Paper ID #33152

An Innovative Approach to Teaching Project Resource Leveling

Dr. David S. Greenburg, The Citadel

Dr. Greenburg is an Associate Professor in the Department of Engineering Leadership and Program Man-agement (ELPM) in the School of Engineering (SOE) at The Citadel. He served over 20 years of activemilitary service in the United States Marine Corps. During his military career he served in a variety of pro-gressively responsible command and staff and leadership positions in Infantry, Logistics, Acquisition, andHuman Resources; with peacetime and combat experience. Upon completion of active military service,Dr. Greenburg served in technical program management and leadership positions at Eagan McAllisterAssociates, and Science Applications International Corporation until he joined the faculty at the Citadel.Dr. Greenburg’s research interests include modeling project networks, technical decision making andleadership. Dr. Greenburg earned is bachelors degree from The Citadel (1981), Masters of Science degreefrom the Naval Postgraduate School (1994), and his PhD in Business Administration (Management ofEngineering and Technology) from Northcentral University (2010). He is a certified Project ManagementProfessional (PMP) by The Project Management Institute (PMI).

Dr. Nahid Vesali P.E., The Citadel

Dr. Nahid Vesali is an Assistant Professor in the Department of Engineering Leadership and ProgramManagement (ELPM) in the School of Engineering (SOE) at The Citadel. She joined the program in Aug2020. She teaches project management, technical planning and scheduling, and construction managementcourses at The Citadel. Dr. Vesali earned her PhD in Civil Engineering from Florida International Uni-versity. She holds M.Sc. in Construction Engineering and Management from IAU, and B.Sc. in CivilEngineering from Iran University of Science and Technology. Prior to joining The Citadel, she worked atPlaza Construction, Florida Group LLC. She worked with the corporate Quality Management team andproject management team for high-rise projects. Dr. Vesali’s past research has been focused on decisionmaking and risk management in existence of deep uncertainty. She is also interested in research relatedto creating inclusive environment for female and minority students in STEM majors.

Dr. Dimitra Michalaka P.E., The Citadel

Dimitra Michalaka, Ph.D., P.E., is an associate professor in the civil and environmental engineering (CE)department at The Citadel, the Military College of South Carolina (SC), U.S.A, the Associate Director forthe Center for Connected Multimodal Mobility (C2M2), and a register professional engineer at the state ofSC. She received her undergraduate diploma in civil engineering from the National Technical Universityof Athens in 2007. Shortly thereafter she moved to the United States to pursue graduate studies at theUniversity of Florida. She graduated with a M.S. in CE in 2009 and a Ph.D. in 2012. Dr. Michalakais passionate about teaching in college and K-12 levels and conducting research in both transportationengineering, focused on traffic operations, congestion pricing, and traffic simulation, and engineeringeducation. Recently, in December 2020, she is also graduated with a Master’s of Science degree inProject Management from The Citadel.

c©American Society for Engineering Education, 2021

An Innovative Approach to Teaching Project Resource Leveling

Abstract

This paper presents an innovative approach using an integrated example for teaching students

effective schedule creation and resource management using Linear Programming. This approach

is designed to deepen student understanding of the various factors that should be considered for

effective project decision making. Successful schedule control requires an understanding of

important project elements to include requirements, schedule, budget, assumptions, constraints,

and objectives. These elements can compete against each other and makes resource allocation

difficult to address without using optimization techniques. Engineering students in introductory

project management courses are typically taught how to identify and sequence activities to

develop a project schedule using simple example problems. These examples tend to be composed

of only a few activities and resources which support development of an initial schedule and often

do not address the impact of scope changes that require reallocation of resources and revisions to

the schedule. Successfully adjusting resource allocation to address project scope and activity

duration changes requires a solid understanding of project crashing. Project crashing involves

shortening project duration by reducing the time of one or more activities. Crashing is done by

increasing the resources to the project, and involves cost and schedule trade-offs. The integrated

example focuses on minimizing the total cost that results from (a) resource allocation, (b)

activity dependencies, (c) timing of deliverables using the available spreadsheets. The method

has been introduced in both undergraduate and graduate introductory project management

classes. Student feedback shows that the method supports concept mastery by demonstrating

how to achieve balanced solutions.

