-SQA- SCOTTISH QUALIFICATIONS AUTHORITY HIGHER NATIONAL UNIT SPECIFICATION GENERAL INFORMATION -Unit Number- 7481684 -Superclass- -Title- RB OPERATIONAL RESEARCH B ---------------------------------------- -DESCRIPTION- GENERAL COMPETENCE FOR UNIT: Formulating, solving and interpreting the solutions of operational research models for project management, inventory control and queuing in relation to business and commerce. OUTCOMES 1. apply network analysis to project management; 2. use mathematical models to obtain optimal inventory policies; 3. use simulation to analyse inventory policies and queuing systems. CREDIT VALUE: 1 HN Credit ACCESS STATEMENT: Access to this unit is at the discretion of the centre. However, it would be beneficial if the candidate had basic algebraic skills as evidenced by possession of National Certificate Module 7180321 Core Mathematics 3 or SCE Standard Grade Mathematics at 3/4. It would also be beneficial if the candidate were familiar with the Poisson and normal distributions as evidenced by possession of National Certificate Module 91064 Mathematics: Statistics 2 or Higher National Unit 7481714 Inference and Estimation. ---------------------------------------- For further information contact: Committee and Administration Unit, SQA, Hanover House, 24 Douglas Street, Glasgow G2 7NQ. Additional copies of this unit may be purchased from SQA (Sales and Despatch section). At the time of publication, the cost is 1.50 (minimum order 5).
UNIT NUMBER: 7481684 HIGHER NATIONAL UNIT SPECIFICATION STATEMENT OF STANDARDS UNIT TITLE: OPERATIONAL RESEARCH B Acceptable performance in this unit will be the satisfactory achievement of the standards set out in this part of the specification. All sections of the statement of standards are mandatory and cannot be altered without reference to SQA. OUTCOME 1 APPLY NETWORK ANALYSIS TO PROJECT MANAGEMENT PERFORMANCE CRITERIA (a) (b) (c) (d) (e) (f) (g) The production of a project network from a precedence table is correct. Identification of the critical path(s) is correct. Determination of project duration is correct. Calculation of activity floats is correct. Scheduling of the activities on a Gannt chart is correct. Drawing of a resource histogram for the project is correct. Extraction of information from the Gannt chart and the resource histogram is correct. RANGE STATEMENT Activity float: total float; free float. EVIDENCE REQUIREMENTS Project network, Gannt chart and resource histogram produced manually or by computer. Written evidence of extraction of information from the project network, Gannt chart and resource histogram. 2
OUTCOME 2 USE MATHEMATICAL MODELS TO OBTAIN OPTIMAL INVENTORY POLICIES PERFORMANCE CRITERIA (a) (b) (c) (d) Determination of the parameters for the simple model with instantaneous replenishment is correct. Determination of the optimal order policy for the simple model with instantaneous replenishment and quantity discounts is correct. Determination of the economic batch quantity for the simple model with gradual replenishment is correct. Solution of variable demand problems is correct. RANGE STATEMENT Parameters: economic order quantity; time between orders. Variable demand: low demand Poisson distributed; high demand normally distributed. EVIDENCE REQUIREMENTS Solutions of problems, at least one covering PCs (a) and (b), one covering PC(c) and two covering PC(d), and between them covering the full range for this outcome. OUTCOME 3 USE SIMULATION TO ANALYSE INVENTORY POLICIES AND QUEUING SYSTEMS PERFORMANCE CRITERIA (a) (b) Simulation and costing of an inventory system are correct. Simulation and costing of a queuing system are correct. RANGE STATEMENT Simulation: using random number tables; using a computer. 3
EVIDENCE REQUIREMENTS Manual simulation using random number tables. Evidence of the computer simulation. One of the above simulations will be of an inventory system, the other of a queuing system. MERIT A candidate who achieves all performance criteria for all outcomes will be awarded a pass. A pass with merit may be awarded to a candidate who demonstrates superior performance throughout the unit in each of the following aspects: consistently high level of accuracy outstanding skills of analysis consistently logical presentation of work. Evidence which satisfies the criteria for merit may be generated by either: solving the problem to a level beyond that defined as pass or where this is not possible, including in the assessment a further section which would allow the candidate to demonstrate skills which satisfy the criteria for merit. ---------------------------------------- ASSESSMENT In order to achieve this unit, candidates are required to present sufficient evidence that they have met all the performance criteria for each outcome within the range specified. Details of these requirements are given for each outcome. The assessment instruments used should follow the general guidance offered by the SQA assessment model and an integrative approach to assessment is encouraged. (See references at the end of the support notes.) Accurate records should be made of the assessment instruments used showing how evidence is generated for each outcome and giving marking schemes and/or checklists, etc. Records of candidates' achievements should also be kept. These records will be required for external verification. 4
