BMAN60101 Mathematical Programming and Optimisation

Your coursework assignment is the case INTERNATIONAL COAL.

Approach this as if it were a piece of commercial work (e.g. external or internal 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! Think about what he needs to know in order to make the decisions necessary in his job, what closely-related issues arising from your modelling that he should be informed about, and how he would want to receive this information.
The style to be adopted for the submission is StyleA: Consulting or Managerial Report (see the Guidance on submission styles document on Blackboard).
• The Management Report should be no more than 10 or 12pages long, including cover page, executive summary, contents etc.

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• There is no hard limit for the Technical Appendices, but all components must be relevant, annotated, neatly presented and referred to in the Management Report. 20 pages might be a reasonable expectation. It must include some documentation for the models, concentrating on how the model is structured and how to use it, not on general background about how to build a model in Excel etc. The models should be in electronic form and accompany the Technical Appendices.
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 necessary, 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 (that Bob Manchester could commission from you)
• Your models in electronic format, with some accompanying documentation, so that Bob Manchester and his team may do some checking, further ‘what-if?’ analyses and potentially develop them for further use.

(N.B. The above guidance is not indented to be prescriptive or a contents list, but gives more detailed prompts than usual since this is your first individual assignment.)

Marks breakdown
Management report
Presentation 10%
Exec summary 10%
Conceptual explanation of the modelling 20%
Critical analysis on the results 20%
Basic recommendations 10%
Technical applications
Presentation 10%
Structuring of models 10%
Modelling 10%

You must submit your individual report to this coursework assignment to the programme administrator no later than 15.00 on Monday 9/12/2013.

You must also submit your individual report to this coursework assignment to Blackboard no later than 15.00 on Monday 9/12/2013.

INTERNATIONAL COAL
Coal-fired Power Generation
Compared with other fossil fuels, burning coal produces relatively large amounts of atmospheric pollutants: carbon dioxide (CO2), nitrogen oxides (NOx), sulphur dioxide (SO2) and particulates. Therefore over recent decades there has been a decline in the use of coal for power generation. However, as supplies of other easily-accessible fossil fuels dwindle there remain vast deposits of coal, and the International Energy Agency estimates that coal will 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 can be treated as an additional fuel cost. This may be extended to SO2, but currently 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 can reduce emission levels of SO2 and NOxrespectively 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 often used so that trade-offs can be made between costs, energy and the various emissions produced.
Recently 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 (e.g. straw and olive cake ). In the UK the Department of Trade and Industry (DTI) has set the target that by 2010 renewable sources should contribute 10% 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, especially 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, however biomass has to be stocked separately. Transport costs are factored into the fuel prices. The plant has 35% efficiency, 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 relatively 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 types of coal that can be ordered for burning in September and October, and wood-chip biomass which can 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% 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 current coal stockpile at the plant (including coals previously 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 major 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 currently 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 explain a prototype model
• Use your model to recommend a schedule of burning and, if necessary buying fuels
• Use your model and its results to offer:
o 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
o any insights you can into the issues of FGD and sulphur-trading

Data
Table 1: Characteristics of Fuels
Fuel Pricea Calorific value SO2
£/tonne GJoules per tonne %b
Coal: Stockpile 42.56 25.81 1.38%
Coal: Columbian 43.93 25.12 0.70%
Coal: Russian 43.80 24.50 0.35%
Coal: Scottish 42.00 26.20 1.72%
Wood chips 73.77 18.00 0.01%
aconstant fuel prices for the period June- October 2005
ba 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
Electricity Market
Forward Prices June July August September October
Period: £ per MWh £ per MWh £ per MWh £ per MWh £ per MWh
WeekdayPeak 36.00 36.35 37.65 38.35 43.70
Weekday Off-peak 27.00 27.00 28.20 28.50 31.70
WeekendPeak 33.50 34.30 35.65 35.80 38.70
Weekend Off-peak 26.20 26.30 27.50 27.65 30.10

Table 3: Currency Conversiona
British pound per US Dollar 1.0000
British pound per Euro 0.6667
aconstant exchange rates for the period June- October 2005
About the contributors
Dr Nathan Proudlove, Senior Lecturer in Operational Research at Manchester Business School, University of Manchester, UK.
Dr. Cathy McClay, former Business Strategy Manager at First Hydro, a part of International Power Plc. She now works for Eon.
Appendix
CO2 trading
• Companies are allocated a CO2 emission limit by Government. The EU emissions trading scheme allows companies to sell unused CO2 allowance, or purchase further emission allowance from a market. The result is that in this case all CO2 emissions from the plant should be costed at the tradable value (the company’s allowance can be considered to have been used elsewhere or earlier in the year)
• Background information can be found atwww.defra.gov.uk/environment/climatechange/trading/index.htm [accessed 10 Feb 2006]
sulphur bubble
• The ‘sulphur bubble’ is assigned by Government, as part of the Large Combustion Plant Directive agreed by the European Parliament; www.defra.gov.uk/environment/airquality/lcpd/ [accessed 10 Feb 2006]
ROC
• “The Obligation requires suppliers to source an annually increasing percentage of their sales from renewables. For each megawatt hour of renewable energy generated, a tradable certificate called a Renewables Obligation Certificate (ROC) is issued.”
• Background information can be found atwww.dti.gov.uk/renewables/renew_2.2.2.htm [accessed 10 F
eb 2006]