Mathematical Programming and Optimisation

Individual Assignment

Approach this as if it were a piece of commercial work (e.g. internal and external consulting) rather than an academic submission. The deliverable is a report addressed to Bob Manchester at International Coal. To approach the writing of the report and presentation of your accompanying model(s), try to put yourself in Bob Manchester's shoes.

Bob Manchester is a busy, bright middle-manager, with an engineering background. He does not have a knowledge of or great interest in the details of linear programming or the academic literature.

The focus is solving the problem as presented, and potentially providing International Coal with a methodology for continuing this approach. Academic/theoretical material or research into the context and regulatory background is not required. If you regard some as strictly necessary, try to confine it to the technical appendices and remember to use the MBS 'house style' for referencing (the Harvard system: there should be examples in the Programme Handbook).

A high standard will also be expected in presentation, English, grammar, formatting etc.

The report should cover:

• The recommended schedule of burning and, if required, buying fuels
• Input and output data used in developing your recommendation.
• An insight into the method, logic and tools used
• Information about the constraints to greater profit

• Insights into the effect on the burning schedule of FGD
• The impact of potential changes in the ROC payment rate
• Suggestions for further work

• Your models in electronic format, with some accompanying documentation, so that Bob Manchester and his team can do some checking, further 'what-if?' analyses and potentially develop them for further use.

International Coal

Coal-fired Power Generation

Compared with other fossil fuels, burning coal produces comparatively large amounts of atmospheric pollutants: carbon dioxide (CO₂), sulphur dioxide (SO₂), nitrogen oxides (NO_x) and particulates. Thus over recent decades there has been a decline in the use of coal for power generation. Thus, as supplies of other easily-accessible fossil fuels dwindle there remain vast deposits of coal, and the International Energy Agency estimates that coal may still be used to generate 38% of the world's electricity in 2020.

Within the European Union, environmental concerns have led to limits on emission of pollutants. A market has been established for trading CO₂ emissions. A generator has to pay for CO₂ emissions at the market rate, so they will be treated as an additional fuel cost. This can be extended to SO₂, but presently generators are allocated a limit (a 'sulphur bubble') for a year running from October to October (the 'sulphur year').

Flue-gas desulpherisation (FGD) and 'scrubber' technology will reduce emission levels of SO₂ and NO_xrespectively from the exhaust gases.

Coals from different regions of the world have different composition, with different calorific values and pollutant content. Combinations of coals are usually used so that trade-offs can be made between costs, energy and the various emissions produced.

Currently some coal-fired plants have started to 'co-fire', blending coal with biomass. Biomass includes waste products from forestry (e.g. wood chips), from paper production, and from agriculture. In the UK the Department of Industry and Trade (DTI) has set the target that by 2010 renewable sources should contribute 10 percent of the UK electricity supply, and generators are paid a supplement for each MWh of power generated this way (this is known as the Renewables Obligation Certificate, ROC). The DTI foresees the combustion of biomass, both domestic and imported, as being the fastest growing component of the renewable energy.

International Coal

International Coal (IC) operates a large (1,000 MW) coal-fired plant in the UK. They employ a team who purchase different fuels in order to maximise margin (profit) whilst keeping within environmental limits, particularly on sulphur. IC has been allocated a sulphur bubble of 30 kilo tonnes for the year (to the end of October). CO₂ emission is taken to be 0.8 tonnes per MWh of electricity produced.

Coal is typically bought three or more months ahead of planned burn and stockpiles are kept at the plant. Stockpiled coal is stored in mixed piles, thus biomass has to be stocked independently. Transport costs are factored into the fuel prices. The plant has 35% competence, i.e. 35% of the calorific energy released in a burn is converted to MWh of electrical power.

Power is sold to the electricity markets, and fuel buying is done on the basis of future prices in these markets. Each month is divided into four price bands: categorised by weekend or weekday, and peak or off-peak. (Peak periods consist of a 12-hour block). Thus there are four future prices for each month. Power is distributed by the National Grid Company which charges IC a transmission rate of 65p per MWh.

The Problem

The fuel-buying team at IC is led by Bob Manchester. The buying decisions have been comparatively straightforward, but as the sulphur bubble has become more restrictive, pressure is increasing to show that the best fuels are being used. Bob thinks there must be a systematic way of considering the tradeoffs involved in the decisions being made.

It is now the end of May 2005. To test the feasibility of a modelling approach, Bob wants to investigate power generation to the end of October, considering the stockpile of mixed coals at the plant, three kinds of coal that can be ordered for burning in September and October, and wood-chip biomass which may be bought with short lead-times. Fuel is to be paid for now, ignore discounting of any of the cash flows.

Biomass is more difficult to handle than coal, having more variable combustion characteristics (low density, extremes of particle shape, tendency to entangle and demix plus moisture has a large effect has on their behaviour), so may not provide more than 10 percent of the mix (by calorific value) in any of the generating periods.

Bob has provided fuel characteristics (Table 1) and future-price data (Table 2). The existing coal stockpile at the plant (including coals earlier ordered and en route) is 600,000 tonnes and there is 30% of the 'sulphur bubble' left this sulphur year. CO₂ emission is trading at 15 Euros per tonne on the European market, which IP must pay for any CO₂ produced. The ROC is £45 per MWh from renewables. The currency conversion data is given in Table 3.

Bob has also mentioned a couple potential future issues. SO₂ emissions are a main concern for IC. One possibility is to invest in FGD. There is also the possibility that SO₂ emissions may become tradable (and so a direct cost) in the way CO₂ presently is. Either of these is likely to have a major impact on operations at the plant, but Bob is unsure how to start quantifying the potential benefits.

Assignment

Your charge is to

• Build and describe a prototype model
• Use your model to recommend a schedule of burning and, if required buying fuels
• Use your model and its results to offer:
  • any further guidance on the impact of the costs of the fuels in particular, since these are futures prices,  the effects of any drops in price
  • any insights you can into the issues of FGD and sulphur-trading

Data

Table 1: Characteristics of Fuels

constant fuel prices for the period June- October 2005

a coal with an SO₂ rating of 1% will produce 0.01 tonne of SO₂ for each tonne of the fuel burnt

Table 2: Future Electricity Prices

Table 3: Currency Conversion