Key Words: Resource Allocation, Scheduling, Optimization, Linear Programming

Introduction

Translating customer requirements into work activities and then developing an effective plan for

accomplishing them is a key aspect of project management. Project managers are challenged

with taking a set of activities that need to be performed in a certain sequence and completed

within a specified time and cost [1]. An effective project schedule provides the framework for

the assignment of resources and sequencing of activities to be performed to carry out the plan of

work [2]. The ability to create resource estimates and build project schedules is an essential

multi-disciplinary management tool and the importance of engineering practitioners and

managers having a working knowledge continues to rise [3]. As the project progresses project

managers and their customers tend to learn additional information that often leads to scope

changes involving revising activity completion times by applying additional resources. The

complexity of schedule control and resource allocation grows significantly as changes to scope

and activity durations occur. Network based techniques such as the Critical Path Method (CPM)

and Project Evaluation and Review Technique (PERT) have proven useful in planning,

scheduling and controlling projects. Reducing project duration often involves adding more

resources to the performance of the activity to shorten its duration while increasing the overall

cost of the project [1].

Schedule development, resource management, and control is taught as part of The Citadel’s

undergraduate and graduate technical project management courses which explore the principles

and applications of project scope, project requirements and work breakdown structures (WBS);

development and control of schedules, risk management, project execution and closeout. The

students are introduced to scheduling as a management tool for recognizing the sequence of

project activities, identifying critical activities, planning efficient use of resources and

completion of the work scope to manage risk. They develop an understanding of how accurate

scheduling reduces variances and downstream problems and contributes to effective project

management. A common cause of variances between schedule estimates and actual work

performance arises when the severity of problem impacts were not seen or known [3]. Students

are also exposed to the use of assumptions and constraints to cover gaps in information that can

cause variance between planned and executed activities.

The specific course learning outcomes include:

1. Developing:

a. Schedule Management Plan

b. Activity List with Attributes and Milestone List

c. Project Schedule Network Diagrams

d. Activity Resource Requirements and Resource Breakdown Structure

e. Project Schedule with Model Data and Schedule Baseline

f. Activity Cost Estimates with Activity Cost Supporting Detail

2. Creating, updating, and analyzing project schedules to determine integrity and validity.

3. Applying resource management techniques to identify resource requirements and to level

resources in order to meet project objectives.

However, test results and end of course feedback reflected that while the students were learning

the mechanics of identifying requirements, creating a project schedule and assigning resources,

they did not necessarily have a full grasp of dealing with the impact of scope changes on the

schedule and resource allocation. In response the faculty brainstormed on ideas they could

incorporate into the instruction to better teach students to create schedules and how to plan for

and manage scope changes. An instructional goal was to develop an integrated exercise that

could be used to demonstrate and tie together key concepts through a comprehensive example

project. The authors decided to develop an integrated spreadsheet model which are easy to use

and provide a natural interface for model building [4].

Description

This paper discusses the development of an integrated exercise to teach students how to create

and control technical project schedules and optimize resource allocation using PERT/CPM and

Linear Programming (LP) techniques. The instruction is designed to complement several existing

courses (PMGT 650, PMGT 651, CIVL 411, and CONE 410).

Due to their ease of use and availability we chose to build a spreadsheet based exercise.

Spreadsheet applications have an advantage over other software programs in that most students

already have spreadsheet programs on their computers. Spreadsheets are also an attractive

technology because students are likely to use spreadsheets in future projects, careers and in

personal life. Spreadsheet programs are flexible, familiar, and relatively easy to use [5]. The

specific PERT/CPM and LP techniques we will discuss in this paper are implemented using the

standard Excel Solver function. We introduce students to the concepts of integrated schedule and

resource optimization using a simple project involving the relocation of a work facility. The

Facility Relocation Project shown in Table 1 consists of ten activities.

Table 1. Facility Relocation Activities and Precedence’s.

