Cost management Assignment 1 project crashing and break-even

Posted: February 24, 2026/Under: Uncategorized/By:

PRMG 135 – Cost Management for Engineering Projects (AUC)
Assignment 1: Project Crashing and Break-Even Analysis

Course and Assessment Context

University: The American University in Cairo (AUC) – School of Sciences and Engineering, Professional Program in Project Management.

Course Code/Title: PRMG 135 – Cost Management for Engineering Projects.

Assessment Type: Assignment 1 – Quantitative Problem Set (Individual).

Timing: Weeks 3–4, after introductory lectures on cost estimation and project scheduling.

Weighting: 15% of total course grade (typical for PRMG 135 multi-problem assignments).

Length/Format: 5 quantitative problems, equivalent to approximately 4–6 pages of calculations and short written comments.

Submission: PDF upload to LMS (Turnitin enabled) by 11:59 p.m. Cairo time on the due date.

Assignment Overview

Assignment 1 in PRMG 135 typically combines project cost optimization with basic engineering economy and break-even analysis. In the current cycle, students tackle a small construction project where they must determine the optimum project duration using crashing concepts, then evaluate contingency, labor productivity, and break-even behavior for a contractor considering cost and schedule trade-offs.

Assignment 1: Project Crashing and Break-Even Analysis

Objective: Apply cost management tools to a simplified engineering project by calculating optimum duration, analyzing crashing scenarios, estimating contingency, evaluating labor productivity and unit costs, and developing a basic break-even model for profit planning.

Instructions

Answer all five problems. Show each step of your calculations clearly, label your variables, and state any assumptions you make. Round monetary values to the nearest whole unit and time to one decimal place unless otherwise specified. Where requested, add a short written comment (2–3 sentences) interpreting your numerical results for a project manager audience.

Problem 1 – Project Crashing and Optimum Duration (30%)

The following table summarizes the normal and crash data for a small project. Indirect (overhead) cost is 400 per day. Activities are connected in a network as shown in Figure 1.

  • Activity A: Normal duration 5 days, crash duration 3 days, normal cost 2,000, crash cost 3,000.
  • Activity B: Normal duration 4 days, crash duration 3 days, normal cost 1,600, crash cost 2,200.
  • Activity C: Normal duration 6 days, crash duration 4 days, normal cost 3,000, crash cost 4,200.
  • Activity D: Normal duration 3 days, crash duration 2 days, normal cost 1,500, crash cost 2,000.
  • Activity E: Normal duration 4 days, crash duration 3 days, normal cost 1,800, crash cost 2,400.
  • Activity F: Normal duration 2 days, crash duration 1 day, normal cost 900, crash cost 1,400.

Network logic (precedence):

  • A and B start at project start.
  • C follows A.
  • D follows B.
  • E follows both C and D.
  • F follows E and finishes the project.
  1. Construct the project network and determine the normal project duration and normal total direct cost.
  2. Calculate the crash cost per day for each activity and identify which activities are candidates for crashing on the critical path.
  3. Stepwise crash the project to find the optimum project duration and corresponding total project cost (direct + indirect). Present your results in a table showing duration, direct cost, indirect cost, and total cost at each crashing step.
  4. Write a brief comment (about 3–4 sentences) explaining why the optimum point is attractive from a cost management perspective for the contractor.

Problem 2 – Contingency for Imported Materials (15%)

A project uses an imported electrical component whose price is affected by exchange rate uncertainty. The base estimate assumes a cost of 250,000 with a probability of 0.5. There is a 0.3 probability that the cost will increase to 280,000 and a 0.2 probability that it will decrease to 230,000.

  1. Compute the expected cost of the component.
  2. Determine an appropriate contingency allowance using the standard deviation approach (you may assume a 1σ contingency is acceptable).
  3. Write 2–3 sentences advising the project manager on how to communicate this contingency to the client.

Problem 3 – Labor Productivity and Unit Cost (20%)

A crew of 6 workers is assigned to lay concrete blocks on a site. In one 8-hour shift they complete 960 blocks. The daily wage per worker is 75, and equipment cost allocated to the crew is 200 per day. Material cost per block is 1.2.

  1. Calculate the crew productivity in blocks per labor-hour.
  2. Compute the labor cost per block and the total unit cost per block (labor + equipment + material).
  3. Suppose productivity falls by 15% due to site congestion. Recalculate the unit cost per block and comment briefly on the cost impact for a 10,000-block project.

Problem 4 – Engineering Economy and Break-Even (20%)

A contractor is considering investing in a small batching plant to support multiple projects. The fixed annual cost of the plant is estimated at 120,000. The variable cost per cubic meter (m³) of concrete produced is 32, while the internal transfer price to projects is set at 50 per m³.

  1. Determine the break-even production volume in m³ per year.
  2. Calculate the annual profit (or loss) if the plant produces 9,000 m³ in one year.
  3. Find the production volume required to achieve a target annual profit of 80,000.

Problem 5 – Break-Even with Price Reduction (15%)

Using the same batching plant from Problem 4, management considers reducing the transfer price to 47 per m³ in order to encourage more internal use, while variable and fixed costs remain unchanged.

