The Linear Algebra Modules In Operations Research

Published Date: 02 Nov 2017

There are a number of techniques to estimate the cost and duration of a project in project management. Two main systems used for estimation are recognized as top-down and bottom-up approaches (Larson, 5th ed., page 127). Top-down approaches, also called Analogous, are usually favored to be used for estimation by higher management when there is no clear scope and details available to estimate the costs, or at a time when there is an urgency pressing for a rough estimation. Carrying an innate uncertainty, this approach might satisfy the need for a ballpark estimation but the result might potentially be unreliable for precise operations. Top-down approaches use mainly two methods for their estimations: Consensus Methods and Ratio Method (also Parametric Method) (Larson, 5th ed., page 127) in general and Function Point Methods specifically for the industries like Software and System Projects (Larson, 5th ed., page 135).

The bottom-up approaches tends to produce more accurate and reliable estimation of the project by starting from the bottom and evaluating the finest elements in the project scope. Bottom-up estimation method satisfies project managers more than top-down approaches as they are more accurate and reliable and don’t leave the project to chance by giving just a rough estimation. In process of bottom-up approach, the estimation starts from the most detailed and most bottom tasks in a project WBS and aggregate the entire task costs upward to estimate the deliverables and then the whole project. By summing up the estimation for the deliverables or work packages, the estimator can produce a reliable and accurate calculation of the whole project to be referenced by the stakeholders and clients. Unlike top-down approaches, the bottom-up approach strictly relies on the WBS or OBS of the project and this keeps each task and its cost and accountable and in coherence with the task network of the project and the whole project scope. Two main types of bottom-up techniques are Parametric and Range Estimating Methods (Larson, 5th ed., page 138).

(1)After visiting and consulting with the project clients, the requirements for their desired house are taken and registered into the new ranch house project agreement draft for generating a scope statement and forother processing purposes. Based on our initial requirement analysis sessions we could generate a project scope seen at below:

Project scope:

A one Story ranch house

A covered porch

Slab foundation

Landscaping

Concrete driveway

Exterior Siding

Rear Deck

Screen Porch

Due to urgency of making a decision, our client needs to know about the cost of the project and require us to give him a rough estimation about the project and the duration (it will be a top-down approach as we don’t have WBS yet). The project manager has to utilize the possible techniques for estimation to give the customer a reliable and the most accurate estimation that he can make. Because there is no WBS generated at this stage yet, the project manager can use top-down, analogous and ratio methods to generate initial cost estimation. At this point although he might be able to give the client a ballpark estimation about the duration of the project but he won’t be able to back up his price unless he generate the WBS and assign the budget and resources on the task network to come up with an accurate estimation.

Involving several people in the estimation usually helps for careful consideration and results in more reasonable and realistic estimation (Larson, 5th Ed., Page 130), so it is a good idea for our project manager to involve a few other stakeholders like the client (for service/product requirement analysis), and some of the key internal stakeholders like: the higher managers, managers who directly work to process the project , technical managers/experts, line managers, financial manager, Architects/planners. The manager also can consult with external sources like expert companies and government departments to narrow down the estimation and mitigate the possible variances and risks on the project. If available the project manager can extracts the estimation from archive of the previousprojectsif there is such a point of reference available.

Our estimation committee could use whether Ratio Methods- to estimate the cost for house by estimating the segments and portions or estimate based on the phases for the construction of the house in ratios and sum them up to surrogate the estimation into the total price of the project. Consensus Method is also the other option to pool the whole expert ideas into estimation of the cost and duration for each deliverable of the house and add them up into a final price for the project.

(2) Once the WBS for the project is in hand, our project manager could use bottom-up estimations for more reliable and accurate evaluation of the cost and duration for the project and reduce incurring uncertainties resulted by top-down method. For bottom-up estimation, internal stakeholders like technical experts, direct line managers and developers are very important for estimations. All key people that might be working in the production line of the product can bring their estimations into the equation to produce a refined and accurate estimation of the tasks and the total WBS and deliverables. Line managers and technical experts are highly important in bottom-up estimation approaches because only they know enough about the specifications of the product and they are the best people who have jurisdiction on specifications of a task and its duration and cost and the required resources to finish them.

