Management Science Applications: open book examination

BHA0027

Management Science Applications

Time allowed: 2 hours

This is an open book examination.

Candidates should answer any THREE questions from the five on the paper. All questions are marked out of 25.

Materials provided:

Graph Paper
Statistical Tables – Attached at the back of the exam paper

Materials allowed:

An original handwritten crib sheet of a maximum of 2 sides of A4 on the Departmental Paper provided

A scientific but not a programmable calculator may be used in this exam.

Unannotated paper versions of general bi-lingual dictionaries only may be used by overseas students whose first language is not English. Subject-specific bi-lingual dictionaries are not permitted. Electronic dictionaries may not be used.

Access to any other materials is not permitted

Question 1

a) Chemfast Ltd has four factories located at Alphatown, Bravo City, Charlieville and Deltaborough. The company also owns three finishing works at Muirness, Nettleham and Owlerton. The finishing works have the following weekly requirements for a particular chemical:

Muirness 15,000 litres
Nettleham 9,000 litres
Owlerton 21,000 litres
Total 45,000 litres

The four factories forecast the following weekly output for the next few months:

Alphatown 11,000 litres
Bravo City 14,000 litres
Charlieville 12,000 litres
Deltaborough 8,000 litres
Total 45,000 litres

The delivery costs per 1,000 litres from factory to finishing works are:

Cost (£) per 1,000 litres
To
Muirness Nettleham Owlerton From
Alphatown 170 210 220 Bravo City 180 250 240 Charlieville 220 220 210
Deltaborough 190 160 200

Required:

i. Using the “cheapest cell” method to obtain an initial feasible solution, apply the transportation algorithm to allocate the output of the factories to the finishing works at minimum delivery cost, and
(8 Marks)
ii. Calculate the minimum delivery cost.
(2 Marks)

b) Because of recent flooding, no delivery can be made from the Alphatown factory to the Nettleham finishing works for a week, so the chemicals for Nettleham will have to be delivered from another factory for the week.

Required:

i. Specify the revised delivery plan that would result in the least cost increase, and

(8 Marks)

ii. Calculate the new minimum delivery cost for that week.

(2 Marks)

c) Briefly explain the method used for dealing with unbalanced transportation problems, where demand does not equal supply. Your answer should specify how any costs of over-production or supply shortfall are dealt with in such a problem.

(5 Marks)

Total 25 Marks

Question 2

A small company manufacturing circuit boards produces most of the components for the boards in their own factory; however, some are bought in from specialist suppliers.

The management of are concerned that unexpected shortages with some of the components for the boards have affected production in their factory.

a) Component A is bought from a specialist outside supplier at a cost of £6.67 per unit. Stock holding costs have been estimated at 20% of stock value per annum, and for each order there is a cost of £50, irrespective of the quantity ordered. The lead time with the supplier is 3 weeks. The weekly requirement for component A follows a normal distribution with a mean of 150 units and a standard deviation of 50 units. The company works a 50 week year.

i. Calculate the economic order quantity (EOQ) and order frequency for component A.

(6 Marks)
ii. The management at of the company are prepared to accept a 95% service level for the availability of component A in production. Calculate the reorder level that should be adopted. Specify the level of safety stock that should be held, and the cost of holding this level.

(6 Marks)

b) The demand for component B produced in-house by the company is 2,500 units per month. The production cost is £17.50 per unit, each production run has a set up cost of £200, and stock holding costs per annum have been estimated as 15% of stock value. The production rate is 700 units per week.

i. Advise the management of the company of how often a production run of component B should take place, and what the production order quantity (POQ) should be. Calculate the total annual cost of inventory.
(7 Marks)

ii. The company have the option of purchasing component B at £18.50 per unit from an outside supplier. Each order would cost £130 in set up and delivery costs. Stock holding costs will remain at 15% per annum.

Use the economic order quantity (EOQ) model to calculate the total cost of inventory, and decide whether buying in this component is a worthwhile option.

(6 Marks)
Total 25 Marks Question 3
Universal Hydraulics Ltd have quality control procedures in place to monitor the production of hydraulic pipes. Samples, size four, are selected at hourly intervals and the diameters of the pipes measured. The mean and range charts for the past fifteen hours are shown below:

Required:

a) Comment upon the state of statistical control of the pipe production process over this period.

(5 Marks)

b) Often, on range charts, the lower warning and action limits are omitted. Why is this?

