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176 CH A P T ER 5 / S CH ED UL IN G T H E P R OJECT 9. When using AON networks, how does one indicate an event such as a project milestone? 10. A probabilistic network has a critical path of 21 days and a .95 probability of completing this path in 24 days. Therefore, the project has a .95 chance of being finished by the end of the 24th day. True or False? Briefly explain your answer. 11. “Not uncommonly, the Gantt chart is deceptive in its apparent simplicity.” Briefly explain. 12. When activity times are known with certainty, the critical path is defined as the set of activities on a path from the project’s start event to its finish event that, if delayed, will delay the completion date of the project. Why must this definition be modified in situations where the activity times are not known with certainty? Are there any dangers associated with not modifying the definition? DISCUSSION QUESTIONS 1. Should a PM manage critical path tasks differently than noncritical path tasks? 2. How might you use the network approach to help prepare cost estimates? 3. When would it be accurate to determine the probability of project completion by multiplying the probabilities of all the paths through the network together? When would it not be accurate? 4. Reconsider Question 3. If this approach is not accurate, would the probability of completion considering the critical path alone be more accurate? How might you estimate the correct probability without resorting to simulation? 5. Why do you think most PMs use MSP’s Gantt chart format (see Figure 5-20) more commonly than the network format? 6. Which of the linkages in precedence diagramming do you think is most commonly used? Why? 7. In the calculation of variance for optimistic and pessimistic activity duration estimates made at the 95 or 90 percent level, the denominator of the fraction that approximates the standard deviation of the time distribution changes from the traditional (b − a)/6 to (b − a)/3.3 for 95 percent and to (b − a)/2.6 for 90 percent. Where did the 3.3 and the 2.6 come from? 8. Given all the estimating done to determine the duration of project activities, what does it mean to say that “only after the fact do we know which path was actually the critical path?” 9. It was noted that “the PM must manage the project team as well as the project.” Explain why. 10. Why do you think scheduling has been the major focus of effort throughout the history of project management rather than performance or budgeting? EXERCISES 1. 2. 3. Refer to the network in Figure 5-14. What is the probability that path a‐b‐c‐f will interfere with the promised project completion of 50 days? Recall that the critical path, a‐b‐d‐g‐h, had a probability of .86 for a 50‐day completion. What is the probability that both paths will be complete in 50 days? Refer to Table 5-4 and Figure 5-14. Recalculate the variance for each activity on the assumption that the optimistic and pessimistic estimates were made with a 95 percent probability. Recalculate the probability that the critical path will be completed in 50 days. Refer to Table 5-4 and Figure 5-14. Recalculate the variance for each activity on the assumption that the optimistic and pessimistic estimates were made with a 90 percent probability. Again, recalculate the likelihood that the critical path will be finished in 50 days. 4. Given the information in the following table: Activity a b c d e f g h i (a) (b) (c) (d) (e) Duration Predecessor 4 6 4 2 4 5 3 4 2 None a a c b b, d c f, g e, h Construct the network diagram. Find each activity’s ES, EF, LS, and LF. Identify all paths. Which path is the critical path? Calculate the slack for each activity. How long will it take to complete the project? 1 77 E XERC ISES 5. In the following table, task durations are given in weeks. The estimates were made at the 95 percent level (see Section 5.2, Calculating Probabilistic Activity Times subsection). Activity a b c d e f g 6. Opt. Normal Pess. — — a a b, c d e 2 3 4 4 4 3 3 4 5 5 6 5 4 5 6 9 7 10 7 8 8 (a) Find the expected time and variance for each task. (b) Draw the network (either AOA or AON) and find the path with the longest expected time. What is the expected time to complete this path? (c) Find the probability using the analytical approach that the path with the longest expected time will be completed in 23 weeks. (d) Find the probability that the other paths will be completed in 23 weeks. (e) Using simulation, what is the probability that the entire network will be completed in 23 weeks? Given an auditing project with the following activities: Activity a. Add b. Balance c. Count d. Deduct e. Edit f. Finance g. Group h. Hold 7. Predec. Std. Dev. Critical 2 1 0 3 1 2 2 0 Yes Yes Yes Yes Yes Duration (wks) 2 3 4 2 1 6 4 2 Using the analytical approach find: (a) The probability of completing this project in 12 weeks or less, as the client desires. (b) The probability of completing this project in 13 weeks or less. (c) The probability of completing this project in 16 weeks or less, the client’s drop‐dead date. (d) The number of weeks required to assure a 92.5 percent chance of completion, as guaranteed by the auditing firm. Resolve the previous exercise using computer simulation and compare your answers. Explain any differences you observe. Which methodology do you have more confidence in and why? 8. 9. Referring to the previous two questions, modify your simulation model to develop distributions for the slack time of each path. What do these distributions tell you? Given the following information regarding a project involving an initial public offering (IPO): Activity Duration (weeks) Preceding Activities 3 1 3 4 4 5 2 — — a a b b c, e 3 f a. Check feasibility b. Determine funding c. Find possible banks d. Select two possibles e. Interview two banks f. Analyze funding costs g. Determine chance of success h. Sign contract (a) Draw the network. (b) What is the critical path? (c) When will the offering be available (end of the project)? (d) What is the effect on the project if activity e (approvals) takes an extra week? Two extra weeks? Three extra weeks? 10. Enter the following information into an Excel® spreadsheet. The time estimates were made at the 90 percent level (see Section 5.2, Calculating Probabilistic Activity Times subsection). All activity times are in days. Activity a b c d e f g h i j k Predec. Opt. Normal Pess. — — — a b b c c d, e f, g h 5 4 7 6 4 12 8 7 10 6 7 6 4 9 6 5 16 12 9 14 12 9 9 6 15 6 7 17 20 16 18 20 14 (a) Draw the network. (You may use MSP, or draw an AOA or AON network by hand.) (b) Using Excel®, calculate the expected time (TE) and variance for each activity. (c) Using the expected times, find the path with the longest expected time. What is the expected time to complete this path? (Use the analytic method.) 