  1. Recalculate the new break-even production volume.
  2. Assuming demand increases to 9,800 m³ at the new price, determine the new annual profit.
  3. Write 3–4 sentences evaluating whether the price reduction appears reasonable from a cost management perspective and what non-financial factors the project manager should consider.

Requirements and Formatting

  • Submit a single PDF file that includes all five problems in order.
  • Use clear headings (Problem 1, Problem 2, etc.) and show all intermediate steps.
  • Where appropriate, include diagrams (for example, the network in Problem 1) and simple tables.
  • Use standard engineering notation; clearly indicate units (days, EGP, hours, m³, etc.).
  • If you consult external references for formulas, list them at the end in APA 7th or Harvard style.

Learning Outcomes Assessed

  • Apply cost estimation, crashing, and cost optimization techniques to engineering projects.
  • Use probability and statistical tools to handle contingency and uncertainty in cost estimates.
  • Evaluate labor productivity, unit rates, and break-even points to support project cost decisions.

Marking Rubric (Assignment 1 – 15%)

Criterion Excellent (A) Good (B) Satisfactory (C) Needs Improvement (D/F) Weight
1. Problem 1 – Crashing and Optimum Duration Network and critical path fully correct; crashing steps logically sequenced; optimum duration and total cost correctly identified; written comment shows clear cost-time insight. Minor errors in times or costs but overall method is correct; optimum point reasonable; explanation mostly clear. Significant calculation or logic errors; critical path or optimum point partially incorrect; explanation superficial. Network incorrect or missing; no coherent crashing process; optimum duration and cost not obtained. 30%
2. Problem 2 – Contingency and Expected Value Expected cost and standard-deviation-based contingency correctly computed; advice to client is concise, realistic, and aligned with probabilistic reasoning. Expected cost correct; minor issues in contingency or explanation but overall rationale reasonable. Partially correct calculations with unclear or incorrect contingency basis; explanation generic. Incorrect or missing calculations; no meaningful interpretation for the client. 15%
3. Problem 3 – Productivity and Unit Cost Productivity and unit costs correctly derived for both scenarios; impact on total cost clearly quantified and briefly interpreted for project decision-making. Most calculations correct; minor rounding or interpretation issues; cost impact roughly estimated. Some correct steps but inconsistent or incomplete; limited attempt to quantify impact. Incorrect method; no clear productivity or unit cost values; no useful commentary. 20%
4. Problems 4 & 5 – Break-Even and Profit Analysis Break-even volumes and profits correctly calculated; effect of price change clearly analyzed; written evaluation recognizes both financial and managerial considerations. Mostly correct calculations with minor errors; interpretation addresses financial implications with some depth. Basic break-even formulas applied but with errors; interpretation brief and mainly descriptive. Incorrect or missing calculations; no meaningful analysis of pricing decision. 25%
5. Presentation, Structure, and Professionalism Work is clearly organized, neatly formatted, with labeled steps, tables, and diagrams; notation and units are consistent; any references correctly cited. Generally clear layout; a few minor formatting or labeling issues; units mostly consistent. Readable but disorganized in places; steps not always labeled; frequent missing units. Hard to follow; calculations scattered or unlabeled; missing units and poor presentation suggest minimal effort. 10%

Academic Integrity and Use of Tools

Numerical assignments in PRMG 135 are designed to strengthen your own cost-management skills. Calculator and spreadsheet use is acceptable, and many engineers use Excel or similar tools in practice. However, copying solutions from online repositories or using AI tools to generate complete answers without understanding the steps is considered a violation of AUC’s academic integrity policy and may result in a failing grade for the assignment or the course.

Sample Response

Project managers often discover that the cheapest solution on paper is not the schedule with the shortest duration, but rather the point at which the marginal saving in indirect cost no longer compensates for the additional crashing cost. In the scenario above, the optimum duration usually appears at the point where one or two critical activities are fully crashed and a second path becomes critical, since any further crashing would increase direct cost without reducing overall project time. Cost-time trade-offs of this sort are at the heart of cost management for engineering projects, and they help contractors negotiate realistic schedules and bonus clauses with clients (Sakr, 2020). When students work through the full crashing table themselves, they tend to develop a more intuitive sense of how sensitive project cost is to relatively small changes in duration, especially when daily overhead is high.

References / Learning Materials (APA 7th)

  • Sakr, T. (2020). Cost management in engineering projects. The American University in Cairo Press. (Course materials summarized in PRMG 135 content).
  • Kerzner, H. (2019). Project management: A systems approach to planning, scheduling, and controlling (12th ed.). Wiley. https://doi.org/10.1002/9781119556779
  • Pinto, J. K. (2019). Project management: Achieving competitive advantage (5th ed.). Pearson. https://www.pearson.com/…/9780134730332
  • Touran, A., & Ismail, K. A. R. (2018). A new approach for budgeting of large-scale projects using a cost breakdown structure. Journal of Construction Engineering and Management, 144(3), 04017116. https://doi.org/10.1061/(ASCE)CO.1943-7862.0001444
  • Fleming, Q. W., & Koppelman, J. M. (2016). Earned value project management (4th ed.). Project Management Institute. https://www.pmi.org/…/earned-value-project-management

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