Essay 1) Sketch a network and use it as an example as you discuss the four different logical relationships between activities. Answer: The four types of logical relationships between tasks are 1) finish to start, 2) finish to finish, 3) start to start, and 4) start to finish. The most common type of logical sequencing between tasks is referred to as the finish to start relationship. A finish to start relationship is shown by Activity A and Activity B can begin. Finish to finish relationships require that two linked activities share a similar completion point. A finish to finish relationship is exhibited by the relationship between Activity C and Activity B. Often, two or more activities can start simultaneously or a lag takes place between the start of one activity after an earlier activity has commenced. Activity E and Activity D have a start to start network relationship. Perhaps the least common type of lag relationship occurs when a successor's finish is dependent upon a predecessor's start. Activity D and Activity F have such a relationship. 2) What is a Gantt chart, what information does one provide, and what are the benefits of using one? Answer: A Gantt chart is a useful tool for creating a project network. Gantt charts establish a time-phased network, which links project activities to a project schedule baseline. Gantt charts also can be used as a project tracking tool to assess the difference between planned and actual performance. Some benefits of Gantt charts are: 1) they are very easy to read and comprehend, 2) they identify the project network coupled with its schedule baseline, 3) they allow for updating and project control, 4) they are useful for identifying resource needs and assigning resources to tasks, and 5) they are easy to create. 3) Use the information in the table to create a baseline Gantt chart for the project where activity lengths are given in days. Activity A B C D E F G H J K Answer: Duration 6 3 7 5 10 8 6 4 10 5 Predecessor -A A B C D, E F G G H, J 4) A project manager ascertained that five different resources are needed to complete a project that has been estimated to last 37 days. Just to be on the safe side, the project manager told the client that the project would definitely be delivered in 40 days and 40 nights and arranged to rent the resources for that period of time. The project manager goes to the local rental center at the start of day 1 of the project, signs a 40-day lease agreement for all five resources, and brings them to the site to begin the project. Analyze the Gantt chart and resource list (activity durations are in parenthesis) and determine how much money is being wasted with this rental plan. If each resource could be rented for just the time it takes to complete each activity, what would the charge to the project be? Resource Number 1 2 3 4 5 Activity H M P B R F Daily Rate $1,000 $1,200 $500 $750 $800 Length 3 9 6 7 9 5 Activity S J W T G K Length 3 1 4 4 4 10 Answer: The project manager has paid for 40 days of capacity for each resource and the sum of the resources costs is $4,250. The total rental cost is 40 x $4,250 = $170,000. The actual use of the resources is as follows: Resource 1 = 18 x $1,000 = $18,000 Resource 2 = 15 x $1,200 = $18,000 Resource 3 = 5 x $500 = $2,500 Resource 4 = 14 x $750 = $10,500 Resource 5 = 13 x $800 = $10,400 The total cost for actual use is $59,400, so there is $170,000 - $59,400 = $110,600 wasted. 5) What is project crashing and what are three reasons why it might be important to do so? Answer: The process of accelerating a project is referred to as crashing. Crashing a project directly relates to resource commitment. The more resources we are willing to expend, the faster we can push the project to its finish. There can be good reasons to crash a project, among them are: - The initial schedule may be too optimistic. - Market needs change and the project is in demand earlier than anticipated. - The project has slipped considerably behind schedule. - The contractual situation provides even more incentive to avoid schedule slippage. 6) What are the three principal methods for accelerating a project and under what circumstances might these methods yield little gain? Answer: There are three principal methods for crashing project activities: - Improving the productivity of existing project resources; - Changing the working method employed for the activity, usually by altering the technology and types of resources employed; - Increasing the quantity of project resources, including personnel, plant and equipment. In order to improve the productivity of existing project resources, the project manager must find a more efficient ways to work with the people, equipment, and materials. More efficiency means less waste and there are few that would argue that waste is beneficial. The project manager may change the working method by altering technology or resources types. Increased automation, more powerful equipment, and more senior personnel might all be deployed to accelerate the project. The author indicates that the most common method for shortening activity durations involves the decision to increase project resources, either by working the current resources for longer hours or by adding to the number of resources in the pool. A feature common to all of these approaches is that at some point the resources will stretch to their limit and the marginal gain will be prohibitively expensive, even to the point that any efforts to squeeze another fraction from them will yield negative results. Changes in the middle of a project might disrupt project team harmony, throwing them off of a learning curve and adversely affect team morale. 