BNM860 - Paint Transportation Problem - Accounting Assignment Help

Assignment Task

Paint transportation problem

A company has two factories, one each at Bristol and Leeds. The factories produce paints which are sold to five wholesalers. The wholesalers are either supplied directly from the factories or through one of the company warehouses, the transportation costs being paid by the company. The company has three warehouses, one each in London, Birmingham and Glasgow. Table 1 shows the transportation costs per ton for deliveries from the factories to the warehouses or wholesalers and also from the warehouses to the wholesalers, omitting entries when delivery from a certain supplier or warehouse is impossible for some destination.

The two factories at Bristol and Leeds can produce up to 40,000 and 50,000 tons per week respectively. No more than 20,000, 15,000 and 12,000 tons can be moved each week through the warehouse in London, Birmingham and Glasgow, respectively. Wholesalers 1, 2, 3, 4 and 5 require at least 15,000, 20,000, 13,000, 14,000 and 16,000 tons per week respectively.
a) Formulate a linear programming model to determine the minimum cost transportation schedule. Explain clearly the variables you use and the constraints you construct. What is the minimum cost transportation schedule and what are the corresponding costs?
b) Discuss the effect on the minimum transportation cost when capacity at each factory or warehouse is altered by adding or subtracting one ton. What are the minimum capacity changes at Glasgow that will alter the optimum set of routes and what will those alterations be? Explain how you arrive at each one of your answers.
c) The management of the company is considering the possibility of closing down one of the warehouses as this is expected to result in substantial labour and maintenance savings. Further, the manager of the Birmingham warehouse is considering sub-letting some of the capacity of this warehouse. Such sub-lets would have to be in exact multiples of 1000 tons. It is estimated that each 1000 tons of capacity could be let for £21,000 per week. Formulate a mixed integer linear programming model – or, if necessary, different model variants – to examine and evaluate the alternative courses of action. What would you recommend the company to do, and why? Discuss
the alternatives, also taking into account the solution from part (a) and explain which additional information you might need (if any) to give the company more specific advice.

New product development problem
A company has developed a new product. It needs to decide whether or not to product test and market test before launch, and has been advised that, even though these processes do cost money, they increase the likelihood of success for the product. (Note that it has been agreed within the company that you can only market test a product once it has passed product testing. If a product fails either test it is regarded as worthless). You have been able to obtain details of the costs of these testing processes, together with historical data which suggest how much the likely success of the product is enhanced by successful testing. Launching the product will cost €300,000 and the estimates of profit are as follows:
Highly successful = €2,000,000
Moderately successful = €1,000,000
Low level success = €500,000
Failure = €100,000

a) Construct a decision tree and write a very brief report advising the company on its best course of action.
b) What would be the ‘best’ decision if the profit from the highly successful product were estimated to be €3,500,000 rather than €2,000,000?
c) Discuss your solution to part b) by listing all the possible outcomes that could happen if the company is to follow the recommendation suggested by your solution.
d) Refer to the settings specified under part b) once again and imagine that you were the decision maker of this company. What would you really decide to do? Would you follow the recommendation obtained by the decision tree model? Why yes or why not?

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