178 11. 12. 13. 14. (d) Find the probability that the critical path will be completed in 38 days or less. (e) Are there any serious sources of merger problems? What are they? Calculate the probability of finishing the project on or before day 38 when merger considerations are included. (f) Assume that the times in the table were made on the 99+ percent level. Recalculate the activity variances with this assumption and find the probability that the critical path will be complete in 38 days. (Note, the altered assumption will change activity variance, but not the expected activity durations.) Briefly explain the difference in probabilities. (g) How many days are required for the critical path to have a .9 probability of completion? Given the project in Exercise 5, simulate the completion of the project 1,000 times, assuming that the activity times follow a normal distribution and that the time estimates are made at the 95 percent level. (a) Determine the probability of each path becoming the critical path. (b) What is the probability that the project is completed in 23 weeks? (c) How do your answers compare with your answers in Exercise 6? The project referred to in Exercise 11 has been partially completed. Task a required 4 weeks, task b 9 weeks, task c 4 weeks, and task d 5 weeks. Update the simulation model you developed for Exercise 11 and calculate the probability that the project will be finished in 23 weeks. Explain why the probability of completing the project in 23 weeks has changed. Given the project in Exercise 11, simulate the completion of the project 1,000 times, assuming that the activity times are at the 99+ percent level and follow a triangular distribution. (a) Determine the probability of each path becoming the critical path. (b) What is the probability that the project is completed in 32 days? In 34 days? In 38 days? (c) How do your answers compare with your answers in Exercise 11? *Additional task precedence information about the Textbook Revision Project described in Exercise 10 in Chapter 3 is now available. JR and Mike are preparing to revise their project management textbook. The project of revising the book begins with devel- CH A P T ER 5 / S CH ED UL IN G T H E P R OJECT oping a revision plan. Developing a revision plan includes four activities that each take 1 week to complete. First the authors go over the reviews provided by a sample of current adopters of the book. The second task involves benchmarking other project management books. Benchmarking other books can either be done in parallel with going over the reviews or done after the reviews have been studied. After both the reviews have been gone over and the benchmarking is completed, the changes to make to the book are decided on. The final step in developing the plan is allocating the work between the authors. The work can be allocated once the authors finalize the changes to be made to the book. After the plan has been developed, the book is revised which is expected to take 24 weeks. Once all the chapters have been revised, the page proofs are reviewed which is expected to take 8 weeks. After the page proofs have been reviewed, the index for the book is created which takes 2 weeks. Finally, after the book has been revised, the supplements to the book can be updated which takes 8 weeks. Update the information previously entered to include the precedence relationships among the tasks. Assuming the project begins on March 7, 2016, when is its expected completion date? 15. *Given the information in the following table, draw the AOA network. Using the same information, enter the data into MSP assuming a 7‐day workweek. (To change the calendar in MSP from its 5‐day week default, click “Help,” type “calendar change,” and follow directions.) Develop the appropriate AON network and Gantt chart. Using any method you wish, find the critical path and critical time for the network. Then find the slack for all activities. Activity a b c d e f g h i j k l Predecessor — — — a b b c d, e d, e f, g, h i j * This problem is included for instructors who supplement their course with additional content on Microsoft Project. Duration 5 days 7 4 6 9 6 4 6 8 9 10 9 1 79 I NC IDENTS FO R D I SCU SSIO N DISCUSSION EXERCISE 1. The following activities were listed during a brainstorming session on product development. Find the appropriate predecessor‐successor relationships and then construct an AON network to reflect the project using the activity duration times given in the information table. Assume a 5‐day workweek. Find the critical path and time for the project. Find the slack for all activities. 1. Organize the sales office: Hire sales manager. (6 weeks) 2. Hire sales personnel: The sales manager will recruit and hire the salespeople needed. (4 weeks) 3. Train sales personnel: Train the salespeople hired to sell the product to the distributors. (7 weeks) 4. Select advertising agency: The sales manager will select the agency best suited to promote the new product. (2 weeks) 5. Plan advertising campaign: The sales office and advertising agency will jointly plan the advertising campaign to introduce the product to the public. (4 weeks) 6. Conduct advertising campaign: The advertising agency will conduct a “watch for” campaign for potential customers. (10 weeks) 7. Design package: Have packaging engineer design the package most likely to “sell.” (2 weeks) 8. Set up packaging facility: Prepare to package the products when they are received from the manufacturer. (10 weeks) 9. Package initial stocks: Package stocks received from the manufacturer. (6 weeks) 10. Order and receive stock from the manufacturer: Order the stock from the manufacturer. The time given includes the time for delivery. (13 weeks) 11. Select distributors: The sales manager will select the distributors whom the salespeople will contact to make sales. (9 weeks) 12. Sell to distributors: Take orders from the distributors for the new product, with delivery promised for the product‐introduction date. If orders exceed stock, assign stock on a quota basis. (6 weeks) 13. Ship stock to distributors: Ship the packaged stock to distributors in accord with their orders or quota. (6 weeks) Question: What managerial problems and opportunities do you see as a result of your work? INCIDENTS FOR DISCUSSION Springville Fire Department Attack of the Killer Worm The city of Springville is building a new fire station in their city. The city is expanding and is in need of a second fire station closer to the newer areas of the city to ensure shorter response times. The project manager and the project team have been selected for the project. The team is very interested in selecting