7) Crashing costs for a project are governed by the function: where t represents the number of days crashed (see graph). The project manager wants to crash the project, and is willing to pay up to $1,000 per day saved. How many days can be saved before the per-day cost is too high? Answer: We can crash the project to the point where the per day cost of crashing equals $1,000, so the manager needs to find the value of t where the slope of the crash cost function equals that amount. The slope is given by the first derivative of the crash cost function: 8) What is the cost to finish this project (all activity durations are in weeks and costs in US dollars) as quickly as possible? Activity A B C D E F G H I Predecessor A A B, C B D E F, G H Normal Minimum Time Time 12 10 5 3 9 7 14 10 4 3 9 8 7 5 11 8 8 6 Normal Crash Cost Cost 1000 1500 1200 1950 1500 2100 1800 2100 1400 1875 1000 1450 700 1200 2000 3000 1100 1700 Answer: The initial project duration is 63 weeks thanks to the valuable contributions of path ACDFHI. Path ABEGHI is 47 weeks and path ABDFHI is 59 weeks long. The base project cost is $11,700. Purchases from least expensive to most expensive are as follows: - Activity D reduced 4 days for $300 - Activity A reduced 2 days for $500 - Activity C reduced 2 days for $600 - Activity I reduced 2 days for $600 - Activity H reduced 3 days for $1,000 - Activity F reduced 1 day for $450 The new project length is 49 days with path lengths of ACDFHI=49; ABEGHI=40; and ABDFHI=45. The total project cost is now $15,150. 9) What is the minimum completion cost of this project if there is a penalty of $1,000 for each day the project lasts longer than 27 days? Activity durations in days and crash costs in dollars are given in the table. Activity A C D E J Reg Length 7 1 9 9 2 Crash Length 6 1 6 7 1 Reg Cost 400 450 550 500 600 Crash Cost 1,200 450 2,350 1,650 1,800 Activity L N R S Y Reg Length 7 6 4 10 8 Crash Length 5 5 4 8 6 Reg Cost 800 500 600 450 675 Crash Cost 1,500 1,250 600 1,350 1,750 Answer: The initial project duration is 34 days. Path analysis and purchases made in order of least expensive to most expensive are given in the table. Step 1 2 3 4 5 Starting Path Lengths JALSY=34 JANDCY=33 JAERY=30 JALSY=33 JANDCY=33 JAERY=29 JALSY=31 JANDCY=31 JAERY=27 JALSY=30 JANDCY=30 JAERY=27 JALSY=29 JANDCY=29 JAERY=27 Activity Crashed # Days Crashed Cost per Day Total Cost L 1 $350 $350 A 1 $800 $800 Y 2 $537.50 $1,075 L D 1 1 $350 $600 $950 Subsequent purchases will exceed the $1,000 penalty, so the project manager is better served by paying two penalty days at $1,000 each. The total cost of the project including the penalties is $10,700. 10) Consider the project described by the table where all durations are in days and the costs in dollars. What is the minimum cost of completing this project in 150 days? Activity A B C D E F G H J K L M N P Q Normal Predecessor Time 15 A 30 A 45 C 20 D 5 B 10 F 30 J,E 50 F 25 G 35 K 40 L 15 K 30 H 20 N,P 5 Minimum Time 12 22 37 17 4 7 25 45 20 33 33 13 26 15 5 Normal Cost 800 2,500 21,000 15,000 3,000 13,000 41,000 30,000 20,000 6,500 16,500 14,400 23,500 15,250 5,000 Crash cost 1,100 4,100 33,000 22,000 3,300 15,500 46,000 37,500 25,000 7,200 19,400 18,600 27,500 23,500 5,000 Answer: The crash cost per day has been added to the table. Possible routes through the network are: ABFGKLM=175 ABFGKNQ=155 ABFJHPQ=155 ACDEHPQ=160 and the initial project cost is $227,450. Activity A B C D E F G H J K L M N P Q Normal Predecessor Time 15 A 30 A 45 C 20 D 5 B 10 F 30 J,E 50 F 25 G 35 K 40 L 15 K 30 H 20 N,P 5 Minimum Time 12 22 37 17 4 7 25 45 20 33 33 13 26 15 5 Normal Cost 800 2,500 21,000 15,000 3,000 13,000 41,000 30,000 20,000 6,500 16,500 14,400 23,500 15,250 5,000 Crash cost 1,100 4,100 31,000 22,000 3,300 15,500 46,000 37,500 25,000 7,200 19,400 18,600 27,500 23,500 5,000 $/day 100 200 1500 2333 300 833 1000 1500 1000 350 414 2100 1000 1650 Purchasing critical activities from least expensive to most expensive without switching critical paths proceeds as follows: Purchase Activity # Days 1 A 3 2 B 8 3 K 2 4 L L 5 1 5 E L 1 1 6 C F 1 3 7 C G 3 3 8 C 3 Path Lengths ABFGKLM=172 ABFGKNQ=152 ABFJHPQ=152 ACDEHPQ=157 ABFGKLM=164 ABFGKNQ=144 ABFJHPQ=144 ACDEHPQ=157 ABFGKLM=162 ABFGKNQ=142 ABFJHPQ=144 ACDEHPQ=157 ABFGKLM=157 ABFGKNQ=142 ABFJHPQ=144 ACDEHPQ=157 ABFGKLM=157 ABFGKNQ=142 ABFJHPQ=144 ACDEHPQ=157 ABFGKLM=156 ABFGKNQ=142 ABFJHPQ=144 ACDEHPQ=156 ABFGKLM=153 ABFGKNQ=139 ABFJHPQ=141 ACDEHPQ=153 ABFGKLM=150 ABFGKNQ=136 ABFJHPQ=144 ACDEHPQ=150 Extra Cost 300 1,600 700 2,071 414.30 300 414.30 1,250 2,500 3,750 3,000 3,750 Total reduction is 25 days at an additional cost of $20,050, for a total project cost of $247,500 3A's = 300 8B's = 1600 7C's = 8750 1E = 300 3F's = 2500 3G's=3000 2K's=700 7L's=2900 11) What is the minimum cost completion time for this project if the activities have normal and crash costs as indicated and there is