SPECIAL NEEDS Proposals to modify outcomes, range statements or agreed assessment arrangements should be discussed in the first place with the external verifier. Copyright SQA 1994 Please note that this publication may be reproduced in whole or in part for educational purposes provided that: (i) (ii) no profit is derived from the reproduction; if reproduced in part, the source is acknowledged. 5
UNIT NUMBER: 7481684 HIGHER NATIONAL UNIT SPECIFICATION SUPPORT NOTES UNIT TITLE: OPERATIONAL RESEARCH B SUPPORT NOTES: This part of the unit specification is offered as guidance. None of the sections of the support notes is mandatory. NOTIONAL DESIGN LENGTH: SQA allocates a notional design length to a unit on the basis of the time estimated for achievement of the stated standards by a candidate whose starting point is as described in the access statement. The notional design length for this unit is 40 hours. The use of notional design length for programme design and timetabling is advisory only. CONTENT/CONTEXT Corresponding to outcomes: 1. Decompose a small project into its constituent activities and determine precedences. Given a precedence table, construct a project network, identify the critical path(s), critical activities and project duration. Activity on arrow and/or activity on node conventions. Determine activity floats and relate them to the actual progress of the project. State the effect of the project duration of a change in the duration of one of its activities. Early start time, late start time, early finish time, late finish time. Gannt charts and resource histograms. Rescheduling of non-critical activities to use of resources. Use of a computer package for project management (see the reference section at the end of the support notes). 2. The simple model for the re-order level system of stock control and the assumptions of the model. Calculation of the economic order quantity. Calculation of cost saving to be made by changing to the optimal order policy. The effect of quantity discounts. The effect of gradual replenishment. Determination of the re-order level for variable demand which has a given risk of stockout. Periodic review system. 3. Advantages and disadvantages of simulation. Simulation using random number tables and using a suitable computer package, eg a spreadsheet. Simulation of demand patterns; Poisson distributed; distribution specified by historical data. Simulation and costing of an inventory system including the penalty costs associated with stockout. Simulation of various arrival and service patterns. Examples of queuing systems. Characteristics of a queue: arrival pattern; service pattern: number of service channels; queue discipline; capacity and population. Arrival rate, service rate. Simulation and costing of a queuing system. 6
APPROACHES TO GENERATING EVIDENCE It is recommended that candidates be given real-life examples to illustrate the statistical concepts and techniques used in this unit. These examples could be linked to relevant vocational areas, such as: - business and finance - quality control - personnel - adminstration - production and manufacturing The consolidation of skills should be achieved by including investigations of a practical and vocational context and not only by mechanical exercises. The design of the unit is such that the use of computer packages is required and encouraged to achieve the outcomes. These packages will, by their nature, develop and therefore it is not possible to give an exhaustive list of all suitable packages (see the reference section at the end of the support notes). Thought should be given when developing the course and assessment to the nature of the packages candidates are likely to use in their employment and those which have been used in other units studied as part of a course. Candidates are advised to maintain a workfile. This could comprise the candidate's own notes, class handouts, worksheets, exercises, a logbook of computer activities, project notes and other relevant material. ASSESSMENT PROCEDURES Centres may use the instruments of assessment which are considered by tutors/trainers to be most appropriate. During assessments candidates should have access to their notes and textbooks. Examples of instruments of assessment which could be used are as follows: Corresponding to outcomes: 1. Graphical/calculation/written exercise which consists of a single problem covering all the PCs. 2. Calculation/graphical exercise which consists of four problems as specified in the evidence requirements. 3. Simulation exercise which consists of a manual simulation and computer simulation. one simulation will be a queuing system and the other of an inventory system. 7
EXEMPLARS Corresponding to outcomes: Outcome 1 Immediate Duration Staff Activity Processors (Weeks) Required A - 3 1 B - 1 3 C A 1 2 D C 2 2 F E 1 4 G B 4 4 H A,G 3 2 I D,F,H 5 1 J A,G 4 2 Draw the network for this project and determine its minimum duration. Which activities are critical? State the total float and free floats for each of the non-critical activities. Draw a Gannt Chart with each activity starting at its early start time. What are the maximum staff requirements when all activities start at their early start time? If only six staff are available at any one time, which activities need to be rescheduled? For each rescheduled activity state the number of weeks by which the start of the activity is delayed. Outcome 2 NB You should assume throughout this assessment a 50-week year. 1. The Inverness Instruments Company manufactures pocket calculators. One of the components of these calculators is CR2032 batteries. They use 150 a week and they buy them at a cost of 1.20 each. The cost of placing an order is 20 and the lead time is 2 weeks. The annual inventory carrying cost is 25% of the value of stock. Because the company uses the batteries at a constant rate, they carry no buffer stock. (a) (b) Determine the economic order quantity and the re-order level. The supplier of the batteries offers Inverness Instruments a 10% discount on orders of 5000 or more. Should Inverness Instruments take advantage of this discount? 8