(3) To obtain an accurate estimation of the project, the manager must use bottom-up approach for estimation. In general, bottom-up approaches are more accurate and reliable than top-down approaches in estimating cost and duration for a project that has a clear scope. Bottom-up approach tends to create a more accurate estimation because the estimations are made considering all the tasks and their inter-relation on WBS. As the detailed hierarchy and network of the tasks are estimated with precision and by and expert mind, the estimation renders the most reliable cost for house project. In comparison, other approaches rely on mostly a guestimate on the duration and cost of the project scope or any portions of it. Top-down estimations are made mostly base on guesstimate overa part or the whole project and thus are susceptible to mistakes or variance from theactual costs. If the data regarding the previous and accomplished projects are available and reliable, it can also be instrumental in estimation or a back-up estimation in case the projects are similar or for the identical projects in details and conditions.

Answer to question 2:

Since the advent of programming in computer world in over four decades of his life cycle, Software Developing Systems have tried to answer the need for more productivity of business community with leaner, lighter and more thorough solutions in software development process by evolving ITILliterature of IT Project Management systems and PM methodologies in running software projects. The evolutionary growth in the body of knowledge for programming projects has been toward producing more objective strategies and efficient deliverables for the projects. The techniques that have been emerged from the evolutionary path of product and service development have been tested and emulated in the small and big scale projects.

Two common systems for processing and producing the products and services in IT fields are Agile and Traditional (Waterfall) systems. Both systems have proven to be instrumental in relevant environments, but it seems that recently there has been a growing tendency to apply agile methods in running programming projects. Studies approve a greater success for agile programming than its waterfall counterpart. Based on 2011 study, "The Chaos Manifesto" from the Standish Group, agile projects often are three times more successful than non-agile projects, (2011, Chaos Manifesto, from the Standish Group).

The practitioners of both models have speculated about the pros and cons of both models. While traditionally in some environments waterfall model has been utilized to produce efficient results, agile models are proving to be a growing trend in modern project management. In complex programming environment, a program needs to exactly meet the requirements in the defined time and with precise specification. In waterfall system, a program cannot be implemented and delivered until all modules of the program are planned, designed, and tested. This is a flaw in the waterfall type of programming projects which causes inefficient and rigid use of time, resources and creativity. Agile systems on the other hand tend to be phase based, lean, and flexible which is iterative in the process and breaks down the whole structure into defined deliverables and values. The result of each phase is a functional product which can create value to the customer in shorter time and with a leaner budget and can be integrated into whole product once all the phased evolve in their production life cycle. This system can satisfy needs for defining and production stages of the project in separate modules and at the same time meet the instant needs of the clients with more productivity and dexterity.

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(1) In our example of the programming project, the program can be broken down into a number of modules which each could be defined and processed as a separate project and be delivered to the customer in separate functional forms but in fact as an integral part of the whole program. For example, as discussed about it, in the waterfall model, a project basically is defined for the whole program at the beginning of the project before it starts for developing any part of the program. Then the programmers develop the product with all features and modules to the testing and implementing stage. This way the program won’t be functional and deliverable until whole program finishes and tested to assure its readiness for rolling out. In agile model, each segment of the program which can be used in different departments like accounting, inventory management, purchase, orders are designed in functional module format and can be built separately in shorter time with primary functions stressed at first and let the customer provide the actual feedbacks based on their experience on its trial application. Then company takes feedbacks and inputs to troubleshoot the bugs and expand the features until the program becomes desirable. Waterfall Model in programming projects usually is cumbersome with a lot of waste in time and resources without enough assurance that the program will meet the needs or will finish on time. However, Agile Programing, while breaking down all this risks and complexities, try to respond to the most urgent needs and functions of the products and integrate the process in the whole system in an iterative way until accomplishing the desired goal.

(2)One example of the difference between the two approaches can be applied on scheduling method. A waterfall model tends to define the schedule at the beginning of a project for the whole lifecycle of the project ignoring the uncertainties that can lie on the way of any programming project. So, use Waterfall Model for this project, Bob has to put all the elements of the product, deliverables, budgets, resources, and duration into consideration to be able to schedule the project in planning phase. Since Bob sets the default schedule at the definition stage any deviation from the baseline will create considerable variance in the project plan jeopardizing the project with various pitfalls.

However, in a cyclic agile system, while Bob has chance to involve the client in every step of the product development, he can starts the project with the most basic definition of the program and modules required by the client and still be on track to produce the whole product anytime as required. This way, both the company and client will have change to bring any modification and requirement into the project process and have the merit of both producing a functional product which is focused on the business requirements and production priorities. The task for Bob for scheduling the project will be leaner and Bob will have to apply the main schedule and resources only on the required module. After completion any module he can work on the next modules of the product at the request of client.

