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In: Operations Management

ONLY PART B REQUIRED: Question 1 The towns in Kent with their corresponding x and y...

ONLY PART B REQUIRED:


Question 1

The towns in Kent with their corresponding x and y coordinates as well as their population are given overleaf. This data is also in an excel file that can be downloaded from Moodle under the name “Kent-Towns”.

(a) Using Excel Solver, or otherwise, establish a location in the plane, that minimises:

(i) the sum of distances to all Kent towns,

(ii) the sum of weighted distances to all Kent towns, with populations as weights,

(iii) the maximum distance to any Kent town, and

(iv) the maximum weighted distance to any Kent town.

(b) Assume from now on that facilities can only be established at the given towns, rather than anywhere in the plane.

(i) Establish at which town a single facility should be built, if the aim is to minimise the sum of distances from the facility to all Kent towns.

(ii) Having established this facility, use the ADD heuristic to find the location of a second facility. Allocate every town to its nearest facility. Explain why these two facilities are not necessarily the optimal solution to the p-facility discrete location problem (p=2). Can you find (using your own heuristic thinking) a pair of locations that gives a better result?

In your answers to the above, clearly explain how you have arrived at your results.

TOWN/CITY

X

Y

POPULATION

Ashford

600985

142805

58,178

Broadstairs

639320

167760

24,370

Canterbury

614880

157830

42,249

Chatham

575785

167920

70,540

Dartford

554200

174325

50,000

Deal

637510

152745

29,248

Dover

631650

141835

39,078

Faversham

601530

161425

18,000

Folkestone

622765

135915

53,411

Gillingham

577350

168385

99,773

Gravesend

564730

174170

51,150

Herne Bay

617900

167945

31,000

Maidstone

576150

155705

75,000

Margate

635460

170580

58,465

Northfleet

562235

174310

13,590

Ramsgate

638365

165180

37,967

Rochester

574375

168475

25,000

Royal Tunbridge Wells

558360

139265

45,000

Sevenoaks

552375

155295

18,588

Sheerness

591955

174725

20,000

Sittingbourne

590740

163660

55,000

Tonbridge

559080

146600

31,600

Whitstable

610670

166740

30,000

Solutions

Expert Solution

Excel Model was made as shown above.

a) i)Hence, facility location in this case should be at 591388,163105.

The formula sheet is given below :-

a) ii) The formula sheet for the above excel is

Hence, facility location, in this case, should be at 588642,162573

a) iii)

Hence, facility location, in this case, should be at 595734,162316.

a) iv)

Hence, facility location, in this case, should be at 597844,168222.

Formula Sheet for the above step is given below:-

Part B

The formula sheet is given below:-

Part b -2

The formula sheet is given below


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