The following case presents a real project $($in aggregate form$)$ that allows the student to compare the

critical path solution approach for both completion time and cost as well as a simulated solution for time

variability and then also for both time and cost variability. The student should better understand the risk

of projects running late and over budget after this exercise.

Wesley James had recently arrived in Boston from Manchester, UK for a position as Project Owner at

NutriStar Energy, Inc. He was now meeting with Ava Smith, President of NutriStar, to discuss his

upcoming duties and responsibilities associated with their latest product, the Nutri$$Sports Energy Bar.

As Ava explained: $$NutriStar produces a line of vitamins and nutritional supplements. We recently

introduced our Nutri$$Sports Energy Bar, which is based on new scientific findings about the proper

balance of macronutrients in the body. Fortunately, the energy bar has quickly become popular among

elite athletes and others 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. We were able to include EPA in our sports bars because we had previously developed and

patented a process to refine EPA for our line of fish$$oil capsules.$$

$$Because of the success of the Nutri$$Sports Energy Bar in the United States, we are considering offering

it in Latin America. With our domestic facility currently operating at capacity, we have decided to

investigate the option of adding approximately $10,000$ square feet of production space to our facility in

Latin America, at a cost of $$5\mathrm{.}1$ million.$$

$$This is where you come in$,$ Wesley. 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 project owner, that will be you, is chosen to

oversee all four phases of the project and given a budget to develop a plan. The outcome of the concept

development phase consists of just 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 will be needed.$$

$$In the plan definition phase, the project owner selects and works with 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 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. I have compiled two tables here for you. 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$.$

Questions

$1-$Draw a network diagram for this project

$2-.$ Identify all paths through the network diagram. Identify which path you expect to be the critical path and its expected completion time? $3-$ which paths are most likely to threaten this path in terms of becoming critical $?4-$simulate the completion of this project $1,000$ times assuming that activity times follow a PERT distribution. $5-$ Estimate the mean and standrad deviation of the project completion time and the project cost. $6-$ develop histograms for both the project completion time and the cost to complete the project. what do these histograms tell you $?7-$ Using the results of your simulation analysis, A$-$ calculate the probability that the project can be completed in $30$ months? B$-$ what is the probability that the project will take longer than$40$ months? C$-$ what is the probability that the project will take between $30$ and $40$ months? D$-$ what is the probability the project will cost $$5\mathrm{.}1$ million or less to complete? E$-$ THe probability the project will cost between $$5$ and $$6$ million to complete $?$ GIve the netwrok diagram clearly.