Planned Project Start Date 1/2/2020 P1 P2 P3 P4 Max

Activity Task

Working

Days Predecessors Start date End date

S Start 1 1/2/2020 1/3/2020

A Locate Facility 8 S 1/2/2020 1/14/2020

B Order Furniture 9 A 1/15/2020 1/29/2020

C Interview 10 S 1/2/2020 1/16/2020

D Hire & Train 12 C 1/17/2020 2/5/2020

E Remodel 8 A 1/15/2020 1/28/2020

F Furniture Setup 8 B 1/30/2020 2/11/2020

G Inspect 8 D E F 2/12/2020 2/25/2020

H Occupy 8 G 2/26/2020 3/9/2020

I Start Operations 1 H 3/10/2020 3/11/2020

At the start of the exercise students were provided the work scope statement with a project

completion date. They were tasked with identifying the activities, determining precedence

relationships, estimating task duration and developing a project network diagram similar to the

one shown in Figure 1.

Figure 1. Network Diagram for the Facility Relocation Activities.

Students use the Estimate tab in the exercise spreadsheet to calculate a three-point PERT

estimate for each of the activity durations. The spreadsheet uses built in Excel functions to

calculate a 95% confidence interval for the project completion date.

A

B

D

F

E

C G H I J

Figure 2. PERT Estimate for the Facility Relocation Activities.

Once the activity durations and relationships are established and the network diagram is created

students are shown how to calculate the critical path using an LP formulation to determine the

earliest start time (ES) subject to activity precedence. The LP formulation is:

Objective Function: Minimize EST = X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 + X10

Subject to Constraints:

X1 = 0 X2 - X1 >= 1 X3 - X2 >= 8 X4 - X1 >= 1

X5 - X4 >= 10 X6 - X2 >= 8 X7 - X3 >= 9 X8 - X7 >= 8

X9 - X8 >= 8 X10 - X9 >= 8 X1....X10 >=0

Figure 3. LP Formulation to Minimize Early Start Times in Excel.

The Excel Solver formulation for the ED times is shown in Figure 4.

Figure 4. LP Formulation to Minimize Early Start Times in Excel Solver.

Using the ES times students are shown how to calculate the earliest finish (EF) which is the

activity ES plus its duration, the (LF) which is the previous activity’s EF minus its duration, and

the latest start (LS) which is the activity’s LF minus its duration as shown in Table 2. Activity

float is calculated by subtracting ES from LS and EF from LF. Conditional formatting is applied

to the cells to identify those activities on the critical path in red font.

Table 2. LP Formulation to Minimize Early Start Times in Excel.

The result shows that the expected completion time for the project is 43 days (which takes into

account non-workday holidays) and a critical path (CP) of A > B > C > G > H > I. The PERT

calculations reveal that based on the critical path activities there is a 95% confidence interval of

project completion between 41.02 and 45.64 days as shown in Figure 2.

Resource estimates are integrated into the problem by having the students assign various project

personnel to work on each activity. Hourly rates for each personnel resource are multiplied by

the time durations personnel are assigned to work on tasks which feed into the project cost

estimate shown in Table 3. At this point students have created a baseline schedule, identified the

critical path and cost estimate to complete the project. This is a good point to introduce students

to scope changes and the impact of changing client requirements on schedule and costs. Project

managers often have to shorten the planned schedule to expedite the completion date [6]. It is

often valuable to be able to present to the customer options for shortening the project as well as

the resulting cost impacts [7]. We show the students how to accomplish this by expanding on the

initial project calculations and continuing with our Facility Relocation exercise by employing the

crashing technique to shorten the critical path duration. Through the exercise students are tasked

with determining the optimal way of expediting the project by applying additional resources to

shorten activity durations times and evaluating time-cost trade-offs by employing crashing

techniques.

Table 3. Project Resource Allocation and Costs.

In the exercise the cost of crashing specific activities is calculated using a factor of 1.85 times the

normal activity cost multiplied by the change in duration due to crashing as shown in Table 4.

Table 4. Project Activity Crashing Costs.

