Discuss the effect on the minimum transportation cost when capacity at each factory or warehouse is altered by adding or subtracting one ton.

Paint Tran-shipment 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 suppliers 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.
Warehouse
Wholesaler
Supplier
London Birmingham Glasgow 1 2 3 4 5
Bristol
25 23 80 90 100 86
Leeds
30 27 30 70 54 100
London
37 31 40 44
Birmingham
36 40 43 40 46
Glasgow
45 42 30 36

TABLE 1: TRANSPORTATION COSTS IN £’S/TON DELIVERED
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.

Answer the following three parts of the problem. Parts A and B are worth 30% each while part C is worth 40% of the overall mark for this problem.

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 subletting some of the capacity of this warehouse. Such sublets 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.

Discuss the effect on the minimum transportation cost when capacity at each factory or warehouse is altered by adding or subtracting one ton.

Place your order
(550 words)

Approximate price: $22

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
$26
The price is based on these factors:
Academic level
Number of pages
Urgency
Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more