a $1,000 fixed cost for each day on site plus a $500 penalty for each activity that is crashed? The crash costs represent the cost of a fully expedited activity. For example, reducing activity Y from 13 days to 12 days costs an extra $100 on top of the $500 expediting cost for a total cost of $2,600. Reducing Y from 13 days to 10 days costs an extra $300 on top of the $500 expediting cost, for a total activity cost of $2,800. Activity Z Y X W V U T S R Q P N Predecessor Z X Y W V U R, S T P, Q Normal Time 2 13 19 18 10 13 18 4 6 15 13 4 Normal Cost $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 Crash Time 2 10 15 15 9 11 14 3 5 13 12 4 Crash Cost $2,000 $2,300 $3,000 $3,000 $3,000 $3,000 $4,000 $3,000 $3,000 $3,000 $3,000 $2,000 Answer: The project before any expediting takes 55 days thanks to path ZWTPN. Path XVSQN has a 52-day duration and path YURQN has a 51-day duration. The initial cost of the project is $24,000 for the uncrashed activities plus $55,000 for the fixed cost for a total cost of $79,000. Crashing should take place in this sequence: 1st: Reduce activity W by 3 days. This costs $1,000 plus the $500 expediting charge but trims three days off the fixed cost saving $3,000 for a net savings of $1,500. The project is now 52 days thanks to path ZWTPN and XVSQN at a cost of $77,500. Any further action may reduce the project length but will increase the project's cost. Crashing activity T by one day and activity X by one day add $1,750 to the cost column and save only $1,000 for a net cost of $750. 12) Sketch the network described in the table in AOA format. Activity A B C D E F G H K L Answer: Predecessor -A A B B, C D D F, G G H, K 13) Determine early start and early finish times for all activities in this network. Activity duration in days appears under each arrow. Answer: Early start and early finish times for all activities appear in the table. Task A B C D E F G H K L Early Start 0 1 1 8 8 9 9 23 23 31 Early Finish 1 8 6 9 16 18 23 31 26 37 14) What are the strengths and weaknesses of AOA and AON techniques? Answer: Both activity on arc (AOA) and activity on node (AON) create a sequential logic for all activities within a project. AON techniques are easier to learn and are the format of choice for project management software. AON mode allows for ease of labeling and interpretation as long as the number of activities is not too large. AOA is widely used in the construction industry and can be easier on the eyes if the project has a large number of activities. Another advantage is that the use of arrows can provide some indication of activity length, which may be difficult to visualize in AON format. Milestones at the start or end of an activity are easy to locate in AOA format. AOA suffers from the difficulty of dummy activities and data dispersion (instead of having all duration and early and late start and finish times in a node, these tidbits may be spread along the length of the arrow). 15) How might a project manager alter a straightforward PERT network to accommodate an inordinately large and complex project? Answer: A large project may require a network with thousands of activities, relegating the classic 8.5x11 sheet of paper to the same drawer as a the buttonhook and the 8-track tape. The project manager and his network artist should try to simplify the network logic and reduce it to the most obvious or meaningful relationships. Rather than showing every possible path through the network and every activity sequence, a meta-network that shows only the key subroutines or network paths can be created. These subroutines can be further broken down by the project manager or administrator responsible for their completion, but the overall project network is streamlined to include on the most general or relevant project activities. 16) What are four criticisms and caveats to bear in mind as you develop a project activity network? Answer: There are several criticisms and caveats that must be considered as we develop project activity networks, the first of which is that networks can become too large and complex to be meaningful. For a project that is hugely complex, the number of discrete activities can run into the thousands and the project duration can extend for years. The complex interrelationships of all these activities and the difficulty of forecasting activity lengths some time into the future makes a fully detailed activity network difficult to realize. Second, faulty reasoning in network construction can sometimes lead to oversimplification or incorrect representations. A multiple tiered approach sometime compromises the information sharing aspect that is vital to project management. Third, networks are sometimes used for tasks for which they are not well suited. As the adage goes, "If it doesn't fit, get a bigger hammer," applies with the use of this valuable project management tool. In addition, networks used to control the behavior of subcontractors have special dangers. Subcontractors must be privy to the overall network and all subs must use consistent timeframes scaling and network techniques. Finally, there is a strong potential for positive bias in PERT estimation used in network construction. Most activity estimations using PERT methods lead to overly optimistic activity duration estimates.