NutriStar produces a line of vitamins and nutritional supplements. It recently introduced its Nutri-Sports Energy Bar, which is based on new scientific findings about the proper balance of macronutrients. The energy bar has become extremely popular among elite athletes and other people who focus on eating an optimal balance of macronutrients. One distinguishing feature of the Nutri-Sports Energy Bar is that each bar contains 50 milligrams of eicosapentaenoic acid (EPA), a substance strongly linked to reducing the risk of cancer but found in only a few foods, such as salmon. NutriStar was able to include EPA in its sports bars because it had previously developed and patented a process to refine EPA for its line of fish-oil capsules. Because of the success of the Nutri-Sports Energy Bar in the United States, NutriStar is considering offering it in Latin America. With its domestic facility currently operating at capacity, the President of NutriStar has decided to investigate the option of adding approximately 10,000 square feet of production space to its facility in Latin America at a cost of $5.1 million. The project to expand the Latin American facility involves four major phases: (1) concept development, (2) definition of the plan, (3) design and construction, and (4) start-up and turnover. During the concept development phase, a program manager is chosen to oversee all four phases of the project and the manager is given a budget to develop a plan. The outcome of the concept development phase is a rough plan, feasibility estimates for the project, and a rough schedule. Also, a justification for the project and a budget for the next phase are developed. In the plan definition phase, the program manager selects a project manager to oversee the activities associated with this phase. Plan definition consists of four major activities that are completed more or less concurrently: (1) defining the project scope, (2) developing a broad schedule of activities, (3) developing detailed cost estimates, and (4) developing a plan for staffing. The outputs of this phase are combined into a detailed plan and proposal for management specifying how much the project will cost, how long it will take, and what the deliverables are. If the project gets management's approval and management provides the appropriations, the project progresses to the third phase, design and construction. This phase consists of four major activities: (1) detailed engineering, (2) mobilization of the construction employees, (3) procurement of production equipment, and (4) construction of the facility. Typically, the detailed engineering and the mobilization of the construction employees are done concurrently. Once these activities are completed, construction of the facility and procurement of the production equipment are done concurrently. The outcome of this phase is the physical construction of the facility. The final phase, start-up and turnover, consists of four major activities: pre-start-up inspection of the facility, recruiting and training the workforce, solving start-up problems, and determining optimal operating parameters (called centerlining). Once the pre-start-up inspection is completed, the workforce is recruited and trained at the same time that start-up problems are solved. Centerlining is initiated upon the completion of these activities. The desired outcome of this phase is a facility operating at design requirements. The cost to complete an activity depends on both the amount of time required to complete the task and the cost rate of performing the activity. Table A provides optimistic, most likely, and pessimistic time estimates for the major activities. Table B provides similar estimates for the cost rates to complete the activities. Like time estimates, the cost rate to complete the facility expansion project can vary for a number of reasons such as using more or less expensive resources, price changes in labor and materials, the need to outsource work that was expected to be performed in-house, and so on. According to the data in Tables A and B, Concept Development is expected to cost $24,000 (12 month most likely duration  $2; 000=month most likely cost rate).

1. Draw a network diagram for this project. Identify which path you expect to be the critical path and its expected completion time. Which paths are most likely to threaten this path in terms of becoming critical?
2. Simulate the completion of this project 1000 times assuming that activity times follow a triangular distribution and that the cost rates are known with certainty and equal to the most likely cost rate. Estimate the mean and standard deviation of the project completion time and the project cost. How does the time compare to your previous answer based solely on the critical path?
3. Develop histograms for both the project completion time and the cost to complete the project and what does these histograms tell you
4. Using the results of your simulation analysis calculate the probability that the project can be completed within 30 months. What is the probability that the project will take longer than 40 months? What is the probability that the project will take between 30 and 40 months? What is the probability the project will cost $5.1 million or less to complete? The probability the project will cost between $5 and $6 million to complete?
5. Modify your simulation model to determine the probability that the path you expected to be the critical path actually was the critical path? What are the managerial implications of this?
6. Simulate the completion of this project 1000 times assuming that the activity times follow a triangular distribution and that the cost rates are also triangularly distributed. Estimate the mean and standard deviation of the project completion time and project cost. How do these results compare to the results you obtained in Question 2 above?