Planned Crash

Activity Description Duration Cost Duration Cost Critical Path? D cost

D

time (xi) r = D cost/D time

A Start 1 $ 1,580 0.5 $ 1,462 Yes $ 119 0.5 237.00

B Locate Facility 8 $ 13,456 6 $ 18,670 Yes $ 5,214 2 2607.10

C Order Furniture 9 $ 11,400 7 $ 16,403 Yes $ 5,003 2 2501.67

D Interview 10 $ 18,800 8 $ 27,824 No $ 9,024 2 4512.00

E Hire & Train 12 $ 28,880 8 $ 35,619 No $ 6,739 4 1684.67

F Remodel 9 $ 20,576 7 $ 29,607 No $ 9,031 2 4515.29

G Furniture Setup 8 $ 16,256 6 $ 22,555 Yes $ 6,299 2 3149.60

H Inspect 8 $ 24,064 7 $ 38,954 Yes $ 14,890 1 14889.60

I Occupy 8 $ 33,360 5 $ 38,573 Yes $ 5,213 3 1737.50

J Start Operations 1 $ 5,616 0.5 $ 5,195 Yes $ 421 0.5 842.40

Totals $ 173,988 $ 234,860

Students are shown how to formulate the problems using LP methods. The problem is to

minimize the cost of crashing subject to the constraints that the project duration must be less than

or equal to the new desired project completion date of 40 days.

Objective Function:

Min Crash Cost = 237.00Xa + 2607.10Xb + 2501.67Xc + 4512.00Xd + 1684.67Xe + 4515.29Xf +

3149.60Xg + 14889.60Xh + 1737.50Xi + 9547.20Xj

Subject to:

Maximum reduction constraints: Xa <= 1, Xb <= 2, Xc <= 2, Xd <= 2, Xe <= 4, Xf <= 2, Xg <= 2,

Xh <= 1, Xi <= 3, Xj <= 1

Non Negativity Constraints: Xi >= 0, Yi >=0, YFinish >=0

Start Constraints: Yb - Ya+ Xa >= 1 Yc - Yb + Xb >= 8 Yd -Yb + Xb >= 8

Ye - Yd + Xd >= 10 Yf - Yb + Xb >= 8 Yg -Yc + Xc >= 9 Yh - Ye + Xe >= 12

Yh - Yf + Xf >= 9 Yh - Yg + Xg >= 8 Yi - Yh + Xh >= 8 Yj - Yi + Xi >= 8

YFin - Yj + Xj >= 1 YFinish <= 40

Figure 5. LP Formulation to Minimize Cost of Crashing in Excel.

Figure 6. LP Formulation to Minimize Crashing Cost in Excel Solver.

Using LP to crash the project by three working days results in shortening activity A by 0.5 days,

activity E by 4 days, activity G by 0.5 days and activity I by 3 days with a project completion of

40 work days and a new cost of $192,120.

Table 5. Cost of Crashing the Project Duration to 40 Days.

Planned Crashed

Activity Description Duration Cost Duration Cost Critical Path? D cost

D

time (xi) r = D cost/D time

A Start 1 $ 1,580 0.5 $ 1,462 Yes $ 119 0.50 237.00

B Locate Facility 8 $ 13,456 6 $ 13,456 Yes $ - 0.00 0.00

C Order Furniture 9 $ 11,400 7 $ 11,400 Yes $ - 0.00 0.00

D Interview 10 $ 18,800 8 $ 18,800 No $ - 0.00 0.00

E Hire & Train 12 $ 28,880 8 $ 35,619 No $ 6,739 4.00 1684.67

F Remodel 9 $ 20,576 7 $ 20,576 No $ - 0.00 0.00

G Furniture Setup 8 $ 16,256 6 $ 22,555 Yes $ 6,299 0.50 12598.40

H Inspect 8 $ 24,064 7 $ 24,064 Yes $ - 0.00 0.00

I Occupy 8 $ 33,360 5 $ 38,573 Yes $ 5,213 3.00 1737.50

J Start Operations 1 $ 5,616 0.5 $ 5,616 Yes $ - 0.00 0.00

Total Cost $ 173,988 $ 192,120

The Activity List tab of the spreadsheet will automatically generate a Gantt chart showing the

planned schedule in blue and the crashed schedule in grey. The Gantt chart combined with the

cost tables provide a way to visually display the results of planning and can easily support what-

if analysis to determine schedule and cost for various scope changes.

