School / IB / BM HL / Operations management (HL): decision trees and critical path analysis Exam-style + marking analysis
Operations management (HL): decision trees and critical path analysis Quantitative decision-making tools: expected value from decision trees, and critical path analysis for project scheduling.
Business Management HL Operations management (HL): decision trees and critical path analysis
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1 A company is choosing between two investment options. Option A costs $10,000 and has a 0.6 probability of generating a profit of $100,000 and a 0.4 probability of generating a loss of $20,000. Option B costs $5,000 and has a 0.5 probability of generating a profit of $60,000 and a 0.5 probability of generating a profit of $20,000. (a) Calculate the expected value (net of cost) of Option A. (b) Calculate the expected value (net of cost) of Option B. (c) State which option has the higher expected value. Paper 2 style Medium 5 marks Calculator + 2 Marking analysis: A learner attempts the following task: “A company is choosing between two investment options. Option A costs $10,000 and has a 0.6 probability of generating a profit of $100,000 and a 0.4 probability of generating a loss of $20,000. Option B costs $5,000 and has a 0.5 probability of generating a profit of $60,000 and a 0.5 probability of generating a profit of $20,000. (a) Calculate the expected value (net of cost) of Option A. (b) Calculate the expected value (net of cost) of Option B. (c) State which option has the higher expected value.” Their response addresses only this point: “Calculates the expected value of Option A's outcomes: (0.6 × 100,000) + (0.4 × −20,000) = 60,000 − 8,000 = $52,000.” Evaluate the response against the complete 5-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 5 marks Calculator + 3 Using the decision tree from the previous question, explain one limitation of relying purely on expected value when choosing between Option A and Option B, given that Option A carries a real risk of an outright loss. Paper 2 style Easy 2 marks No calculator + 4 Marking analysis: A learner attempts the following task: “Using the decision tree from the previous question, explain one limitation of relying purely on expected value when choosing between Option A and Option B, given that Option A carries a real risk of an outright loss.” Their response addresses only this point: “Explains that expected value is a long-run average outcome and does not capture a decision-maker's attitude toward risk, such as risk-aversion.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 2 marks No calculator + 5 Define 'critical path' in the context of critical path analysis (network planning), and explain why identifying it is important for project managers. Paper 2 style Easy 3 marks No calculator + 6 Marking analysis: A learner attempts the following task: “Define 'critical path' in the context of critical path analysis (network planning), and explain why identifying it is important for project managers.” Their response addresses only this point: “Defines the critical path as the longest sequence of dependent activities through a project network, determining the minimum possible time needed to complete the whole project.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + 7 A project has the following activities: Activity A (2 days) must be completed first. Activity B (3 days) and Activity C (4 days) can both start once A is finished. Activity D (2 days) can only start once both B and C are finished. (a) Calculate the total duration of path A-B-D. (b) Calculate the total duration of path A-C-D. (c) Identify the critical path and state the minimum project duration. (d) Calculate the float (spare time) available on activity B. Paper 2 style Medium 4 marks Calculator + 8 Marking analysis: A learner attempts the following task: “A project has the following activities: Activity A (2 days) must be completed first. Activity B (3 days) and Activity C (4 days) can both start once A is finished. Activity D (2 days) can only start once both B and C are finished. (a) Calculate the total duration of path A-B-D. (b) Calculate the total duration of path A-C-D. (c) Identify the critical path and state the minimum project duration. (d) Calculate the float (spare time) available on activity B.” Their response addresses only this point: “Calculates the duration of path A-B-D as 2 + 3 + 2 = 7 days.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks Calculator + 9 Explain two benefits to a project manager of using critical path analysis before starting a complex project. Paper 1 style Easy 2 marks No calculator + 10 Marking analysis: A learner attempts the following task: “Explain two benefits to a project manager of using critical path analysis before starting a complex project.” Their response addresses only this point: “Explains that critical path analysis identifies the minimum possible time to complete the project, allowing for realistic scheduling and deadline-setting before work begins.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 2 marks No calculator + 11 State one limitation of critical path analysis as a planning tool. Paper 1 style Easy 1 marks No calculator + 12 Marking analysis: A learner attempts the following task: “State one limitation of critical path analysis as a planning tool.” Their response addresses only this point: “States a valid limitation, such as the technique relying on activity duration estimates that may be inaccurate, or that it does not account for resource constraints (e.g., the same staff being needed for two simultaneous activities).” Evaluate the response against the complete 1-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 1 marks No calculator + 13 A project has activities: A (3 days) first; B (4 days) and C (2 days) both follow A; D (5 days) follows both B and C; E (2 days) follows D. (a) Calculate the length of path A-B-D-E and path A-C-D-E. (b) State the critical path and minimum duration. (c) Calculate the float on activity C. Paper 2 style Medium 4 marks Calculator + 14 Marking analysis: A learner attempts the following task: “A project has activities: A (3 days) first; B (4 days) and C (2 days) both follow A; D (5 days) follows both B and C; E (2 days) follows D. (a) Calculate the length of path A-B-D-E and path A-C-D-E. (b) State the critical path and minimum duration. (c) Calculate the float on activity C.” Their response addresses only this point: “Calculates path A-B-D-E as 3 + 4 + 5 + 2 = 14 days.