussed. Many of these features lead to discrete restrictions involving zero-one and general integer variables which make the resulting model a quadratic mixed-integer programming model (QMIP). The QMIP is a NP-hard problem; the algorithms and solution methods for this class of problems are also discussed. The issues of preparing the analytic data (financial datamarts) for this family of portfolio planning problems are examined. We finally present computational results which provide some indication of the state-of-the-art in the solution of portfolio optimisation problems

Linear, integer separable and fuzzy programming problems: a united approach towards automatic reformulation

For mathematical programming (MP) to have greater impact as a decision tool, 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 after suitable algebraic manipulation put in a variable separable form. The methods of reformulating the fuzzy linear programming problem as a Max-Min problem is also introduced. It is shown that analysis of bounds plays a key role in the following four important contexts: model reduction, reformulation of logical restrictions as 0-1 mixed integer programs, reformulation of nonlinear programs as variable separable programs and reformulation of fuzzy linear 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 model reformulation techniques described here