the scheduling technique that will be used to follow the project through to completion. The project manager, city manager, and chief of the fire department have set the following criteria for the process of selecting the scheduling technique: easy to use, shows durations of tasks, shows milestones, can see the flow of work, can see the sequence of events, can depict which tasks can be undertaken at the same time, and can tell how far tasks are from completion. The city manager favors the Gantt chart, the chief likes PERT, and the project manager prefers CPM. Lee Antoinio was the CIO of a large publishing house. Her network administrator, Andy McPester, came to her one sunny September afternoon and informed her that a worm had attacked their network. It had shut down two of their 45 servers and had potential to harm the other servers as well as the 323 personal workstations throughout the enterprise. Andy knew that he could not report this problem to Lee without a recommended project plan for a solution. Andy and Lee had a good, trusting relationship, but Lee insisted that Andy investigate all options and come to her with the most viable solution to any problem. Andy’s project plan outlined that it would take 30 to 45 minutes to touch each PC to protect them from the worm, and longer if they were already infected. It would take almost an hour to check the other servers and repair them. Andy discussed the time estimates with his desktop staff. Andy proposed paying six staff members overtime to work 4 hours after their normal business day for the next week or two to check each personal workstation. He did not Question: If you were the project manager, which method would you use, and why? 180 CH A P T ER 5 / S CH ED UL IN G T H E P R OJECT want to affect productivity of the company’s staff during the day. Andy proposed repairing the servers the same way with two additional staff members in the evenings. Lee felt that the time estimates and costs were too high. She did not think it would take that amount of time for each machine to get repaired. She was concerned that some of C The steering team meeting held August 31 went quite well. Fred felt that his team members had worked well 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Question: How would you recommend they reach a consensus on the project plan? A Friendly Assisted Living Facility Program Plan—5 ID Andy’s staff may have overestimated the time needed. She also was not sold on the notion that all the work would be done at night, paying staff overtime. S E together at determining the steps and the associated costs of the program. The CFO presented the program budget first, and then project team members presented their draft project plans. The COO presented the following project plan: Task Name Operational Implementation Plan Management/Organization structure Recruit & hire Executive Director Interior design issues decided (furnishings, etc.) Determine what was provided with lease and what was furnished in some units Determine budget for interior Carpet and wall finish determined Furniture and room layout Facility and equipment needs defined Staffing determined Office space for physicians Medical staffing needs determined & Director appointed Food service Menus selected Waiting and service staffing needs determined Additional equipment needs Telecommunications services Investigate phone service options Certification/Accreditation requirements Investigate requirements & timing of applicants with Dept. of Health to open facility Develop clinical and operational quality monitoring systems Develop financial systems (billing, etc.) Human resources Work force management recommendations Project plan for recruitment developed Policies and procedures developed Obtain ‘samples’ of assisted living policies & procedures from other institutions Investigate assisted living laws proposed in other states/ federal Technology & information systems Develop plan for technology access for residents (TV, Cable, PC’s) Investigate software/technology options for residents Duration Predecessors 87 days 17.4 wks 20 days 2 wks 10 days 2 wks 2 wks 4 wks 2 wks 4 wks 4 wks 45 days 8 wks 4 wks 4 wks 45 days 45 days 42 days 0 days 0 days 6 wks 79 days 6 wks 2 wks 60 days 4 wks 12 wks Resource Names CFO, Legal, VP Mktg Splient COO 59 59 COO COO, Dr. Link Dr. Link Dr. Link 68FS—3wks Chief Engineer Legal CFO HR Director HR Director 78 Legal Legal 344 days 3 wks CIO 12 wks CIO 1 81 C AS E The Chief Legal Counsel for the medical center presented his project plan. Fred had asked him to join the ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Task Name 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Duration Legal and Licensing Requirements Research licensing requirements for residential care facility Uniform accessibility standard compliance (# hndcp accessible beds) Investigate law firm and outline services Prepare project plan for license File license—by opening date Curb‐cut approval from county (access to County Rd.) Investigate corporate structure for assisted living Determine Board of Trustee membership Appoint Board of Trustees Prepare draft Code of Regulation Prepare document and filing of governance structure Draft service agreement with Friendly Medical Center for services provided Lease issues Research Long Term Care insurance requirements Facility “rules” defined (i.e., smoking, firearms, pets, financial planning) Spell out changes for residents in moving from “light” to “heavy” assisted Lease template prepared Review all marketing materials for compliance The Vice President of Marketing presented her project plan and stated that she and her staff were responsible for every step in the plan. She was still working with her staff to determine who does what. The Marketing VP made it clear to the team that she needed 5 months for the ID team when it became apparent that there were significant compliance and legal issues associated with this project. Predecessors 154 days 38 days 2 wks 4 wks 2 wks 0 days 53 days 115 days 3 wks 4 wks 4 wks 12 wks 4 wks 110 days 12 wks 4 wks Resource Names Legal 39 40 Legal Legal, CFO 44 45 46 47 Legal 48 Legal 50 6 wks 6 wks 154 days 52, 50, 51 Legal marketing plan implementation to be able to meet the occupancy requirements at start‐up. She restated that her team must have this lead time to the completion of the construction and furnishing phase of the Program. Task Name Marketing Community mailing about construction project Initial informational meetings Friendly Medical Center volunteers Community groups Friendly Medical Center staff (all shifts) Presentation prepared for Speaker’s Bureau Provide updates to community Inquiry log established Groundbreaking ceremony—during National Hospital Week