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks Calculator + 15 Explain how a project manager could shorten the duration of a project shown by a network diagram, and state one cost of doing so. Paper 1 style Easy 3 marks No calculator + 16 Marking analysis: A learner attempts the following task: “Explain how a project manager could shorten the duration of a project shown by a network diagram, and state one cost of doing so.” Their response addresses only this point: “Explains that only shortening activities on the critical path reduces total duration, e.g. by adding labour or equipment to them.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + 17 A firm sells a product for $25 with variable cost of $15 per unit; fixed costs are $40,000. (a) Calculate the break-even quantity. (b) Calculate the sales needed to earn a target profit of $20,000. (c) Calculate the margin of safety, as a percentage of actual sales, if 7,000 units are sold. Paper 2 style Medium 4 marks Calculator + 18 Marking analysis: A learner attempts the following task: “A firm sells a product for $25 with variable cost of $15 per unit; fixed costs are $40,000. (a) Calculate the break-even quantity. (b) Calculate the sales needed to earn a target profit of $20,000. (c) Calculate the margin of safety, as a percentage of actual sales, if 7,000 units are sold.” Their response addresses only this point: “Calculates contribution per unit as 25 − 15 = $10.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks Calculator + 19 A firm produced 12,000 units with 40 workers at a total cost of $96,000. Calculate (a) labour productivity and (b) unit cost, and (c) explain one way the firm could lower unit cost without cutting wages. Paper 2 style Easy 3 marks Calculator + 20 Marking analysis: A learner attempts the following task: “A firm produced 12,000 units with 40 workers at a total cost of $96,000. Calculate (a) labour productivity and (b) unit cost, and (c) explain one way the firm could lower unit cost without cutting wages.” Their response addresses only this point: “Calculates labour productivity as 12,000 / 40 = 300 units per worker.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks Calculator + 21 Evaluate the use of just-in-time (JIT) production compared with just-in-case stock holding for a supermarket. Paper 1 style Medium 4 marks No calculator + 22 Marking analysis: A learner attempts the following task: “Evaluate the use of just-in-time (JIT) production compared with just-in-case stock holding for a supermarket.” Their response addresses only this point: “Explains the JIT benefit: lower storage costs, less waste of perishable goods and less cash tied up in stock.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Medium 4 marks No calculator + 23 Explain how a business adopting total quality management (TQM) may reduce its costs in the long run despite higher short-run costs. Paper 1 style Easy 3 marks No calculator + 24 Marking analysis: A learner attempts the following task: “Explain how a business adopting total quality management (TQM) may reduce its costs in the long run despite higher short-run costs.” Their response addresses only this point: “Explains that TQM requires short-run spending on training, process redesign and monitoring.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + 25 Explain two potential benefits and one drawback to a manufacturer of introducing greater automation. Paper 1 style Easy 3 marks No calculator + 26 Marking analysis: A learner attempts the following task: “Explain two potential benefits and one drawback to a manufacturer of introducing greater automation.” Their response addresses only this point: “Explains a benefit such as higher productivity and consistency of output with fewer errors.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks No calculator + 27 Explain two limitations of break-even analysis as a decision-making tool. Paper 1 style Easy 2 marks No calculator + 28 Marking analysis: A learner attempts the following task: “Explain two limitations of break-even analysis as a decision-making tool.” Their response addresses only this point: “Explains that it assumes a constant selling price and linear costs, whereas prices may fall with volume and variable costs may change with bulk buying.” Evaluate the response against the complete 2-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 2 marks No calculator + 29 A decision tree shows an investment costing $20,000 with a 0.7 probability of a $80,000 return and a 0.3 probability of a $10,000 return. Calculate the expected net value and state whether the firm should proceed if the alternative is to do nothing (net value $0). Paper 2 style Easy 3 marks Calculator + 30 Marking analysis: A learner attempts the following task: “A decision tree shows an investment costing $20,000 with a 0.7 probability of a $80,000 return and a 0.3 probability of a $10,000 return. Calculate the expected net value and state whether the firm should proceed if the alternative is to do nothing (net value $0).” Their response addresses only this point: “Calculates expected return as (0.7 × 80,000) + (0.3 × 10,000) = 56,000 + 3,000 = $59,000.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks. Marking analysis Easy 3 marks Calculator + Self-assessed 0 / 0
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