(3) As a project manager, I would advise agile system for the production of this program. As the company will use the product in different defined departments, the product requirements from each department can be obtained and integrated in a total product package. Then each module can be defined and produced along with the client’s requirements and feedbacks until we finish the module that is used in the first required department and move on the next module to meet the need of other department. At the end the team can assemble all modules and integrate them in whole package. This way, the project will move thriftily and swiftly to satisfy both parties in a leaner time and in more flexible manner. One of the cons for this method might be the need for extension of the budget or the time due constant changes in the scope of the product by the client which will require anupdate in the project and the scope accordingly. The other uncertainty may lie in the success rate in the integration phase of the program which can cause scope creep or a deviation from initial estimation of the project. To remove this risk the technical department must take require precautions and measures at the planning phase of the project.

Originating initially in defense projects(ref. Wikipedia), Critical Path Method, CPM, is a technique in analysis and defining the critical streamline and path for the set of the activities in a defined project. CPM or PERT Analysis is a kind of sensitivity analysis which is studied under linear Algebra modules in Operations Research (OR) or Management Science. CPM initially is emulated in the scheduling phase of a project enabling the analyzer to measure and recognize the logical dependency and interdependency of the tasks on the network of the activities on the project and assist the PM to incorporate all the efforts in a project into the final product. CPM usually takes a minimum of three inputs from the WBS to formulate the critical path for the project operation. The three key elements are: all the activities and tasks derived from WBS and product requirement, the duration of the each activity required to be completed, and the logical relation and dependencies among these activities.

This method basically builds mathematical relations between the values of a predecessor and successor of a task and in a relevant estimation moving forward by longest duration (value) and backward by the shortest duration (value) and by subtracting the difference between these two values recognizes the slack (float) time for each task and for the chain of the task. Then recognizes the task with longest duration or minimum slack time on the path which can create delay in a project once they are sluggish and this way create a critical path for the activities on the project streamline. This formulation concludes for the longest path in the network of the activities and highlights which path is highly likely to create a bottleneck in the duration of the project from the start point to the end.

Although CMP is a very instrumental metrics in the hands of a PM to level the designed path, its logical relations, and duration for each activity and overall project, but it can pave the ways to project pitfalls if the complementary consideration aren’t taken into account. This deficiency originates from inherent limitations in the model. These limitations are whether derived from the nature of the method or can be incurring by miscalculation of them on the project. Putting in two main categories of man-made andMechanical,some of the limitations that I can enumerate are as follow:

It is susceptible to give out inaccurate estimation and impose risk on the project. CPM is complicated and as it is mostly estimated manually, it can produce wrong estimating results if the estimator makes a mistake in one or some of the value allocations and estimations. This will cause a pseudo-fact that might result in false confidence for the accuracy of the measuring and allocation of the resource, while in fact it is not.

As it is complicated, it requires knowledgeable teams to be able to conduct the evaluations accurately. Firstly, experts are costly, and secondly in long projects, some of the team members might leave the company and expose risk onto the project (Professor Guy Le Roy, Projects’ Analysis through CPM, Page 24).

Once any change in the scope and duration of the activities in the project occur, the CPM has to change and adapt accordingly. Other than imposing the need for a new estimation, it might make the updated estimation prone to mistakes as essentially the process needs to be repeated manually to match the new scope requirement.

On multiple projects, estimation of the critical path gets very complicated.

In presence of multiple Critical Paths, it makes the estimation of the critical path and the interconnection of the activities and allocation of the resources highly technical and burdensome when the parallel paths go into a converging node. Sometimes prioritizing which path should receive the highest attention and resources will not be an easy job (Professor Guy Le Roy, Projects’ Analysis through CPM, Page 25).

In a novel project recognizing the critical path might not be an easy job, as defining a valid critical path requires a full knowledge on the scope and duration of a task on the project streamline. In unique projects this might be very tricky and cause pitfalls for the PM somewhere on the life cycle of the project.

The CPM process can become complicated as the scope and extent of the project increases. Too many interconnecting activities can result in the network diagram becoming very complicated. The risk of making a mistake in any estimation will increase in such situations.

In agile project, as the scope and duration of the project activities might be subject to frequent changes, critical path will require to change based on the updates on the scope. It won’t be easy to conduct this complex process very often.