Marketing plan developed and implemented PR firm contracted Marketing plan developed Determine name and signage for facility Hire Marketing Director Marketing plan ready to implement Implementation of marketing plan—5 months before facility ready, then ongoing Duration 270 days 0 days 16 days 1 day 4 days 3 days 0 days 0 days 0 days 0 days 180 days 4 wks 8 wks 0 days 4 wks 0 days 20 wks Predecessors 88 92 88 97 98 98 98, 100 101 182 CH A P T ER 5 / S CH ED UL IN G T H E P R OJECT As Fred was explaining that the next job of the group was to complete a final version of all project plans and firm up the schedule of the Program, the Construction Project Manager stated that it was his turn to present his broad ID 1 2 3 4 5 6 7 8 9 10 11 project plan for construction of the facility. He also added that he had a major scheduling issue to bring to the team. The Construction Project Manager presented the following broad project plan for facility construction. Task Name Duration Construction & Furnishing Facility construction Phase 1 ‐ Foundation & excavation (basement/1st floor slab) Phase 2 ‐ Structure (steel/framing) Phase 3 ‐ Enclosure (masonry/windows/roof) Phase 4 ‐ Interiors (drywall/ceiling/flooring/case goods) First 45 (light assisted) units ready to prepare for occupancy First 45 units ready for residents Remaining 57 units (light & heavy) ready to prepare for occupancy Construction complete Building ready for residents The construction PM proceeded to explain that the scheduling constraints that the Board of Trustees gave the team were not feasible. The Board wanted construction to begin immediately after the elections in November and to be ready for occupants by June. The contractor did not want to begin the project at the beginning of winter. The first phases of the project plan detailed work that needed to be completed outside. If the weather was bad, the construction PM knew the schedule would be affected. The construction project manager also pointed out that the schedule created by the contractor was designed around a 40‐hour, 5‐day workweek. If the building project began in 369 days 329 days 95 days 113 days 134 days 234 days 0 days 8 wks 0 days 0 days 8 wks Predecessors 3FS—60 days 3 3 6FS—5 wks 7 6 9 10 November, the estimated project duration would be increased by 1 to 2 months, during which time some construction crewmen would have to be paid, thereby increasing the building cost. The PM recommended that construction begin in February or March of the following year, which would give the facility a shorter build time and a lower cost. The budget and project duration submitted were based on a March 1 start date. He stated that the construction phase of the project did not need to hold up the other members of the Program team—they could begin their work on their projects anytime. QUESTIONS 1. 2. 3. Draw a Gantt chart for the construction phase of the program. What is the completion date if construction starts in March? What is the completion date of the project if construction is started in November? Why is it not possible to meet the scheduling constraints set by the Board? What is your recommendation to handle the scheduling problem? When will the program be completed based on your recommendation? C A NutriStar 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 4. 5. Develop a Gantt Chart of the Marketing Plan and Implementation Phase of the Program. Determine the start date of the Marketing Plan project in order to meet your recommended facility ready for occupancy date. What is the next step the team members must take in order to complete their project plans? S E balance of macronutrients. The energy bar has become extremely popular among elite athletes and other people who follow the diet. One distinguishing feature of the Nutri‐ Sports Energy Bar is that each bar contains 50 milligrams of 1 83 QUES T IO NS 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 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 Activity (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 following table provides optimistic, most likely, and pessimistic time estimates for the major activities. Optimistic Time (months) Most Likely Time (months) Pessimistic Time (months) 3 12 24 1 0.25 0.2 0.2 2 0.5 0.3 0.3 12 1 0.5 0.6 2 8 0.5 1 3 12 2 3 6 24 4 12 0.25 0.25 0 0 0.5 0.5 1 1 1 1 2 4 A: Concept Development Plan Definition B. Define project scope C. Develop broad schedule D. Detailed cost estimates E. Develop staffing plan Design and Construction F. Detailed engineering G. Facility construction H. Mobilization of employees I. Procurement of equipment Start‐up and Turnover J. Pre‐start‐up inspection K. Recruiting and training L. Solving start‐up problems M. Centerlining QUESTIONS 1. 2. Draw a network diagram for this project. Identify all paths through the network diagram. Simulate the completion of this project 1,000 times, assuming that activity times follow a betaPERT 3. distribution. Estimate the mean and standard deviation of the project completion time. Develop a histogram to summarize the results of your simulation. 184 4. CH A P T ER 5 / S CH ED UL IN G T H E P R OJECT 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? C A Launching E‐Collar Pet Technologies Inc. has completed the development of a revolutionary pet collar code named e‐collar. E‐collar is designed for dogs and allows pet owners to identify the location of their dog using their smartphones. In addition to purchasing the e‐collar, the pet owners must download a free app for their smartphone and pay a small monthly fee that is yet to be determined in order to connect the e‐ collar to a cellular network. In the past, Pet Technologies has used the services of Ad Jungle to develop its advertising campaigns. Ad Jungle is located in the same city as Pet Technologies and is a boutique advertising agency with 25 full‐time employees and a similar number of people it contracts with on an ad hoc basis. Pet Technologies has reached out to Ad Jungle and has requested an estimate for the cost of developing an advertising campaign for the e‐collar. Ad Jungle begins the process of developing an ad campaign by first meeting with the client to learn about the product to be advertised. Based on what is learned, Ad Jungle works with the client to define the target audience for the advertising campaign. Because the target audience may be different than its current customer base, market research is often required. Historical data suggests that defining the target market typically takes 80 hours (2 weeks). In some cases, determining the target audience is fairly routine and can be done in as little as a day and a half (12 hours in total) while in other cases much less is known about who will use the product and defining