For what purpose might the lower control limits be used?
(2 Marks)

c) The specification for pipe diameter is 25mm ± 2 mm. Use the process capability analysis output below to assess the capability of the process to meet specifications, quoting and explaining any measures used.

(5 Marks)

d) Universal Hydraulics produce pressure relief valves and use a p-chart to monitor the percentage of defective valves in sample size 50, taken at hourly intervals. Use the data below, for samples 1 to 10, taken at a time when the process was considered to be in control, to set up the p-chart. Give details of your calculation for the positions of the control limits. DO NOT plot the data for samples 1 to 10 on the chart.

Sample Number 1 2 3 4 5 6 7 8 9 10
Number Defective 2 0 1 3 1 1 3 0 3 2

The process is allowed to continue and the results for samples 11 to 20 are given below. Plot these results on the chart.

Sample Number 11 12 13 14 15 16 17 18 19 20
Number Defective 1 2 1 2 3 4 3 2 2 1

(10 Marks)

e) Assess the state of control of the process over this period.
(3 Marks)

Total 25 Marks
Question 4
The monthly closing share prices of Axel Plc over the past 12 month period are shown in the table below:

Month Closing price Month Closing price
May 2014 322 Nov 2014 348
Jun 2014 360 Dec 2014 349
Jul 2014 350 Jan 2015 398
Aug 2014 312 Feb 2015 374
Sep 2014 340 Mar 2015 404
Oct 2014 331 Apr 2015 368

Required:

a) Use an exponentially weighted moving average steady model, with smoothing constant α = 0.2, to calculate the forecasts of closing share prices for June 2014 to May 2015.

(7 Marks)

b) Calculate the forecast errors and give a 95% confidence interval for the May 2015 forecast.

(4 Marks)
error
c) A Tracking signal T = is used to monitor the performance of the forecasting model,
forecast
which is considered to be satisfactory if the value of T does not exceed 0.15. Calculate the tracking signal values and comment upon the performance of the model.

(4 Marks)

d) The Excel spread sheet model on the next page has been set up to calculate and monitor the forecasts for monthly closing share prices.

State the formulae that you would store in the cells C5, C6, D5, F5 and E18.

(7 Marks)

e) In the light of your answer to part (c) and the Excel printout, how would you intervene in the spread sheet model in order to give more accurate forecasts?

(3 Marks)

Total 25 Marks
Spreadsheet for Question 4 on the next page

Question 5

Alpha Ltd is planning the research and development time for a new product and has listed the following necessary activities, along with their estimated duration:-

Activity Preceding
Activities Duration (Weeks)
Optimistic Most Likely Pessimistic
A – 3 5 7
B A 2 4 6
C A 2 5 8
D C 2 4 6
E D,B 1 3 5
F D,B 4 7 10
G E 3 5 7
H F 4 6 8
I G,H 5 8 11
J I 5 7 9

a) Using the program evaluation and review technique (PERT) estimate the mean and standard deviation for the duration of each activity.
(5 Marks)

b) Draw the network diagram for the project and find the estimated total project time and the critical path.
(7 Marks)

c) Find the 95% confidence interval for the overall project time.
(6 Marks)

d) What is the probability that this project will take longer than 43 weeks?
(7 Marks)

Total 25 Marks

TABLE 1: AREAS UNDER THE STANDARD NORMAL CURVE
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0
0.0000 0.0040
0.0080 0.0120
0.0160
0.0199 0.0239
0.0279 0.0319
0.0359
0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753
0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141
0.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.1517
0.4 0.1554 0.1591, 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.1879

0.5
0.1915 0.1950
0.1985 0.2019
0.2054
0.2088 0.2123
0.2157 0.2190
0.2224
0.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.2549
0.7 0.2580 0.2611 0.2642 0.2673 0.2704 0.2734 0.2764 0.2794 0.2823 0.2852
0.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.3133
0.9
0.3159 0.3186
0.3212 0.3238
0.3264
0.3289 0.3315
0.3340 0.3365
0.3389

1.0 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4
0.4192 0.4207
0.4222 0.4236
0.4251
0.4265 0.4279
0.4292 0.4306
0.4319