Critical Path only takes the inputs from interdependencies of the tasks into account. It is inherently blind to the external facts and resource constraints. For this reason it basically might reflect a hypothetical and theoretical metrics, and the preference finishing the project at earliest time by the limited inputs. For example CPM neither can recognize nor take the limitation and constraints of resources and resource allocation into account. So, sometime an indicated bottle neck might be a pseudo-fact or sometimes it might overlook the potential resource to eradicate the bottleneck and critical tasks on time or in a shorter time.

CPM tends to produce the optimal schedule for the project. However, CPM lacks any insight on resource constraints. For example, for a task, duration of the schedule leans on the availability of the resources. As resource might or might not be available at the defined time for a considered task, makes CPM presupposition of resource availability false. In multiple projects this case might even get more complicated but CPM plans the duration optimistically and this might violate the validity of the schedule. Thus CPM model might not be based on reality and this factor imposes revision on the schedule by PM.

One weakness that CPM imposes on the managing a project is that it only focuses on the time/duration aspect of the tasks and project and thus totally ignores the concerns regarding cost, quality of strategic aspects of the project.

And finally, one lesson we learned from our readings in regard to CPM is called Student syndrome or procrastination Larson, 5th edition, page 296). When CPM presents the critical path and the slack on the duration of some tasks, the slack time might be used up by the team somehow and this will make the path (although it had slack on it) a critical path demanding attention and re-schedules the task and the path. This might not be one of the inherent flaws in the system, but psychologically people tend to over consume or waste time when they realize that is it abundant. This might be categorized as a misuse of the model more presenting a flaw in the CPM itself.

Answer (1)

The WBS for John’s project based on the information in the question is as follows:

Task Number

Task Name

1

A Set of Plans

2

Plans Approval

3

Budget Allocation

4

Materials Procurement

5

Tools Preparation

6

Assistant Technicians

7

A 12’ x 16’ Screened

8

A Rear Deck

9

A Concrete Patio

10

An Asphalt Shingle Roof

11

A Decking Boards for the Floor

12

Posts for Supports 4’ x 4’

13

Bracings

14

Staining the Deck

15

Staining the Walls

16

A Set of Stairs(Down to the New Concrete)

17

A Building Permit

18

A Rear Property Line

19

A Rear Property Line Survey

Answer (2)

As a house owner, John has a few possibilities in estimating his building expansion project.

At the brain storming stage of the plan for the project John can figure out the cost by a top-down method. He can just set a ballpark price on the project. He also can compare his plan and its deliverables to one of the neighbor’s similar plan which was completed in a few months ago in the same neighborhood to a house of similar range. ( Top-down, Analogous)

John can use a consensus or expert idea on how much his project will cost. To gather enough information he can refer to a few of his friends who have relative expertise on construction and such home-based modification for normal for similar buildings and put their ideas together and compare them to come to a guesstimate for the cost of his expansion project. (Consensus Approach)

John can use PERT model in his estimation. He can put the most pessimistic, optimistic and realistic estimations together and use the formula for PERT estimation of his project:

C= P+4R+O/6

In this equation the abbreviations are as follows:

C= Cost

P=Pessimistic Estimation

R=Realistic Estimation

O= Optimistic Estimation

After consulting with his company and/or expert friends and preparing an approved blueprint for his plan, he needs to prepare tasks and subtasks for his project. Based on his design he also needs to prepare an initial estimation of the materials and duration needed. Then he can refer to local vendor to get information about the cost of materials, tools, and possible human resources’ and calculate them all into his final estimation. (Bottom-up Model)

(3)In this project John is dealing with the separate additions to different parts of his house instead of building a new house from scratch. So, john has a chance to build each part as separate deliverables which at the end will serve to complete his dream plan for his house. He can define each deliverable separately and estimate the cost and allocate the resources in most part separately without having any part interfere with the other deliverables or impede them from progressing separately. Plus, by using agile system in his construction he will have chance to chunk down the period for the construction on each deliverable and conduct it in his free time or by a companyasdesired. He will have advantage of modifying his plan in various ways as he will deal with separate deliverables. This might be a common method that some handy men in the USA do with their house hold building. Not only they do that gradually, but also they have luxury of performing their plan as they pay or as they can afford through the time. So, agile system would be absolutely beneficial to John and his plan. As it seems from his plan and the WBS, there would be no significant or observable cons to his approach if he uses this method in this project, but he will have many advantages at his hand. As an advisor I would recommend utilizing agile method to him.