the target market can take as long as 4 weeks (160 hours). Also, the number of people working on the task at any one time varies as does their hourly bill rate. Given this, the average amount the customer is billed for the work to determine the target audience typically averages $170 per hour. In some cases, however, the hourly rate was as low as $100 per hour and in other cases as high as $450 per hour. Once the target audience has been defined, alternative concepts for the advertising campaign are developed. A key aspect of developing the concept is deciding on the tone the campaign will use such as humorous, dramatic, or informative. Concept development is a highly creative 5. What path has the longest expected time? What is the probability that this path will be the critical path? S E process and often requires several iterations between Ad Jungle and its clients. On average, concept development takes 2 weeks (80 hours) but has been completed in as little as 1 week (40 hours) or as long as 5 weeks (200 hours). Only one person from Ad Jungle works on concept development, and typically these employees are billed out at $125 per hour. However, the least experienced employee is billed out at $75 per hour and the most experienced person is billed out at $200 per hour. Once the client signs off on the concept, the development of the creative collateral (brochures, print ads, scripts for TV commercials, and so on) and determining the mix of media are done concurrently. The amount of time it takes to develop the creative collateral depends on how many media channels will be used (e.g., print, TV, online), how many people are assigned to work on developing the creative collateral, and how much involvement the client wants to have in the process. Typically, developing the creative collateral requires 3 weeks (120 hours) but has been done in as little as 1 week (40 hours) and on other occasions required 6 weeks (240 hours). Furthermore, the number of people and their bill rates varies from project to project. On average, the hourly bill rate for developing the collateral is $275 but has been as low as $145 and as high as $425. Determining the mix of media is almost always done by the same person at Ad Jungle. This person is currently billed out at $150 per hour. The amount of time it takes to determine the mix of media that will be used ranges from half a day (4 hours) to 2 days (16 hours), but it typically takes 1 day (8 hours). Once the collateral has been developed and the mix of media determined, the final step is production where the advertising materials are developed. The production of the advertising materials is outsourced to firms, and Ad Jungle assigns one account manager to oversee the work. The account managers are billed out at an hourly rate of $200. On average, 80 hours of the account manager’s time is needed to oversee production. In some cases, as little as 30 hours of the account manager’s time was required, while in other cases as many as 160 hours were needed. 1 85 B IB LIOG RA PHY QUESTIONS 1. 2. Draw a network diagram for this project. Identify all the paths through the network diagram. Simulate the completion of this project 1,000 times, assuming that activity times and costs follow a triangular distribution. Estimate the mean and standard deviation of the project completion time. Also, estimate the mean and standard deviation of the amount the client would be billed for the project. 3. 4. What is the probability the project can be done for less than $100,000? What is the probability the project will take between 350 and 450 hours? Based on the results of your simulation analysis, how would you respond to Pet Technologies’ request for an estimate of the project costs and duration? BIBLIOGRAPHY De Meyer, A., C. H. Loch, and M. T. Pich. “Managing Project Uncertainty: From Variation to Chaos.” MIT Sloan Management Review, Winter 2002. (This article provides a useful classification of uncertainty faced in projects and provides specific suggestions for managing each type of uncertainty.) Goldratt, E. M. Critical Chain, Great Barrington, MA, North River, 1997. Hulett, D. T. “Project Schedule Risk: Monte Carlo Simulation or PERT?” PM Network, February 2000. (Hulett comes to the same general conclusion that we do. Simulation is superior to the statistical methods of PERT for complex problems. In stating his case, however, he fails to note that for a PM to use simulation effectively, the PM should understand the statistics of simulation.) Kamburowski, J. “New Validations of PERT Times.” Omega, International Journal of Management Science, Vol. 25, No. 3, 1997. Keefer, D. L., and W. A. Verdini. “Better Estimation of PERT Activity Time Parameter.” Management Science, September 1993. Lawrence, J. A., Jr., and B. A. Pasternak. Applied Management Science, New York: Wiley, 1998. (This book has solution techniques for finding the critical path and time for a network using Excel’s® Solver.) Leach, L. “Schedule and Cost Buffer Sizing: How to Account for the Bias between Project Performance and Your Model.” Project Management Journal, June 2003. (This article identifies a variety of sources of schedule and cost biases and provides recommendations for coping with them.) Liberatore, M. J. “Project Schedule Uncertainty Analysis Using Fuzzy Logic.” Project Management Journal, December 2002. (Our discussion in this chapter addresses schedule uncertainty from both a probability theory approach and using computer simulation. This article demonstrates the use of fuzzy logic for assessing project schedule uncertainty.) McMahon, C. S. “Using PERT as an Approximation of the Fuzzy‐Project Network Analysis.” IEEE Transactions on Engineering Management, May 1993. Mantel, J. R., and S. J. Mantel, Jr. Project Management: A Managerial Approach, 8th ed., Hoboken, NJ: John Wiley, 2012. Pritsker, A. A. B. “Gert Networks.” The Production Engineer, October 1968. Ruskin, A. M. “Using Unders to Offset Overs.” PM Network, February 2000. C H A P T E R 6 Allocating Resources to the Project Trade-Offs In this chapter we consider the problem of allocating physical and human resources to projects.