1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441
1.6 0.4452 0.4463 0.4474 0.4484 0.4495 0.4505 0.4515 0.4525 0.4535 0.4545
1.7 0.4554 0.4564 0.4573 0.4582 0.4591 0.4599 0.4608 0.4616 0.4625 0.4633
1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706
1.9
0.4713 0.4719
0.4726 0.4732
0.4738
0.4744 0.4750
0.4756 0.4761
0.4767

2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817
2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857
2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890
2.3 0.4893 0.4896 0.4898 0.4901 0.4904 0.4906 0.4909 0.4911 0.4913 0.4916
2.4
0.4918 0.4920
0.4922 0.4925
0.4927
0.4929 0.4931
0.4932 0.4934
0.4936

2.5 0.4938 0.4940 0.4941 0.4943 0.4945 0.4946 0.4948 0.4949 0.4951 0.4952
2.6 0.4953 0.4955 0.4956 0.4957 0.4959 0.4960 0.4961 0.4962 0.4963 0.4964
2.7 0.4965 0.4966 0.4967 0.4968 0.4969 0.4970 0.4971 0.4972 0.4973 0.4974
2.8 0.4974 0.4975 0.4976 0.4977 0.4977 0.4978 0.4979 0.4979 0.4980 0.4981
2.9
0.4981 0.4982
0.4982 0.4983
0.4984
0.4984 0.4985
0.4985 0.4986
0.4986

3.0 0.4987 0.4987 0.4987 0.4988 0.4988 0.4989 0.4989 0.4989 0.4990 0.4990
3.1 0.4990 0.4991 0.4991 0.4991 0.4992 0.4992 0.4992 0.4992 0.4993 0.4993
3.2 0.4993 0.4993 0.4994 0.4994 0.4994 0.4994 0.4994 0.4995 0.4995 0.4995
3.3 0.4995 0.4995 0.4995 0.4996 0.4996 0.4996 0.4996 0.4996 0.4996 0.4997
3.4 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4997 0.4998

TABLE 2: PERCENTAGE POINTS OF THE STANDARD NORMAL CURVE

TABLE 3: PERCENTAGE POINTS OF THE t-DISTRIBUTION

TABLE 4: PERCENTAGE POINTS OF THE 2-DISTRIBUTION

TABLE 5: PERCENTAGE POINTS OF THE CORRELATION COEFFICIENT r WHEN  = 0

One Tail 5 2.5 1 0.5 0.1 0.05
Two Tails Q% 10 5 2 1 0.2 0.1
 = 2 0.900 0.950 0.980 0.990 0.998 0.999 3 0.805 0.878 0.934 0.959 0.986 0.991
4 0.729 0.811 0.882 0.917 0.963 0.974
5 0.669 0.754 0.833 0.875 0.935 0.951

6 0.621 0.707 0.789 0.834 0.905 0.925
7 0.582 0.666 0.750 0.798 0.875 0.898
8 0.549 0.632 0.715 0.765 0.847 0.872
9 0.521 0.602 0.685 0.735 0.820 0.847
10 0.497 0.576 0.658 0.708 0.795 0.823

11 0.476 0.553 0.634 0.684 0.772 0.801
12 0.457 0.532 0.612 0.661 0.750 0.780
13 0.441 0.514 0.592 0.641 0.730 0.760
14 0.426 0.497 0.574 0.623 0.711 0.742
15 0.412 0.482 0.558 0.606 0.694 0.725

16 0.400 0.468 0.543 0.590 0.678 0.708
17 0.389 0.456 0.529 0.575 0.662 0.693
18 0.378 0.444 0.516 0.561 0.648 0.679
19 0.369 0.433 0.503 0.549 0.635 0.665
20 0.360 0.423 0.492 0.537 0.622 0.652

25 0.323 0.381 0.445 0.487 0.568 0.597
30 0.296 0.349 0.409 0.449 0.526 0.554
40 0.257 0.304 0.358 0.393 0.463 0.490
50 0.231 0.273 0.322 0.354 0.419 0.443
60 0.211 0.250 0.295 0.325 0.385 0.408

Statistical Process Control
Number in Sample n For Upper Limits For average value of R (Ṝ)
Inner Outer
D0.025 D0.001 d2
2 3.17 4.65 1.128
3 3.68 5.05 1.693
4 3.98 5.30 2.059
5 4.20 5.45 2.326
6 4.36 5.60 2.534
7 4.49 5.70 2.704
8 4.61 5.80 2.847
9 4.70 5.90 2.970

End of Exam Paper