Figure 7. Project Gantt Chart for Schedule Options.

Usage

The integrated spreadsheet model presented in this paper is a useful tool for professors teaching

schedule development, resource leveling and project crashing. Spreadsheets are readily available

to both students and faculty and our integrated example uses standard excel functions without

macros. The model is easily modified to expand additional tasks and incorporate more complex

examples by using a few copy commands. While students are informed of the math behind the

calculations the spreadsheet only requires the student to input required data and the model is

generally set up to auto calculate and produce the output and charts for analysis. This allows

students to concentrate on properly describing the problem and analyzing the solution while not

having to perform tedious calculations. We have used our model in both undergraduate and

graduate introductory project management courses to reinforce key concepts and broaden student

understanding of not just developing a schedule but managing it. The responses from students

have been favorable as most students like the ease of use and do not have to deal with the

learning another software program. They also state that the integrated exercises make it easier for

them to understand the relationships between schedule, resources and requirements. Prior to the

exercise faculty covered schedule development, resource allocation and project crashing as

separate lecture topics. The integrated exercise has allowed us to spend less time on each of the

individual topics and more time demonstrating through practical application how these topics

overlap and influence each other. For future research we are planning to perform before and after

analysis of grades for the exercise in order to measure any improvement in student performance

after completing the integrated exercise problem. We are planning to introduce a simple exercise

in which students will manually build a schedule, assign resources and crash the schedule

followed by the integrated spreadsheet exercise. The majority of undergraduate students are

engineering majors while less than 50% of our graduate students have engineering degrees. For

the graduate students we have been able to compare two classes, pre-introduction and post-

introduction. The average score for our post-introduction facility Relocation Exercise class were

8% higher than the pre-introduction class.

Conclusions

Integrated spreadsheet models are an effective means of enforcing key project management and

decision-making skills in students. Automating many of the analytical techniques allows students

to focus on understanding the concepts and applying that understanding to analyze potential

solutions to meet customer needs. The integrated exercise can also be used to show the students

how to pin-point the part of the project that if delayed beyond the allotted time would increase

the completion time of the project as a whole. It further assists in allocating resources and thus

helps to make the total cost of the project a minimum by finding the optimum balance between

various costs and time involved. This paper describes one approach to expanding student

comprehension of schedule development and management using an integrated spreadsheet

example based on built in functions and formulas that support sensitivity analysis for decision

making. As student feedback on using the example has been positive we intend to continue its

use and expand the scenario to include a more complex schedule.

References

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linear programming: case study. International journal of scientific & technology research, 4(8),

222-227.

[2] Arcuri, F. J., & Hildreth, J. C. (2007). The principles of schedule impact analysis. VDOT-VT

Partnership for Project Scheduling, Blacksburg, VA.

[3] Hildreth, J. C. and Munoz, B. P. (2005). An Introduction to the Management Principles of

Scheduling, TR-05-04, A report presented to the Virginia Department of Transportation and the

VDOT-VT Partnership for Project Scheduling Advisory Board.

[4] Seal, K. (2001) A generalized PERT/CPM implementation in a spreadsheet. INFORMS

Transactions on Education 2(1):16-26, https://doi.org/10.1287/ited.2.1.16

[5] Baker, J. and Sugden, S. J. (2007) Spreadsheets in Education –The First 25 Years,

Spreadsheets in Education (eJSiE): Vol. 1: Iss.1, Article 2.

[6] Stenbeck, J. (2008). Five keys to estimating. Paper presented at PMI® Global Congress

2008—North America, Denver, CO. Newtown Square, PA: Project Management Institute.

[7] Agyei, W. (2015). Project planning and scheduling using PERT and CPM techniques with

linear programming: case study. International Journal of Scientific & Technology Research Vol.

4(8).