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The Bestclean is a new cordless vacuum cleaner. An analysis of the task of building the Bestclean reveals the following list of relevant activities, their immediate predecessors, and their duration. JobDescriptionImmediate PredecessorsNormal Time(Weeks) AProduct Design6 BMarket research Plan2 CManufacturing and engineering A3 DPrototypeA5 EMarketing BrochureA3 FCost EstimateC2 GTestingD3 HMarket surveyB,E4 IPricing and forecastH2 JFinal reportF,G,I2

Using the mentioned case: 1. Draw a Gantt chart for the project mentioned above. 2. Calculate the number of week required to complete the project. (a)Draw the network as an activity-on-node network (b)Fully analyze the network (c)State (i) the critical path activities; (ii) project duration; (iii) floats of the non-critical activities (d)Construct an early-start Gantt chart and resource profile for the project Please note that you need to justify your answers. Answers )Using the list of activities, its duration and predecessors from the case study a Gantt chart for the proposed sequence of activities is drawn below, showing also the late start, for the activities beyond the Critical Path (assuming that all relationships among the activities and its predecessors are End-to-Start) Figure 1 – Gantt chart for the project 2) The number of weeks to complete the project is the sum of the duration of the activities in the Critical Path, which is: A – E – H – I – J ? 6 + 3 + 4 + 2 + 2 = 17 weeks. a) We can draw the AON network, as below, with the critical path activities highlighted in red.

Figure 2 – Network Diagram (AON) for the project (Early and Late dates shown) b) As no lag has been mention, the analysis for the above network is shown below, with emphasis to the activities in the Critical Path. WBSTask NamePredecessorsDuration (weeks)StartFinishFree SlackEarly StartLate StartEarly FinishLate Finish AProduct Design61601666 BMarket Research Plan 21271829 CManufacturing & Engineering A3794 711913 DPrototype A57111 781112 EMarketing Brochure A37907979 FCost Estimate C21011410141115 GTesting D31214112131415 HMarket survey B,E41013010131013

IPricing and forecast H21415014151415 JFinal report F,G,I21617016171617 c) i) The critical path activities are those whose float is zero, i. e. , cannot be delayed without delaying the whole project. In this example the Critical Path activities are: A – E – H – I – J. ii) Project duration is the sum of the Critical Path activities’ duration: 17 weeks. iii) The activities that have floats are highlighted in the table above – Market research Plan, 7 weeks; Manufacturing & Engineering , 4weeks; Prototype , 1week; Cost Estimate , 4 weeks; Testing , 1 week. ) In an early-start Gantt chart, the bar of each activity starts at the activity earliest start time and finishes at the earliest finish time. Figure 3- Early-start Gantt chart for the project The resource profile for a project or activity describes the utilization of such resource (men, machinery, materials, cash, etc. ) throughout the whole duration of the project. The desired profile for most resources would be a constant utilization of the resources against time, and while it not always possible to achieve such ideal profile the project manager should work with that target in mind.

While in real life there might be peaks and valley in the resource profiles along the project this is highly undesired, as it denotes the need to deallocate resources which may be difficult to allocate in a another project for the duration of the engagement gap, or it would imply in having different resources, within the same specialty, working at the same project, potentially causing communication and other continuity issues. Usually when analyzing networks to calculate the minimum overall project completion time, we take no account of any resource restrictions.

However in real-life projects, resources availability are limited by its own nature, then according to Beasley, the resources are typically subject to two types of restrictions: resource smoothing (also known as resource leveling) problems and resource constrained (also known as resource allocation) problems. To establish the resource profile for the project, we would have to take the next step in planning: Assigning the required resources to complete each activity and then verify if at any given time the demand surpass the availability for that resource.

Case it does then we would have two options: bring additional resource to fulfill the demand, which implies additional cost, or reschedule the activity to a point in time where there would be no conflicting demand for such resource. In the case study presented there is not enough information in terms of the effort required or the maximum allocation per resource to identify any potential demand conflicts or over allocation of a resource.

However we can infer a little and produce the following scenario, fictitiously allocating common resources: WBSTask NameDurationStartResource Names AProduct Design6 weeksMon 03/01/11Engineering, Product Management BMarket research Plan 2 weeksMon 03/01/11Marketing CManufacturing & Engineering 3 weeksMon 14/02/11Engineering, Manufacturing DPrototype 5 weeksMon 14/02/11Engineering EMarketing Brochure 3 weeksMon 14/02/11Marketing FCost Estimate 2 weeksMon 07/03/11Marketing, Product Management GTesting 3 weeksMon 21/03/11Engineering HMarket survey 4 weeksMon 07/03/11Marketing

IPricing and forecast 2 weeksMon 04/04/11Product Management, Marketing JFinal report 2 weeksMon 18/04/11Product Management, Engineering[50%],Marketing[50%] As the result of this, as shown below, now the Manufacturing & Engineering and Prototype as well as Cost Estimate and Market Survey have conflicting demands for the Engineering and Marketing resources respectively. Figure 4 – Resource Profile Once the resource profile has been analyzed and over allocated resource identified, the project manager should work to fix the situation.

A method that can be used is the resource leveling, where, according to Kerzner (2009), we, for example, would use the slack to deliberately delay the start of the Prototype activity so that it would only start after the Manufacturing & Engineering has finished, eliminating the conflict, but that would also cause the overall duration to stretch by two weeks more than previously, in an undesired, but inevitable, given the underline cost and resource allocation conditions, effect.

As described by Beasley (2002), the drawbacks that arise from Leveling are: i)When dealing with multiple resources, by leveling one resource it makes the other resources less smooth, which implies the need for tradeoffs among resource profiles; ii)Once an activity has been delayed to smooth a resource profile, if the remainder tasks don’t follow as planned, then the time “lost” cannot be recovered. Figure 5 – Leveled Gantt We can see in the Gantt chart above, resulting from leveling both resources, that also the Critical Path has changed, including more activities now,

A-D-E-G-H-I-J, than it had before, which indicates additional risk for the project to complete in time. Therefore some precaution is required when applying this method. References Bibliography Kerzner, H (2009). Project Management: A System Approach to Planning, Scheduling and Controlling, 10th ed. New Jersey: John Wiley & Sons. Lewis, James P (1995). Project Planning, Scheduling & Control. Chicago: Irwin Professional Publishing. PMI Standards Committee (2008).

A Guide to the Project Management Body of Knowledge (PMBOK) 4th Ed. Pennsylvania: PMI Inc. Internet Resources Beasley, J. (2002). Operations Research Notes. Brunel University, Uxbridge, UK (http://people. brunel. ac. uk/~mastjjb/jeb/or/netres. html) Term Definitions & Formulae (extracted from PMBOK 2008) ExpressionSymbolDescription Activity DurationtThe expected duration of an activity Free SlackFSThe amount of time that a task can be delayed without causing its successor tasks to slip.

For a task without successors, free slack is the amount of time that the task can slip without delaying the finish date of the project Late FinishLFThe latest time an activity can be completed if it is started at its latest start time Late startLSThe latest time an activity can begin without delaying the completion of the project Early finishEFThe earliest time an activity can be completed if it is started at its early start time Early startESThe earliest time an activity can begin if all previous activities are begun at their earliest times

The following formulas establish the correlation among the expressions below: ES = EF (predecessor) * the successor activity would start at the next full time slot, in this case the next week EF = ES + t LF = LS (successor) LS = LF – t

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