2. Inverness Instruments manufacture the pocket calculators at a constant rate of 50 per week. Each calculator contains a microprocessor chip and these are manufactured by Inverness Instruments in batches at the rate of 300 a week. The set-up cost for a production run of chips is 50 and the inventory carrying cost of a chip is 2 per year. The present production policy is to make the chips in batches of 500. Because the chips are used at a constant rate they do not hold any buffer stock. (a) (b) (c) Determine the cost (set-up costs plus stockholding costs) of the present production policy. Determine, correct to the nearest fifty, the economic batch quantity for the production of microprocessor chips. Determine the saving which can be made by changing the production policy. 3. The Inverness Tired Tyres Company fits a large number of new SR55 tyres each week. The demand for this type of tyre is normally distributed with mean 80 per week and standard deviation 25. The company buys the tyres from a national supplier at a cost of 21 each. The cost of placing an order is 50 and the lead time is 3 weeks. The annual stockholding cost is 20%. Determine the economic order quantity and the re-order level which gives not more than 5% probability of stockout. 4. The Inverness Tired Tyres Company also sells a small number of "silver" dolphin mascots each week. The demand for these mascots is Poisson distributed with mean 1.5 per week. The company buys the mascots at a cost of 25 each. The cost of placing an order is 50 and the lead time is 4 weeks. The annual stockholding cost is 20%. Determine the economic order quantity and the re-order level which gives not more than 1% probability of stockout. Outcome 3 1. The cost of holding a particular type of time in stock is reckoned to be 150 per item per year. The cost of placing an order is 25. The cost of running out of stock is estimated to be 1 per item per day. The lead time is 20 days. The current policy is to order a batch of 100 items whenever the number in stock falls below 100. (Take an opening stock of 120). The demand pattern over a 250-day period is shown below. 9
Daily demand Frequency 0 2 1 6 2 23 3 31 4 45 5 42 6 39 7 31 8 22 9 8 10 1 (a) (b) (c) Simulate 4 years operation of the stock control system and estimate the yearly cost of the system. Your printout should include a day-by-day simulation of the first year and summary details for each year. The finance manager has suggested that a better policy would be to order just 20 items whenever the stock falls below 100. Is he correct? (Your answer should be based on print-outs of summary details for each year over a 4-year period). If he is correct, what practical problem might ensue if his policy is implemented? 2. A maintenance engineer works from 9 till 5 each day with a lunch-break from 1 till 2. Each morning at 9am he is issued with a list of emergency repair jobs which he carries out before doing his routine maintenance work. His routine maintenance work takes 3 hours a day. The number of emergency repair jobs received each morning over the last 20 weeks is shown below. Number of jobs Number of days 0 22 1 35 2 28 3 13 4 2 The next table shows the duration of a random sample of 100 of these emergency repair jobs. 10
Duration of job Number of jobs under 1 hour 18 1 hour and under 2 hours 32 2 hours and under 4 hours 30 4 hours and under 8 hours 15 8 hours and under 12 hours 5 Simulate one five-day week of the maintenance engineer, using event incrementation and working to the nearest hour. At the end of each day he will work up to 2 hours overtime, if there is emergency work still to be done. Any emergency work not completed by 7pm is completed the next day before the next day's jobs are started an any routine work not completed is added onto the next day's quota of routine work. PROGRESSION For information on how this unit relates to National Certificate mathematics provision and to other units in the Higher National mathematics framework, please refer to the following grid: Higher National mathematics grid for business REFERENCES 1. Guide to Writing. 2. For a fuller discussion on assessment, please refer to SQA's Guide to Assessment. 3. Information for centres on SQA's operating procedures is contained in SQA's Guide to Procedures. 4. For details of other SQA publications, please consult SQA's publication list. 5. For an up-to-date list of suitable computer packages, please contact SQA's Product Development Department. Copyright SQA 1994 Please note that this publication may be reproduced in whole or in part for educational purposes provided that: (i) (ii) no profit is derived from the reproduction; if reproduced in part, the source is acknowledged. 11
HIGHER NATIONAL MATHEMATICS GRID FOR BUSINESS National Certificate Higher National 7180321 7481664 7481674 Core Maths 3 Mathematics for Business Operational Research A 7481684 Operational Research B 91064 7180225 Mathematics: Statistics 2 7481694 7481704 7481714 Numeracy 3 Business Statistics 1 Business Statistics 2 Inference and Estimation 91063 Mathematics: Statistics 1 HNGRID.DOC