* The physical and human resources are granted to and used by the project in order to meet the project’s objectives. The amount of resources that can be allocated, of course, depends on the timing of the allocation as well as on the total supply of resources available for allocation. Mainly, resource allocation concerns how we allocate specific, limited resources to specific activities (or projects) when there are competing demands for the same limited resources. Projects compete with each other for the same resources in two different ways. First, consider a resource that is limited but is not consumed when used, the services of a specific technical specialist for instance. The problem here is which project gets to use the resource first and which must wait. Second, consider a resource that is limited and is consumed when used, a specific chemical reagent for instance. In this case, the second project may have to wait until more of the reagent can be purchased and delivered. In both cases, the project that must wait may suffer a schedule delay that makes it late. Just as projects may compete for resources, different activities of the same project may compete. Two or more concurrent activities might require the same personnel, or equipment, or even work space. One activity will be given priority, and the other(s) must wait. In order to manage resources in such a way as to optimize the use of a limited supply, trade‐offs must be made. The interaction of project scheduling and resource scheduling is clear, but we will examine several different solutions to the allocation problem. Those include the Critical Path Method (CPM), Goldratt’s “critical chain” (1997), and many different priority rules for allocating scarce resources. The primary cause of concern is resource scarcity. If some resources (including time) were not scarce, the resource allocation problem would be concerned solely with profit maximization—a relatively easy problem. *With few exceptions, we will not make a distinction between human and nonhuman resources in this chapter. We need not distinguish between them in order to consider the allocation problem. The tasks of administering the human and nonhuman resources are quite different, of course. 186 6 .1 EX P E DI TI NG A PR OJ ECT Trade-Offs 6.1 1 87 In Chapter 5 we evaluated project durations solely in terms of time. A project was either on time or not. Now we must also consider when and for what purposes scarce people, equipment, material, and facilities are used. The PM’s performance is judged by the skill with which the trade‐offs of time, resources, and scope are managed, so the PM must make constant use of cost/benefit analysis. There are countless questions to be answered. “If we come in late on this project, we face a $1,000 per day penalty. How much project slack do we need and what resources at what costs are required to get it?” “If I hire Cheatham Engineering Associates as design consultants, can I improve project performance by 3 percent without extending the project’s due date?” “Adding project slack and hiring a consultant require monetary resources that could be used for other things. Are these the best uses for the dollars?” At times, the PM is asked to take on a project in which there are the usual time, budget, and scope goals, but which also constrain the trade‐offs that the PM may wish to make if required to help the project meet its most important goals. For example, some projects are time constrained and must be completed by a fixed time. In such cases, resources (and possibly performance) are variable. Some projects are resource constrained and cannot go over budget or use more than a fixed amount of a specific resource. In these cases, time (and possibly performance) is variable. Occasionally, a senior manager suffers from a case of the micromanagement virus and fixes time, cost, and scope, thereby leaving the PM with no flexibility whatsoever. Such projects are certain to fail unless the micromanager has been profligate with the firm’s resources, which is highly unlikely for micromanagers. The fault actually lies with the PM who accepts command of such a project. (For those who are thinking that such a PM may find him‐or herself without a job following a refusal of an assignment, we would note the senior manager in question is insuring that the PM will fail. Do you want to work for someone who will not allow you to succeed?) We will start our tour through the wilds of resource allocation by reconsidering the problem of dealing with a pointy‐haired boss who insists that a project be completed in much less time than its expected duration. EXPEDITING A PROJECT The unreasonable boss problem in Chapter 5, Section 5.2 could be used as our example here, but a smaller problem will help avoid unnecessary arithmetic. Our problem is set in a deterministic world rather than in a probabilistic one, for the same reason. (Please remember that in reality all projects are carried out under conditions of uncertainty.) Finally, we must also take note of an assumption usually adopted when activities are scheduled, as we did in Chapter 5. That assumption is that all estimates of task duration, whether deterministic or probabilistic, are based on normal or standard resource loadings. The Critical Path Method In traditional PERT/CPM, the rules of “standard practice” apply and the normal task duration estimate is made with the normal or standard‐practice resource usage. Then a second estimate, referred to as the crash duration, is made based on the resources required to expedite the task. More resources of the type already used might be added; more workers and shovels if there is a ditch to be dug. On the other hand, the technology used to dig the ditch might be totally altered, utilizing a backhoe or a Ditch Witch®, for example. When making estimates for crashing, it is important to make sure that the resources required to crash the project are, in fact, available. Using a machine to dig the ditch in three hours instead of the 3 days required for a worker with a shovel is dependent on 188 CH A P T ER 6 / A L L OCAT IN G RESOU RC ES T O T H E P ROJE CT Risk the fact that the machine is available and can be on site when needed. (Of course, the warning about resource availability applies equally to normal resource requirements as well as to crash requirements.) There are times when the PM may expedite activities that have little or no impact on the network’s critical time, such as when the resources used must be made available to another project. It is important to remember that when we change technology, we may also be changing the level of risk in carrying out the activity. Finally, we must remind ourselves that some tasks cannot be crashed. One must not assume that because it takes one woman 9 months to carry and bear a child that nine women can accomplish the same result in 1 month. Consider the project described in Table 6-1. There is a set of activities, predecessors, normal task duration estimates, crash duration estimates, and estimates for normal cost and crash cost. One crash duration is marked with a single asterisk. For this activity, the task may be carried out in normal time or crashed 1 day at a time. Another activity is marked with a double asterisk. In this case, the duration must be one or the other; it cannot be broken down to 1‐day