Assignment
A bio-fuel refining supply chain consists of i) five collection points of wheat straw located in Peterborough, King's Lynn, Norwich, Ipswich and Letchworth, ii) three storages located in Thetford, Cambridge and Bury St. Edmunds, and iii) two bio-refineries located in Cambridge and Colchester, all in the UK. The cost of the wheat straw at the place of collection points is £20 per tonne, and availability at each of the collection points is given in Table 1.
Table 1 Feedstock availability
|
Collection point
|
Availability [tonne]
|
|
Peterborough
|
25000
|
|
King's Lynn
|
35000
|
|
Norwich
|
25000
|
|
Ipswich
|
40000
|
|
Letchworth
|
35000
|
The maximum capacities of the storages are: Thetford 50000 tonnes, Cambridge 20000 tonnes and Bury St. Edmunds 40000 tonnes. All collected biomass has to be transported to storages first and before it is distributed to bio-refineries.
The cost of storing the wheat straw (per tonne of biomass) in all three storages is minimised cost which is a complex relationship of energy requirements ??1, operational cost associated with labour and equipment ??2 and repayment of capital investment ??3, defined as
The available biomass (the wheat straw) is transported between collection points and storages using smaller trucks and at costs of £5 per mile per tonne, whereas between storages and bio-refineries larger trucks are used at the cost of £2.5 per mile per tonne.
The maximum capacities of the bio-refineries are Cambridge 60000 and Colchester 40000 tonnes of straw and they are expected to operate at full capacities. The conversion rate of bio-refining is 30%; 1 tonne of wheat straw produces 0.3 tonne of bio-fuel. The cost of bio-refining is £95 per tonne of biofuel and biofuel is sold at a price of £975 per tonne. Assume that all produced biofuel is sold at the bio-refinery location.
Task
Solve the stated problem by addressing the following issues:
1. Formulate the optimisation problem which will account all costs and revenues in the supply chain and optimise its operation, dominantly the logistic, such that bio-refineries get the maximum profit.
2. Provide a graphical representation (block diagram) of the supply chain and in appropriate way mark all the actors of the supply chain (collection points, storages, bio-refineries, transportation) and proposed variables.
3. Formulate the supply chain optimisation problem mathematically. The complexity of the problem suggests using a matrix formulation. Explain and justify the selection of variables and their meaning in terms of the problem;
4. Implement the optimisation problem(s) in GAMS and hence calculate the optimum using appropriate solvers.
5. Provide a graphical representation (block diagram) of the solution with clearly indicated values of the variables. Explain the results in terms of the set problem. Explain how trustful results are, any additional activity you took to increase trust and why.
6. Assess the sensitivity of the profit gained by the bio-refineries to the most critical parameter used in modelling the supply chain. Explain the results.
Report
Write up report with a full account of your design and solution, which will include:
1. Account of your design which will show supply chain representation, analytical form of the optimisation model, justification of your analytical form in relation to the given problem, selection of the parameters and variables and solver selection for GAMS program. Specify all the costs and distances used in your model;
2. Electronic, non-compressed and fully commented version of the GAMS programme (text or MS word format will be disregarded).
3. Description and explanation of the results which will include result analysis, sensitivity analysis and explanation, graphical representation of results in terms of set problem and description (and verification) of accuracy and trustfulness into obtained results