segments. Activities are charged at the “cost per day” (activity slope) increments shown in the last column. A given activity may have only two or three technically feasible durations. If an activity cannot be split into 1‐day segments, the cost is as indicated. The “slope” information for non‐or‐partially segmented activities is normally given in the slope chart. Activity slope is computed as follows: slope crash cost normal cost crash time normal time When crashing a project, starting with the normal schedule for all project activities, crash selected activities, one at a time, to decrease project duration at the minimum additional cost. To crash a project, follow two simple principles: First, focus on the critical path(s) when trying to shorten the duration of a project. Crashing a noncritical activity will not influence project duration. Second, when shortening a project’s duration, select the least expensive way to do it. Given these guides, consider the network shown in Figure 6-1(a) that was constructed from the data in Table 6-1. It is easier to illustrate the impact of crashing on an activity‐on‐arrow (AOA) network than on an activity‐on‐node (AON) network, so we use that approach here. Also, we use dummy activities in this case not to illustrate precedence but to show time durations and slack on the time axis. As indicated in Table 6-1, activity d can be partially crashed for $30, but it is not on the critical path and will not shorten the project. Activity e involves a technological discontinuity and must take either 3 days to complete at $10 or 1 day at $80. In general, the impact of having such a technological discontinuity is that the best solution for Table 6-1 An Example of a Normal/Crash Project Activity Precedence Duration, Days (norm, crash) Cost (norm, crash) a — 3, 2 $ 40, 80 40/−1 = −40 b a 2, 1 20, 80 60/−1 = −60 Slope ($/day) c a 2, 2 20, 20 — d* a 4, 1 30, 120 90/−3 = −30 e** b 3, 1 10, 80 −70 (2 days) * Partial crashing allowed **Partial crashing not allowed 1 89 6 .1 EX P E DI TI NG A PR OJ ECT b Normal Schedule 8 Days, $120 e c a d 1 2 3 4 5 6 7 8 Days 6 7 8 Days 5 6 7 8 Days 5 6 7 8 Days (a) b c a 7-Day Schedule, $160 e d 1 2 3 4 5 (b) e b 6-Day Schedule, $220 c a d 1 2 3 4 (c) b 5-Day Schedule, $260 e c a d 1 2 3 4 (d) e b 4-Day Schedule, $350 a c d (e) Figure 6-1 A PERT/CPM example of crashing a project, AOA network. crashing n days might not be part of the best solution for crashing n + 1 days. Rather, it may be best to crash the activity with the technological discontinuity at n + 1 days and not crash another activity that could be crashed for n days. This situation is illustrated in the discussion that follows. 190 CH A P T ER 6 / A L L OCAT IN G RESOU RC ES T O T H E P ROJE CT The network’s critical path is a‐b‐e, the project duration is 8 days, and the normal total cost is $120, as illustrated in the network of Figure 6-1(a). The decision about which activities to crash depends on how much we need to reduce the duration of the project. To reduce the total network duration by 1 day, we must reduce the time required by one of the activities along the critical path. Inspecting Table 6-1 to see which critical activity can be reduced at the least cost, we find it is activity a, which adds $40 to the project’s current cost of $120. Activity b could be crashed at an added cost of $60 or we could even crash e 2 days for an additional cost of $70. Of course, crashing e would only shorten the project duration by 1 day because when e is shortened, the path a‐d‐dummy, 7 days long, becomes the critical path and does not allow the project to be shortened to 6 days. Of the three options, crashing a is the lowest cost and therefore preferable, see Figure 6-1(b). Notice that crashing a also shortens a‐d‐dummy and a‐c‐dummy by 1 day. Suppose the project must be crashed by 2 days. What are the options? Reconsidering Table 6-1 and Figure 6-1(a), we see that we could crash activity e for 2 days ($70), but path a‐d‐dummy (7‐days’ duration) must also be crashed at least 1 day. We choose d ($30/day) because it is cheaper than a ($40). The total cost of crashing is $100, and the total project cost is $120 + $100 = $220. Alternatively, we could crash a and b, also for a cost of $100 ($40 + $60). Arbitrarily, we choose the latter option [Figure 6-1(c)]. Now suppose we wanted to crash the project by 3 days, from the original 8 days down to 5 days. Clearly e must be crashed by 2 days, costing $70, and a or b by a day. We choose a, the cheapest, for an additional $40. This leaves d to be crashed by 1 day for another $30, resulting in a total crashing cost of $140 and a project cost of $120 + $140 = $260 [Figure 6-1(d)]. Note that we did not crash b this time, as we did for 6 days. This is due to the technological discontinuity in activity e. Last, let us consider crashing the project by 4 days down to a project duration of 4 days. Since we crashed e, the technological discontinuity, to reach a 5‐day duration, all the remaining activities can be incrementally crashed. Thus, we can simply inspect Figure 6-1(d) to see what else needs incremental crashing to reduce the project by another day. Notice in Figure 6-1(d) that a‐b‐e and a‐d‐dummy are both critical paths. Only b and d can still be crashed so we crash each by 1 day for an additional cost beyond the 5‐day schedule of Figure 6-1(d) of $60 + $30 = $90 for a total project cost of $260 + $90 = $350 [Figure 6-1(e)]. Note that c is now critical; therefore, all paths are critical. Since the critical paths a‐b‐e and a‐c are at their full extent of crashing, the project duration cannot be further reduced, even though activity d could be crashed another day. Thus, Figure 6-1(e) is not the all‐crash network, although it equals the all‐crash time schedule of 4 days. Whether all this crashing is worthwhile is another matter. On the cost side, Figure 6-2 shows the time/cost relationship of crashing the project. On the benefit side, some projects have penalty clauses that make the parent organization liable for late delivery—and sometimes bonuses for early delivery. Starting at the right (all‐normal) side of Figure 6-2, note that it becomes increasingly costly to squeeze additional time out of the project. Charts such as the one shown in Figure 6-2 are useful to the PM in exercising control over project duration and cost. They are particularly helpful in dealing with senior managers who may argue for early project completion dates with little understanding of the costs involved. Similarly, such data are of great benefit when clients plead for early delivery. If the client is willing to pay the cost of crashing, or if the firm is willing to subsidize the client, the PM can afford to listen with a sympathetic ear. (While we advise the PM to ignore overhead costs over which he or she has no control, it should be noted that indirect costs are often altered when a project is crashed.) One final note on crashing projects. The same method is used when the task durations are probabilistic, that is, using three-time estimates. In this case, optimistic, most likely, and pessimistic activity duration estimates are made for the “normal” resource loading and new optimistic, most likely, and pessimistic duration estimates must be made 1 91 6 .1 EX P E DI TI NG A PR OJ ECT 400 All crash a + b +2d + 2e Cost ($) 300 a + d +2e – b 200 a+b a All normal 100 0 2 4 6 8 10 Total Duration (Days) Figure 6-2 CPM crash cost‐duration history. for crash resource loading. The PM should remember that the variance of both the normal and crash activity times largely depends on the technology used to accomplish the activity in question. Thus the variance of the normal activity time may be quite different from the variance of the crash time. The project budget can be determined in exactly the same way. The solution to project duration and resource cost levels can be reached by using the standard analytical method used in the last chapter, or by simulation, also described in Chapter 5. Crashing a Project with Excel * In this section we demonstrate how spreadsheets can greatly facilitate the task of choosing which activities to crash such that the project can be completed by a specified time. To illustrate this, we use the previous example with one minor change. Namely, we assume that partial crashing is allowed for all activities that can be crashed. The network for the example and the spreadsheet developed to solve the problem are shown in Figures 6-3 and 6-4, respectively. 3 e b 1 a c 2 5 d 4 Figure 6-3 AOA network from Figure 6‐1(e) with node labels added. *This section is intended for readers that have a background in linear programming and Excel’s Solver. This section can be skipped without loss of continuity. 192 CH A P T ER 6 / A L L OCAT IN G RESOU RC ES T O T H E P ROJE CT Figure 6-4 Spreadsheet model to find optimal crashing plan. At the top of the spreadsheet shown in Figure 6-4, columns A through F contain the information given in the problem. In column G, the crash cost per day (slope) is calculated by dividing the incremental cost of crashing the activity as much as possible by the maximum number of days the activity can be shortened. For example, the formula =(E2‐ F2)/(C2‐D2) was entered in cell G2 and then copied to other cells in column G (except for activity c which cannot be shortened). Column H contains a formula to calculate the maximum number of days an activity can be crashed by subtracting the crash time from the normal time. For example, the formula =C2‐D2 was entered in cell H2 and then copied to the other cells in column H. Column I corresponds to one of our decision variables, namely, the amount to crash each activity. In column J, the cost of partially crashing an activity is calculated on the basis of the amount of time the activity is to be crashed as determined in column I. For example, the formula =I2*G2 was entered in cell J2 and copied to the other cells in column J. The total crashing cost is calculated in cell J7 as the sum of the cost of crashing the individual activities in cells J2:J6. In column K, the actual time to complete each activity is calculated by subtracting the amount the activity is crashed (column I) from its normal time (column C). For example, the formula =C2‐I2 was entered in cell K2 and then copied to the other cells in the column. The middle of the spreadsheet shown in Figure 6-4 (cells B11:B14) are for the other decision variables needed. More specifically, cells B11:B14 correspond to the event times for each of the nodes in the network diagram. (Node 1 is excluded because we assume it occurs at time zero.) As you will see, we need these decision variables to preserve the precedence relationships shown in the network. For example, we need to make sure that node 4 does not occur until after node 2 occurs, plus the time it take to complete activity d. We now demonstrate how Excel’s Solver can be used to determine which activities to crash so that the entire project is completed with 5 days at the minimum cost. To begin, we select Solver from the Data ribbon (note that Solver is an Excel add‐in and must be added before it can be used). The Solver Parameters dialog box is now displayed (see Figure 6-5). Our objective is to minimize the total crash cost which is calculated in cell J7. To specify this, we enter cell J7 in the Target Cell box and then select the Min 1 93 6 .1 EX P E DI TI NG A PR OJ ECT Figure 6-5 Completed Solver Parameters dialog box. option button. Next, we tell Excel which cells it can change in order to find the solution with the least total crashing cost. In the spreadsheet shown in Figure 6-4, the values that can be changed are the amount of time each activity is crashed (cells I2:I6) and the time when each event occurs (cells B11:B14). Thus, these ranges are entered in the By Changing Variable Cells box. Note that these two separate ranges are separated by a comma in the By Changing Variable Cells box (see Figure 6-5). The last task is to enter the constraints for the problem. Perhaps the most obvious constraint is that we want to complete the project within 5 days. Since node 5 (cell B14) corresponds to the event of the project being completed, we can specify this constraint as follows: B14 5 Another important set of constrains that needed is to make sure that we don’t crash an activity more than the maximum number of days that is can be crashed. For example, to ensure activity a is not crashed more than it can be physically crashed, we could enter the constraint I2
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Page 176 – 177 Exercises
Question 1
The expected duration of path a-b-c-f is 44.5 calculated as (10 4/6 + 12 1/6 + 12 2/6 + 9 2/6) and
the variance for the same path is 6.47 calculated as (1.78 + .25 + 4.00 + .44)
To calculate the probability for the above path to take longer than 50 days (interfering with the
project completion) is calculated as:
𝑍=

50 − 44.5
√6.47

= 2.17

The area in the upper tail of a z-value of 2.17 in Appendix A, is calculated as 1.5% and this is
translated as follows: there is a 98.5% chance that this path will not interfere with the 50 weeks
project completion.
Assuming that the paths are reasonably independent of one another, the probability that both paths
finish by time 50 is .985  .86 = 84.71% (Since both paths have activities a and b common to
them, their variance are counted twice, so probability of 84.71% is more pessimistic than needed
and the tru...


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